ML19260D869

From kanterella
Revision as of 16:39, 26 October 2019 by StriderTol (talk | contribs) (Created page by program invented by StriderTol)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
Potential Reactor Sys Voiding During Anticipated Transients.
ML19260D869
Person / Time
Site: Davis Besse Cleveland Electric icon.png
Issue date: 01/31/1980
From:
BABCOCK & WILCOX CO.
To:
Shared Package
ML19260D868 List:
References
TAC-45218, NUDOCS 8002120531
Download: ML19260D869 (32)


Text

{{#Wiki_filter:' I Docket No. 50-346 h f%- License No. NPF-3 Serial No. 588 February 7, 1980 POTENTIAL REACTOR SYSTEM VOIDING DURING ANTICIPATED TRANSIENTS

                                                               .

PREPARED BY BABC0CK & WILC0X NUCLEAR POWER GENERATION DIVISIO.? LYNCHBURG, VIRGINIA JANUARY, 1980

                                                          .

8002120 5%l

.

'
  .

CONTENTS 1.0 Problem Introduction and Summary 1.1 Introduction 1.2 Summary 2.0 Analysis, Assumptions and Event Descriptions 2.1 Analysis of Steam in the Upper Vessel Plenum 2.1.1 Stagnant " Hot" Water 2.1.2 Residual Heat Stored in Metal 2.1.3 Conclusion 2.2 Analysis of Steam in the Candy Cane 2.2.1 Pressurizer Outsurge Water Mixing in Hot Leg Flow 2.2.2 Residual Heat Stored in Metal 2.2.3 Conclusion 2.3 Event Description for Mass / Volume Balance 2.3.1 Description of Analysis 2.3.2 Derivation of Equations Used 2.3.3 Mass / Volume Analysis 2.3.3.1 Davis Besse 9/18/79 Trip 2.3.3.2 Davis Besse 10/15/79 Trip 2.3.3.3 Davis Besse 9/26/79 Trip 2.3.3.4 Oconee I 10/8/79 Trip

                                                         .

2.3.3.5 Oconee II 1/4/74 Trip 3.0 Conclusion 4.0 References h

       .
     >

.

   .
 .       .

List of Figures 2.2.1 Column Whldment Flow Paths 2.2.2 Upper Plenum Flow Paths 2.3.1 RC Volume Breakdown 2.3.3.1 TECO 9/18/79 Trip 2.3.3.2 TECO 10/15/79 Trip 2.3.3.3 TECO 9/26/79 Trip 2.3.3.4 Oconee 1 10/8/79 Trip 2.3.3.5 Oconee II 1/4/74 Trip A-1 Pressurizer level 52. corrected pressure tap measurements (320" pressurizer) A-2 Pressurizer level vs. corrected pressure tap measurements (400" pressurizer) A-3 Error in level indication vs. indicated level (400" pressurizer) A-4 Error in level indication vs. indicated level (320" pressurizer) AttacNnents Pressurizer Level Error

                                                              .

,

   .-
 .

l.0 PROBLEM INTRODUCTION AND

SUMMARY

1.1 Introduction The NRC has expressed concern that steam pockets can and do fom in B&W primary systems during some reactor trip 5 and furthermore, this steam could collect in the candy cane and potentially hinder natural circulation after loss of offsite power. The source ci this steam is postulated to be from stored heat 11: metal, stagnant pockets of " hot" water, or pressurizer outsurge water (350 F); ,ny or all causing flashing during low pressure periods afe.c a trip. The purpose of this report is to show that the formation of a steam pocket in the primary system during most reactor trips is highly improbable and that the production of a volume of steam required to hinder natural circolation is virtually impossible. 1.2 Summary Based on review of several past B&W reactor trips along with several assumptions and calculations discussed in Section 2, the following statements can be made: (1) Minimum RC pressure after trips occurs about the same time as the minimum coolant temperature (as expected) and not because of a primary system " Steam Pocket" restricting a further pressure decrease. These minimum temperatures errelate with secondary side steam pressures. (2) With the most conservative assumptions steam pockets are virtually impossible during transients where minimum measured pressure is greater than 1740 psig.

  • Specific concern per reference 1 \3
 .-

.

    .

(3) Using more realistic assumptions regarding potential steam production, it is unlikely that any net steam production can occur at measured pressures greater than 1500 psig. 2.0 Analysis, Assumotions and Event Descriotions 2.1 Analysis of Steam in the Vocer Vessel Plenum 2.1.1 Stacnant " Hot" Water Typically, the hottest bundle in a 2772 MWT core is a 1.5 relative peaked bundle. This localized power could conservatively result in localized stagnant water temperatures

  • of s 620*F in the upper control rod guide (column weldment).

For this situation to occur, at least 53 in of flow area in the column weldment (see flow path 2 on figure 2.1.1) would have to be blocked. If this blockage could occur, then the following statement can be made: Any B&W reactor trio resulting in minimum RC tao pre.ssures less than 1740 psig (the tap pressure 1.s s 40 psid lower than core plenum pressure) voiding may occur. Since this blockage is highly unlikely, a somewhat more realistic hot spot assumption would be localized maximum temperatures of 610*F (instead of 620') in the upper vessel plenum. This assumption is based on (1) water stagnating (or having an extremely low flow rate) in the upper plenum (per Fig. 2.1.2)

                                                            ,

and acquiring the steady state enviromental temperature of the 59 column weldment flow temperatures and (2) plugged return holes (per figure 2.1.2, Flow Path 3). This condition would not allow flashing until the pressure decreases to 1660 psia, i.e.,1605 psig at the pressure tap.

  • Typical outlet temperatures were verified from TMI-2 pre March, 1979 100". power outlets thermocouple data.
                                                                                       }
     '
   .

'

 .
       .

The most realistic assumption is the desian condition of s 5% core flow through the guide tubes into the upper pl enum. Following a reactor trip, the coolant temperature in this region will decrease rapidly to below 600F as core outlet temoerature-eliminating the potentid for " hot" water pockets at arty pressures above HPI injection levels. 2.1.2 Residual Heat Stored in Metal After a trip, the metal in the upper vessel will be conservatively assumed to remain at 610 F until a minimum pressure is reached. The upper plenum coolant temperature at this minimum pressure should be s 550 F (in this region) but 575 F will be conservatively assumed due to hypothetical " slow" mixing. The available stored energy in the metal will be: Stored Energy = Cp x Mass x AT m m Cpm = .11 BTU /lh, F AT = 610 - 575 = 35 F Mass s 5x10' lbm = total mass of metal above the outlet hot leg piping including reactor vessel Stored Energy = 1.925x10 BTU's The amount of water in this region is 1366 ft.

  • 3 4 1366 ft.3 x 44.5 lbm/ft = 6.08x10 lb of water Conservatively assuming this energy is instantly released to the water, the water temperature will increase from 575 F to s 601 -

The pressure required for flashing at this temperature is s 1505 psig (at the pressure tap). Therefore, in order to fill this region with

  • This is water density at 575 F, 1600 psia.
         **l.925x106BTU's/6.08x1041b = 32 BTV/lb or s 26 F temperature increase.

950 078

   ..-
 .

. . steam (to cause spillover into the hot legs) from just residual heat, 20 times more mass of hot metal would be required. (s 10 BTU /lb are needed to reach Tsat and another 533 BTU /lb to vapori7.e the water. This equals 543 BTU required to convert a pound of water to lb a pound of steam). 2.1.3 Conclusion The previous calculations and discussion basically show that it is impossible to produce steam in the upper head above a measured pressure of 1740 psig, highly improbable above 1620 psig, and highly .unlikely above 1500 ps.ig. (Very few . transients have ever gone below 1600 psig .) This statement assumes no primary system breaks. 2.2 Analysis of Steam in the Candy Cane 2.2.1 Pressurizer outsurge water mixing with hot leg flow At the time period of mi'.imum pressure after a trip the hot leg coolant temperature is s 550 F during 4-pump operation and s 5700F durin9 natural circulation. The respective hot leg flow 6 6 rates are s 70x10 and 2.5x10 lb/hr during this period. The pressurizer is outsurging s 650 F water at s 40000 lb/hr into the hot leg. Conservatively assuming only10% of the hot leg flow mixes with the pressurizer outsurge , the resulting maximum fluic temperature in the candy cane will be s 551oF for four pump operation and 5810F for natural circulation. Qh

   *
 .

.

     .

The saturation pressures for these temperatures is well below 1500 psig. 2.2.2 Residual Heat Stored in Metal The residual heat stored in the hot leg metal is conservatively 5 calculated to be s 1.89x10 BTV's. This calculation is based on (1) hot leg piping temperature remains at s 605 F for 60 seconds after the trip and (2) the residual heat is dumped instantaneously into the hot leg flow volume at the RTD indicated temperature

       -

of s 550 F and 1600 psia.

                                                          .

Hot leg metal volume = 70.45 ft 3 3 4 Hot leg metal mass = 70.45 ft x 490 lb = 3.45 x 10 lbm ft* The AT driving function will be 605 - 555 or 50 AT. Therefore stored energy released is

                .11 BTU x 50 F x 3.45x10 = 1.89x10 BTU's ib*F 4

The volume of water in the hot leg is s 1.97x10 lb . Therefore: 1.89x10 BTU s10 BTV/lb 4 197x10 lb This is equivalent to s 8 F in temperature addition. Therefore, the saturation pressures for 551oF* + 8oF = 559 F and 5810F + 80F = 5896 F are below 1500 psig.

                                                    .
  • Per previous calculation O
                                                                                .
      *
    .
                           .      . Column Wddgart Flow Path 7                          Fig. 2.1.1
                                  '
  .                                                                               <
                                                                                  -
                                  ,
                                  /
                                                                                                         .
                              \   '
                                  '
                                                                                  /
                                                                                  <
                                  /
                                                                                  '
                                                                                        .

r

                                                                                  '
                                  -
                                                                                  /
                                  '
                                                                                  /                        -PLEN UM
                                  '

s COVER

                                 -                                                -

t+t t t +tt

                                 -

A

                                 '

Flow Path - d 2

                                 '

s

                                 <'                     _                         o
                                                      --
p, 7
                                        -
                                 -
                                                                  ,               <
                                 '                                                /

, d d. t . $ ! 4 I i e ('

                                             .
,
                                                      -
                                                      -
                                 >                                                >

f

                                 '
                                                            +-LEAD
                                 '                                    SCRCW       l,
                                 '                                                -

[ - i - a r/ A h UPPER GRID %\ \ N \ \ s N f GRID PAD \ \ s 7/ '

                              // r rr-i   ~

T-in // ~ '

                                                                                                                      $

b \ \/

                                                                             #

f

      ,/

U

                                    )*l      u t *.*
                                               -
                                                               ' ' I s-
                                                                          -
                                                                                    )          l U

l C # _ _ _-[- .::- r

                                        ~          ~~

w ~ __

                                                                           -

_

         -
         -                              -
                                        -

_- -_ U U J-U PPE R EN D FITTING

           -

p_ _s <

                                           -

_ - - - _s - _ _- _f k

                                                                                                                 \9
                                                                  .
 .-

Upper Plenum Flow Path Fig. 2.1.2 ' ~

                                                                                            '

t 9

                                                                       ,m,              =        ^
                                                                                                   ,-      -- -
                                                                             '

l}  !!yj{2 column X -- _ , weldment  : J: dCD CD CD G ,:

                                                                                          '     t ji
                                ,
                                                     *
                                                           .               lj      ll     H            l'
                                                   '
                                                            ,

Top view of upper plenum [ cover for 177 FA Plants , l

                                                                                                                          .
                                                                                                                          >

b N, Flow Path Flow Path ,\ s x 9 , o c o m o , Ji N s

         ,5%,S U[ $lj[$R
         ///       :   w                  (

e

                                                                    '

W:

                                                                         .
                                                                                 ?e/

a ,

              -
                                                                         -
                                                                               ~
           /  j    -
                                                                         ;
  #4 i.                                   ( )<                           !

P

oxx .

    -
      .. .         20                                                    -
                                                                                                        -
                                                                                                                          ,
W . -
                   .

g . -

           //                                2-                                       ,
                .    -
                     .
                              -     -
. . _ _ ._. . _ ~ _. :_._
                                                                '

nf

_

9 h t ) 7 % 3

            \      j                         li                         g $' N N     1                        id                 .         h'N g9SD g@:i
   *
 .

.

     .

2.2.3 Conclusion Using the conservative as'umptions on residual stored heat and hot leg - pressurizer outsurge mixing, the RC pressure which would allow fla.shing is below 1500 psig. This low pressyre ,. snould not ce reacned during normal transients. 2.3 Evt.nt Description For Mass / Volume Balance 2.3.1 Description of Analysis A mass volume balance on the RC system before and after trips was analysed for five cases. These cases were chosen because of their abnormally low pressuri:or level, low RC pressure, or

                                                               ,

were referred to in reference 1. The method of analysis was basically: (1) To break the RC system down into 4 different temperature / pressure volumes (per figure 2.3.1)- (2) Calculate the ' shrinkage" of each volume at a lower temperature / pressure condition after a trip and (3) Determine how much water from the pressurizer is required to maintain a solic system conditions. (4) Subtract this volume of water from the initial pressurizer volume to get " level 1". (5) Calculate the amount of water that would have flashed in the pressurizer due to the lower pressure condition. This is " level

                                          '

2". -

       .      (6) Fine.lly, calculate the pressurizer level error per attacnment 1. This is " level 3".

(7) Subtract level 2 and 3 from level 1 to get level 4. If

                    " level 4" is less than the plant measured level (" level 5")

then a viable explanation would be potential " steam pockets" h

 .-

.

    .

in the RCS. The results of this study show that the :ndicated pressurizer level (level 5) is less than or equal to the calculation of level 4 and therefore a steam pocket occurring in the RCS is highly unlikely. 2.3.2 Serivation of Ecuations Used The equation used for this analysis is: - 1 1 I l V)p) + V P22+V933+YP44+VP55

                                                    *         +    E              P +VE
                                                                               +V 44       55 l '1        22       P 33 Where      p = Coolant density at tin 0 p = Coolant den'sity at Time 1 V5 = Volume of water in pressurizer et Time 0 V 5 = Volume of water in pressurizer at Time 1 1

Solving for V 5

           ~                 +

V 5 l(P1-P1 2(P2 - P 2) 3+ v (P3-P 3} + 4(P4~P45 5 1 p 5 For raised loop plants (TECO) V 5

           "

(APl } + ( 2 3}+ (P 4 1 + 3.207 (level)] p 5

                                                                     -

1 p 5 9' For lowered loop plants

                                                            .

V

           = 3800(ao)) + 887(ap   2 ) + 3197 (ap3) + 2774 (ap4) + [A) + 3.207 (level)] p 5 1

P5 Eq.2 h

- RC. VOLUME BREAFDOWN e~ Fig. 2.3.1 if*m\,'ftao

                              -
                                                      '
                                                                                                         ,'f          ',,
 .                                                     v
                                                        '
                                                                        .                                ;

m i er. He en

                                                                                                        )
                                                                                                          .

p

                                                              '
                                                                                                                               'e I .2 'u
                 ,,

je e ,

         /'
           #

p ,- 7 c* g

   , ,, e ,          n
                      ,
                               )                        
                                                        ,e i
                                                                         , D,          e j ,' e 'l )
                                                                                                                     '
                                                                                                                                    -
   --                        ,,                         i                 ,,                         .e                           ,'           *- Tube Sheet
   ,                     ,

t lt , c' ,

  • i # #, e ,. ,, f'
                                                                                                                                        '

b / O  ? $ :5* W )  % / t

                              ,                                     ,k                     .                    ,        ,
                                                                                                                             ,
                                                                                                                                '.
                                                                          .

l , . ,.  ;,t ,/

                                *
                                        ,,                          .      .
                                                                                             .                               ,          i_,

i 's .. ,

                                                                                                                          ./          /
   ,
     '
                            ,i "          ,
                                                                    *
                                                                    ,.                , '., .                 [il/
                                                                                                                                 /           .
                        /                                             ..         x      s,                    K             /

e_' . ".

                                '
                                                                    .%.             <    '..                  il' /                 /
                                                                                                                                         ,
                                                                                          ..,'

_., 1..,. u. p; \;w,

                                                                       -
                                                                             .. .                             i.t . . . . .;

m....,,

                                                                                                                .
                                                                                                                       ..

r . . . .. .

                                                                                                                                           '
     ,          .
                         .,                                                                                        y ,             ..
       '
                      <
                           -

O -

                                                                                                  -

Raised Looo Lowered Loro

   '
                                                   ..                                                                                177 NSS (ft3 )       177 NSS (ftJJ V)
                        =

f ,' ,'*.l .' = Cold Water Volume =

                                   ,                                                                                                     3739                  3800
                                  ,                .6
                                     .          .--

V 2

                        '

i ', = Core Water Volume = 887 887

                                 .--,..a
                                     . - - . . . -
                                                '-

V =

                                '3             e          = Hot Water Volume =                                                          3062                   3197 3                    ,       3      ,
i. --,
                               .             .-

V = 2774 2774 4 { = Steam Generator Water Volume = e .- e

                               >            --              Total External to Pressurizer                                             10462                 10,658 V

5

                        =

l l = Pressurizer Water Volume = A + 3.207 X A + 3.207 X l t ;-- Level (inches) Level (inches) A = 263 (Davis Besse)' A = 134 (Oconee) Pz=Ptap 8 1 = f(P) Tcold) - P =P tap + 50 #2 = f(P 2, Tave) 2 3 = f(P3, Thot) P3=Ptap 4 f(P4, Tave) P4=P tap 0 5 = f(P5, Tsat) p5ptap g 395B

. 2.3.3.1 Davis Besse 9/18/79 Trio At 12:43 on September 18, 1979, while operating at s 100% power a test was in progress on the main steam turbine Electro Hydraulic Control System (EHC) at Davis Besse 1. While transferring EHC pumps a low pressure signal in the EHC initiated a turbine trip. The Anticipatory Reactor Trip on Turbine Trip tripped the reactor s 0.4 seconds after the turbine trip. The reactor trip caused the RC pressure, RC T average and pressurizer level to decrease rapidly. The pressurizer level indication dropped off scale.some 50 seconds a,fter the reactor

  • trip, remained down scale for some 50 seconds and then slowly increased. The RC pressure reached a minimum of about 1710 psig at 1 minute after reactor trip and recovered. RC T reached a minimum of 546 F following the trip and stabilized at 550 F.

The initial conditions prior to the trip are listed below. Reactor Power s 100% Rated Power RC Temperature (T,y,): 582 F R.C.S. Pressure: 2200 psig R.C.S. Flow: 4 pumps operating Pressurizer Level: 202 inches

                                                    -
                                                                            .

Tests in Progress: EHC Test The pertinent data during the transient is shown on figure 2.3.3.1. The data analysis is as follows. h

 .

- Davis Besse 9/18/79

   ,                                    Reactor Trip Time (0) Initial Conditions T        =

hot T # eold " tap " Therefore p)

                          =

46.24 p = 44.64 p = 42.57 p = 44.60 4 p5"

                                                        '

Time (1) = 42 sec

  • w T = 557 T = 550 p = 1740 psia hot cold tap Therefore p' = 46.40
                                                  ,                 -
                        '

p/ = 46.27 2 3 p'= E 97 3 1, pi = 46.23 4. p# = 41.18 Solving Equation i V ' = 415 ft 5 -- This corresponds to a calculated pressurizer level of 47.5 inches. (level 1) The indicated pressurizer level was 21.6 incher(level 5), The estimated pressurizer level temperature compensation error (per Attachment 1) is laa inches (level 3). The initial mass of steam in tne pressurizer is 650 'ft x 6.21 lb/ft or 3 4037 lb. The final mass of steam is 1214 ft x 4.37 lb/ft or 5304 lb. This additional 1267 lb (5304 - 4037) of steam will come from s 10" of water . (level 2). Therefore, level 1 - level 2 - level 3 = level 4 = 47.5-14-10 = 23.5". Level 4 is slightly great:r than level 5; therefore, the proba,bility of steam pockets is low.

  • A 4 second hot and cold leg RTO response time delay is incorporated.

Note: Where possibic, data used in thc:e analyses is based on ccmputer print cut. The graphs arc representati ns of this data. h

      ..                    . - - . .          __             . - . ..            ~
     .-

Fig. 2.3.3.1

  *
  • m es ed .C "O 6 & C c) C) @

wO C .c L mN-w a vN M C C 'C y C *- C n -OmCm L C c ~m

                    ~

C* C Gl mN Lao DC L

                  .

3*; cy y, am OwGJL mL)2 o*<

                                                                                                             \                    e- "L5-c; c; 2 c; e a o

mu. >> 3 CJ C 5 g g \ C s c; ca

                 ' x ;c
                                                                                                                   \            -wo-O- O - a' -           -
               ~w                                                                                                    \           d
                         ,
                @ma                                                                                                    \         >

C-m - t w

               -ma                                                                                                               w w

wo L

                                                                                                                          \                                       ._      w
               - - es                                -                                                                     \

ama C C 3 > G) O C. cm t

               .oa8 mv                                                                                                            -\      e-
                                                                                                                                             =

cs m- a n ona

                > UC w

E

                                                                                                                                   \          l o

C3

                                                                                                                                                                               -

o

n. s. - m =>  %

o \ , - m om- m - , .

                                                                                                                                            \                    -        n =

e uvm = t .

                                                                                                                                                                               =

H * - y *a {  : i g a 1 v r- cm. N 1 .: -

                                                                                                                                                                               -

co 1

                                                                                                                                                                              -
   ~                                                                                                                                              s N                                                                                                                                              i.                          -

Cn .

                                                                                                                                                                 -        N u
                                                                                                                                                                              -
                                                                                                     . . ,

o o ' 3 W 11 m l-- *g - IE

                                                                                                                                                     -
                                                                                                                                                .'Il
                                                                                                                               -
                                                                                                                                            ./            .I
                                                                                                                                       ,..-                    ,

e

                                                                                                                              ~",                   ,/
                                                                            / _ ,,, .,                      -
                                                                                                                -:.:~ '~ ~                      '
                                     ,

_ _ ._ .,_ ,....

              ,                                                                                   --....
                                    ,   .

c, . o

           -                  .                   m                                                   a ce wi
                                                                                                                   .

ca >, m o  :.

          =                 ~ w           a       w
                                                                                                    ,_a
         .-                 e      sa     ce      cc 1            e       i a                        l               l                    9:  .                        ,

o cm es e o c3 o o o o - o o , w e o e o o o

3. '3Hn1YH3dN31 .

I i i i - i , , i o c2 o c3 o o o C2 C3 C9 C2 o o gwy N .o o C3 CL

  • P"'"
                                                                                                                                                                   *""

N N N N == SISd '3HASS3Hd '3*H I i i e i e i , , , , o cm es cm em c3 o o c c3 c3 O G3 C43 ai CD 4D ag- N N a .= r. .N .o.

                                                                                       -

(S3H3N!) 13A31 H3ZlHASS3Hd Dbg

                                                                                                                                                \99

..

                                                                                        ._.                                                                             -
   -
 .

e

     .

2.3.3.2 Davis Besse 9/15/79 Trip Figure 2.3.3.2 shows the RC pressure during this trip. Since RC minimum pressure was 1848 psig no steam production was possible per discussion in Section 2.2.

                                   %                 e e
                                                      .
                                                                                                                            *
                                                                                                                                 .
                                                                                                                                   .

TECO 9/15n9 TRIP

                                                                   .             .

21.840 - 21.420 -

                                                                                               .
                .

m[ 21.000 - E 1 { 20.580 - S E g 20.160 -

                                                                               ,

5 O a: a-19.740 - L.- M l,

                       .

19.320 - 2

  • t'
     -                           18.900  -
      -O                                                                                                                      [
       &                                                                                                                      6 C                                        '               '        '          '       '            '     '

18.480 O o 49.410 49.815 50.220 50.625 51.030 51.435 51.840 52.245 52.650 0 2

                                                               -

Time (seconds) (110 ) .- . - . . . . . . - .. - .. . . .. _.__ __ __

   .-
 .

. 2.3.3.3 Daivs Besse 9/26/79 Trio At 20:56:33 hours on September 26, 1979, a high turbine throttle pressure limit alarm was received. The throttle pressure limiter is used to protect against an excessive decrease of steam pressure when steam generation of the NSS falls below the steam demand of the turbine. It acts directly to close the high pressure turbine control valves in an effort to maintain steam header pressure. Rapid closure of the control valves caused a mismatch between heat generation and heat removal with ?

      .

resultant increase in Reactor Coolant System (RCS) temperature and pressure. Seven seconds later (at 20:56:40) the reactor tripped on RCS high pressure and was followed by a turoine trip. RCS temperature and pressure then dropped and the Integrated Control System (ICS) reduced the feedwater flow abruptly. Reactor Coolant System Tave decreased to 548.5 F approximately 57 seconds after the trip. The pressurizer level indication dropped off scale at 21:57:21 and remained below tne indication range for approximately 21 seconds. The initial conditions prior to the trip are listed below. Reactor Power: s 100% Rated Power R. C. Temperature (Tave): 5824

                                                            .

R. C. S. Flow: .4 pumps operating Pressurizer Level: 200 inches The pertinent data during the transient for this analysis is shown on figure 2.3.3.3. The data analysis is as follows. qh

   ..
 .

Davis Besse 9/26/79 - Reactor Trip Time (0) Initial Conditions T = hot T = 559% P = 2215 psia cold tap Therefore p) = 46.18 p = 44.59 2 p3= 42.67 p = 44.56 p5" *

                                                             '

Time (1) = 50 sec T = 552 = 548 p = 1700 psia T hot cold tap Therefore p' = 46.62 1 ~ -

                          '

p/ = 46.53 2 - 3 p - 46.22 3 1 pi = 46.35 4. p'.

                             =       41.00 0

Solving Equation 1 y ' = 243 ft 5 - This corresponds to a calculated pressurizer level of 26.4 inches. (level 1) The indicated pressurizer level was 0 inches (level 5). The estimated pressurizer level temperature compensation error (per Attachment 1) is 15" inches (level 3). The initial mass of steam in the pressurizer is 648 'ft x 6.21 lb/ft or 3 3 4030 lb. The final mass of steam is s1234 ft x '4.23 lb/ft or 5219 lb. This additicnal 1190 lb ( 5219 - 4030) of steam will come from s 9" of water. (level 2)

  • Therefore, level 1 - level 2 - level 3 = level 4 = 26.4 9 = 2:4". Level 4 is slightly greater than level 5; therefore, the probability of stear, pockets is iou.
  • A 4 second hot and cold icg RTD response time delay is incorporated, llotc: 1.'here possible, data used in these analyses is based on computer print out.

The graphs are representations of this data.

                                                                                                 .
 .
     *
                                                                *
                                                            .                                      I

. Fig. 2.3.3.3 I e 1 1 4 c: 5

                                                                               '           O G.                                                                          x    ~

H . ~ N

                                           '

uJ

                                                  .
                                                                                              $

s a i R 5 m 3 o j =.

   $
   '

Y  :

   &                                                                                           "

t

                                                          ^
c. -;
                                                                                    ~

o

                                             =                                             _

E

                                                                                              .-
                                                                                              -
                                                                                      .
       ^^

O 7 - d e f f f f f i

                         $

c

                               $

p k C

                                              $

e

                                                       $

c

                                                                $

o h o (d es) 1 3b I t t I t t 1 1 o S b $ o o o o R N - h  :  : C 2 (alsd) SS3Hd '3'8 f f f f f f I k

              ~

o

                    ~
                               $
                               -

h

                                               -

h h *

                                                                        '

NI) 13A31 'SS3Hd gg3

 .-
                                                        -

. 2.3.3.4 Oconee 1 10/8/79 Trip On October 8, 1979, Oconee 1 was operating at 100% FP with on line Reactor Protection Tests in progress. At 13:27:35, Oconee 1 experienced a reactor trip attributed to RPS activation of pressure / temperature channels A, C, and D. Control Rod Drive Breakers CB 3 and 4 were tripped for the test. An additional breaker for Group 5 was opened which caused Group 5 to drop. This resulted in a P/T Trip. The initial conditions prior to the trip are listed below. Reactor Power , 100.% RCS TAVE 579 F Pressurizer level 221 inches The pertinent data during the transient for this analysis are shown on figure 2.3.3.4. The data analysis is as follows.

                                                                     .
                                              .
                                                                       '

1950

                     .
 .-

Oconee I 10/8/79 , Control Rod Drop Trip Time (0) Initial Conditions T = 602 7 T = 558 p = 2150 psia hot cold tap 3 Therefore p) - 46.26 lb/ft 3 p = 44.75 lb/ft 2 3 p , 42.87 lb/ft p 4

                       =

44.70 lb/ft p5" *

                                                         '

Time (1) = 60 seconds 553 =1750 psia

                                                                        -

T = T = 550 p hot cold tap Therefore p' = 46.55 lb/ft 3 1 . p I' = 46.47 lb/ft 2 3 P'3

                          =    46.40 lb/ft pI       =    46.51 lb/ft 4.

P' = 40.81 lb/ft 3 Solving Equation i V , = 315 ft 5 - This corresponds to a calcalated pressurizer level of 56.2Minches. (level 1) The indicated pressurizer level was 31.0 inches (level 5) The estimated pressurizer level temperature cocpensation error (per Attachment 1) is 15.0 inches (level 3). The initial mass of stesm in the pressurizer is 709 3ft x 5.97 lb/ft or 4236 lb. The final mass of steam is 1283 ft3 x 4.4 lb/ft or 5652 lb. This additional 1416 lb (5652 - 4236) of steam will come from s 10' of water (level 2). Therefore, level 1 - level 2 - level 3 = level 4 = 5G-15-10 31". Level 4 is equal to level 5; therefore, the probability of steam pockets is low.

  • A 4 second hot anc cold leg RTD response time delay is incorporated.

Note: 1.'here possible, data used in these analyses is based on computer print out. The graphs are representations of this data. gCg Q O

      --       . _    -
   . *
  • Fig. 2.3.3.4
 .
         .
                                                                                                           !      S 1
                                                                                                           'l
                                             &                                                               I E                               .o                       .                        .

R d T  !. .

  • m $ w w / S
                                                                                                                    =

r- E E /- i

           ~

s" u i

                                              =

E

                                                           -
                                                                                                       .
                                                                                                         /          i
                                                                                                                    -
           ~
             .
                                "

w u N o N f, ,E w w ' = //'

                                                                                         .
                                                                                                   -           -

g w - =

                                                   #s'                    /                        W 5

O #

                                              #
                                                        /*                       %
                                                                                                   =s N c2
                                                                                         %         u$

gs/ .- "" 1 I I I f f I II 1 o E S S S 3 q .

                        -                   =

e e 2  : SISd '380SS3Ed 38 I f I f f I I f J t S

                          =

S S E $ $

                                            =               n                e             o               n do 3dOITU3dd3138 .

I I I I I I I f I I S

                   ~

S

                                      -

S

                                                       -

3

                                                                          -

S $ (S3H3NI) 13A31 H32IHOSS3Hd

                                                                   .
                                                             .
                                                                                                 .

.- 2.3.3.5 Oconee II 1/4/74 Trio Figure 2.3.3.6 she',s the pertinent transient results of this trip. During this transient the minimum Tap pressure attained was s 1900 psig. Therefore, a 1940 psia upper vessel pressure would require a 631 F temperature to produce net steam. This temperature was never attained at any position or time during this transient. While it is given that operator action (or plant responses) could have been better, the steam production possibility did not exist. Furthermore, a review of the sequence of events of this trip indicate that the severe level and pressure changes at the beginning and later in the transient were primarily cue to a temporary loss of 10.5 power.

                                            .
    ..
                                                                                          -

Fig. 2.3.3.5

   '
        -                                                                                                                             -"
            .

N, ,1

                                             \'                                                                             /

I

                                                              >                             a g                            I 1           -   o
                                                                                                                                          *
                                            \-     .
                                                                                            "
                                                                                                                        /

N 5 I

                                                                                                                    '

u z

                                                           'N.                              5
                                                                                            =>
                                                                                            =

s

                                                                                                                                      -

n

                                        <                                                   *
                                        ~                                      '
                                                                                            =                    l m                                                   -
                                        =                                            ,                          /

g  % - g

                                                                                                              ,1
                                        -                              (.                                   /

E

                =

5 e z E\

                                                              =

m

                                                                          -
                                                                                                    .,

l . .

                                                                                                                                          = ==
                                                                                                                                                ?
                                        "

t m

/  ;;;

w f 3

                -
                                                                     ,
                                                                                                    /

v c:. g 5 -(, / - eE

               -                                             e                                   i                                              ;      i C
               ==

c:3 o .h.

                                                                                            '
                                                                                                                                                .

_-

                                                                                                                                                       '
                                                                                                                                                       .
                                                                                                    \'N
                                                                                                                                                "
                                                                                       -                                                              l.

2 - - o

                                                                                                                                          - -

a

 =I                                                                               e                                                                   j o"
 ..

I

                                                                                .,                                 \.
  • 8 v7 - .
                                                                                                                      /

o.- o

                                        #s#-

_ 1

                                                                             .s .                                                             -

1

                                      /                          ."

p

                                 /                        .
                               '

s

                           /

f EE 28 om ( - - = 1 r' $E 8 N . s~ ' % .N

                                             -w
                  <5
                  -

W -T; I un , [. l i I. f f I' I f f i f ,- l I i o E

   =

E

              =

8 5 2 8 8 8

                       =            =         c                  o                   ,              ,              ,                ,

(3.) 3801YB3d'A31 f f I f t t , c:2 c3 e ca e3 c3 e3 a m m n ~ ~ ~ ~ m - (DISd) 38nSS38d 0 8 i i i i i i i i f , 5

                                             ~
                                                      $
                                                      -

5

                                                                 -
                                                                           $
                                                                           -
                                                                                     $
                                                                                     -
                                                                                             $
                                                                                             -

a'. E $ $

                                                                                                                                                     '

(S3HONI) 13A31 H3Zl80SS38d

.-

'. . 3.0 Conclusion During any B&W reactor trip where a primary system break does not occur or the pressurizer does not empty and HPI is operable - net steam production in the primary system is highly improbable and generation of a volume of steam required to block natural circulation is virtually impossible.

                                                         .

4.0 References

1. 11/15/79 phone conversation between Cf:W and NRC, Suoject:

Potential Voiding in-the RCS During-Anticipated Transients

                                                   .
..-

'. . ATTACHMENT 1 Pressurizer Level Error The pressurizer level indication is based on the pounds of mass the pressure taps measure and then distributed to varying amounts of water and steam at the saturation conditions at the pressurizer pressure. Since pressure is not measured in the pressurizer (only temperature) pressure is assumed from the temperature measurement being at T sat

  • During fast depressurizations the RTD in the pressurizer does not respond efficiently, especially in cases where the RTD is exposed to steam enviroment. The heat transfer time constant can vary from 30 to 180 seconds. Since most depressurization after trips occur in 30 to 50 seconds the RTD will not respond effectively at the low level point.

Figures Al and A2 show potential level errors for 400" and 320" pressurizers. Figures A3 and A4 show what typical errors can be expected as a function of indicated level and system pressure. Inese curves can be used to correct the indicated level if system pressure (i.e. Tsat) and pressurizer RTD temperature are known. The difference between RTD temperature and calculated T (Based on Psat) will give the level error. sat In a typical trip @ Oconee 1/1/77 the system pressure went from 2150 to s 1800 psig in 27 seconds. The alams printer monitored a 643 pressurizer temperature at 1800 psig instead of the expected 621 F. At the indicated level of 70" the real level was s 78" (per figure A-3).

                                                           .
     ,.e rigure n-1 f*                        A

_ = -.- -.___-___7__ . - _ . _ . _ . - . _ _ _ = _ -

_ .. . _. . _ .

__

                                                                                                                                                                                                                                                                                                                                                           '
CZ1-' . _ _ _ _ _ . _ . _ __ '-*=I - _ . 22 -
                                                                                                    * - - - ~

t--__:.____..._-!----

                                                                                                                                                                                                                                                                                                                                                            --

r_ . _ _ . _ _ _ . _ *-_ _-- _ . .__.- -. . g

                                                                                         --

7'~._;-* p; ;,__~~C , *- -- - - 7 Z ".---_- . ._ . .__ ._.-_.-_"E!.2-'-

                                                                                                                                                                                                                                                                                         - ' -

h

                                                                                                   ,
                                                                                                                                                                  .                                                 _
                                                                                                                                                                                                                                                                                                    -._ __                                            ,

3-_-..3_..__._-_..-- _ . . . _ - .

                                                                                                                                                                                                                                                   .-;.-_--                           - - - .
             .. : ~=:- -^ ___: _ . ._:

_ _ _ ,

                                                                                                                                                                                                       - " - *                                                                    *
                                                                                                                                                                  ._
                                                                                                                                                                                                                                     *~
                                                                                                                                                                                                                                                               - . _ - ' ~ - . _ . _ . ^^*                      ._.--                                     L
            ,7__ _             .
                                     - _ - _ . . . _ - - . _ . . _                                                       ._                                       ._.

_

                                                                                                                                                                                                                                                              - . - - _ , - _ _ . _ . - _ - -                                                           __ ,.

_4 I---***'"-- __. ___._. . . ..

                                                                                                                                                                                                                                                                                                                        .
                                                                                                                                                                                                                                                                                                                                            .. _.. ---_q

_ _ _ _ _ _ . . . _ , , , . - . . . + LZ'._..___. \_'**---*-~~-~~--*----*---* +

  • _T7 ^:_ g'_-_

c, -

                                                                               ._g -- r. _.                                                                                                                       .-                  -
                                                                                                                                                                                                                                                                                    --- - ; , _ n - -                                               %
=r- p. : W
                                                                                                                                                                                     ,
                                                ,                   1
                                                                                                                                                                  .
                                                                                                                                                                                                                  - - - -
                                                                                                                                                                                                                                                                                                 =. . _ _                                           . _ . _ .
- == . D .- = - ---~~t +

_: __ _ . . Nq::$n:

                                                                                                                                                                                  -.                                                                                                                                                                   _ ::

t - M = = ;+-- _1. ,. _ _ . _ . _.:-= n= _;_ % ._.

                                                                        ...,,g                  ,

_ . _ _ . _

                                                                                                                                                                                    ,

__ _ . . _ . _ _ _ . _ _. _. r_ = y -* -L_y -- g +

                                                                                   -
                                                                                                                                                                                                  +-

_2 = . _

                           *                                     -t                          -- q __                                      :-                      t
            .._

I'.r__ _

                     .. %  r. .A  = __     .__. _            ____._ ,4 ._lkt.g                    .o         ___q

__ w-_

                                                                                                                           ,                                                                                                                                                                                . . _ . _ .. - _ . .
                                                                                                                                                                                                                                                                                                                                      .
                                                                                                                                                                                                                                                                                                                                           -m   _ ~-
                                                                                                                                                                                                                                                                                                                                                                       ,
            ;_- ;._- g                           . . - . - _ . - -
                                                                                         . .. ,3                    . 4                                 _                                                                                                                    . - . -               . - - . - - . -
                                                                                                                                                                                                                                                                                                                                             ; p; 39 L___. _w
                             @ = -.-*_                                                    d M W _ ( ,[                                                                                               ~

_ ~ 1. /_ . _ . . . . *= . o . gA.,.,,,..y,

                                                                                                     .

g1, g ._ _ _ . _ .

                                                                                                                  .
                                                                                                                                                                                                                                    .

_.--__;.. _. . _ - _ .-- _.

                                                                                                                                                                                                                                                                                                                                           ._ y
                                                                                                                                                                                                                                                                                                                                           . _. -__- _. ..D,
 'T         N_._                                                                                                             .
                                                                                                                                                                                                                                                                      ---

_:- . .. J-~1L k

 -         t- --O:                                                                                h*- *;-     1 _.1t ;;/,N                                                                                                                                                                                                       --

_. g b n =: = C I- -~Y .k-~i_ __

                                                                                                                                                                                                                          ^ ~ ~ ~ ~ ~
                                                                                                                                                                                                                                                     = - - - * - -                                          E T -~                         -N e                        _ _ _ - . _ _ _ . . _ .

pg.;, _ _ _ _ _ _ _ __ ;_ _ ; _ _ e.

- . 7_ _ _up, + -
                                                                                                                                                                                                                                                                               ------=_..___..                                             . _. _ g
                            - -
                                                                                                                                                                 *
           -                                           -
                                                                                                                                                                                                                                                                                     - -
                                                                                                                                                                                                                                                                                                               ==_--
= = :=_ __-. - - -_.- ._,
                                                                                                                       . ;-~:.=   q%.;.y\.                          _.
                                                                                                                                                                                 -~

_.

                                                                                                                                                                                                                                                            .
                                                                                                                                                                                                                                                                                          =~                                 =              .==    .- . .Q
                                                                                                                             *

{ ZZZ -*-- 7__. _ -*-- . *\L *=:'- :- - " - - - - - ____J--

                                                                                                                                                                                                                                                                                                                             ~ -                     -
                                                                                                                                  ~in' *h ath :-t

_,

           ;- n . _ ---                                                                                                     _ f'*g;-
                                                                                                                                                                                                                                                                  .

y

                                                                                                                               '
                                                                                                                                                                                                                                                             .                                        . = 2-j n = ;_ _ _ ::- -                                          :_ -                               ----------_.

Mp_ _ ._

                                                                                                                                                                                                                                                     ---
                                                                                                                                                                                                                                                . _ _ . _ . . . _ _ . _ ._ = p - ,-                                                                       .g
          , _ _ . .                          %_                                                                                         ..                               __.                                                 _

n

                                          .- g y -

y .-- - .- e _ c gQ

                       -
                                                                                                                                                               -g                                                   _-.__.;_---_-_..._..,.-,,j,_

l _x_r,,- = . tch.4 _ .__ _.

                                                                                                                                                                                                                                                                                                      --
                                                                                                                                                                                                                                                                                                                                          . r. _ q pr.                                  g__h.
                                               , . . . . _
                                                                                                  ,

_+ - - - + _ _e

                                                                                                                                              .

q1 . \ _ _. .__ _

                                                                                                                                                                                                                 ,                  _ _ _

_

                                                                                                                                                                                                                                                                                 ._.._..,=__=....._.,e-*=.-                                .._=.

_ g_._..___._.,.__y.

          ._

_N.,_.__-

                                                                                                                                          , _ . _ _
                                                                                                                                               .                           .. _                                                    _. . _ _                             ____. _ __. _ _. _._ ._., __ -_ _- _ ._,

_

                                                                                                                                                                                                                                                                                                                                    ,
                                                                                                                                                                                                                                                                                                                                        .
                                                                                                                                                                                                                                                                                                                                                       ._

_

                                                       .
                                                                            - . , ,                                                                .

4 ,, . _ _ .__

                                                      '=*                  2                                      "

L--*; mart : \ }h -

                                                                                                                                                                                                                                                                                                                                    '
          }         ~ - * -~~ "_; d _ . ._. T. r ., , =_ _ . '"-*                                                                                                                                                                                            ,                                       . . _ .                               _ . -

_ _ _ . . . __ ___ _ . 7- rnx= u_ -- --- --. C : g ;_ _ - _. _ _,_ _ _ _ _ . - . .. _

                                                                                                                                                                 ._ .pg_ _ __                                                _ _ _ _ . . - . . _ .
                                                                                                                                                                                                                                                                              .. _ _ _ .;__._                                                _f..g
          ;-- -* -- ; =r,J =n --+                                                                                                         +
                                                                                                                                                               ,._,        ti:\-?;:---" ._                                          +
                                                                                                                                                                                                                                                                ------==x e          - _ _ _ _ . _ . _ . -. _ . _ . , . _ -                                                                                                                r,         _p                                                                                                                                                                                     9
                                                                                                                                                                                                                                                                                                                                           =N

_ _ _ . . i.si

                                                                                                                                                                                                                                                                                                                          .
          ..

Q=iEBEk._ ._ _-?'"_._._* __n---R W .__.. *__.. '= r==_.==- m=r L_ L_ . .- __ ._,.y/ ..__ Jfq

                                                           =                     pr                          -
                                                                                                                                                                                                                                                                                                                                            . _ .g
                                                                       .n gp+-                                                                       -- :n3_.x                 =.N.N: q..,: -                                     a = =n_ _._= x. _ . __ .

-{ , L_ ._._...g. _ _=-:_

  • A.
-;        g._                                                                         .                 _
                                                                                                                                                                                                                                            . ..__.
                                                                                                                                                                                                                                                                                        ;___.;                               .-

y t _L -x d f =r= ._ ______,___.___t_.. _ _. _ --__ . t___.1. w _ _ n = tr?: = .sv.G;2._... .

                                                                                                                                                                                                                                -3.______._______. = .r n---
                                                                                                                                                                                                                                                                                .
                                                                                                                                                                                                                                                                                                           ,

_24

                                              ._.____                             mr = r A = _t-                                                                                                                                                                                                                                             :oa p          g23                                        e _,= g__.                                        . _ _ _ - _ . .                                          .

_=g .

                                                                                                                                                                                                                                                                                                 ...~__                                           m __ _ ,

Q .__ _r *Fn. _ _. 4 - *@ _ __ ._ . : -" p.L._._(

                                                                                                                                                                                 ,,                                   m A _t ..
                                                                                                                                                                                                                                                -

__ = = . =u .- p

   .      p--
         .= L d_ :--- $'=r=m1Vt tr bg=*-. . _ . . _ _ _ _ _ _

_ '- =c -- _ . . _ _ _ _

                                                                                                                                                                                  .:M=__:.y:\c.3n=                             d -- =: .r_r--                    _ ._.u= = ==                         =r-r -                               -.___

g i==_ o._ p._ _ _ _ . . _

                                                                . 9c                        ___
                                                                                                                      ,___._._.;______.                                                  _
g. . _ . _ . - . _ , - . _ . . .

,, ;

-

3._ .. =n _ __. swx=b.---- -- - c dr . .. - - - d 7_: * = u- W

                                                                =m :'p       m. Q=.__= .._ =.

_ _ : =- -* _:- .__ = __. ggt:=. Y, =n x == --- - -

                                                                                                                                                                                                                                                                                                                                - ;l.,                           .

@, c=__= *=_y-r . . - - c., g&c. w .

                                                                                                                                                                                         ....1-g                   < =__.=__._ =___:._=__ =_                                                                          .4 _.. -

3 ---C: _.; $ _- _ . _ q _ . _

                                                                                                                                                                                                                                                     .                                                            . _ _
                                                                                                                                                                                                                                                                                                                                                  ,

g - - - _ _.gm ----N,g:s _ T __

- --- -

_ _ _ . . . = :==y;:S=  : h.pN w= .N-t=r - +

                                                                                                                .
                                                                                                                                                                                                                                                                      =: _ .=-                                                  --                -

M =_=n  : .@ = _;;r

=:_.72 a 3 ==::--.=L _ _.-- _: 1 ::(L. -- - --

_

L . r_ -
                                                                                                                                                                                                                                                                                                              -
         .=                                                                                                           . -                    -
                                                                                                                                                          , = = .                             - - -

q-c.: w% si. p _:==. .-

         = : ,.3:         u .__ _ g ===.u            ..         = g x = c = _2 = :== - : --- == ====::===r,nu                                                                         =
                                                                                                                                                                                                                                                    ,

c =_= _.

                                                                                                                                                                                                                                                                                                                                                          .
                                                                           ~4
=:- -W= ==5,=n . : ,,,. .a d :cc:-- - :n== -: .;.,_ _ _.:=: n2  : . ._. _== :-
                                                                                                                                                                                                                                                                          -
                                                                                                                                                                                                                   -4 =v h'_= Kq \gc._=_                                                     : ---                    __
                                                                                           - :==                                     . =:                             .=+=.--                                                                                    -
2.: - n :

r . . . _w: n = >:'M z o ;r=t:2ca.  :  ; =.  :-

                                                                                                                                          .

t=.=:= ,g .1 = ::rn:= ...u==l:;===m:x: = =. . .1:___:n-*_

                                                                                                                                                                                      . . = = . ==                         = w\. n.s:_=      ; 2 =: .- %w\ o = . . _                                                                                             _
h. C n ni=:._ ; M .-. . _r. :. x_ b. _. . i. . 2 . T ' E_ _ .='_~__:i. '_~-3. . _ d. _2
                                                              .              _

_ . . _ . . . .. _ _ . - ;_ -.. - -- . _ . - _--M. . . _i. r e . N. x .1. si\'~ .

i. . . . . _. . : ~ '. . . _ . . ' Z :.'L_ . ._. ! (l :" T . * * '

7 l ._. _ . f" . . .. 12. . _l '! --* _ .i ~. . *f _...J _.J Z ' . b. .: ;.: . '. l - . _ _l _. _ 4'*J. C . ';  : : .1:='m .\ [_\\ . i ._ _. . . p.-  ;=-i._ . ,-  : ==E _i .[- __ +E ==1.1 c= := .! zq_g=g.g='Q$.ig; _ ,

                                                                                                                                                                                                                                                           '._._.7.
                                                                                                                                                                                                                                                                                                                                            ~n_
                                                                                                                      ..           _                            .       ..                       . . _ _ . _ .                      __                                                         . g         i                    . . _ %J .
            . _ _~ .'__~*"
                       ~~'
                                  ^

a' ##.

                                                ~'^         ,4l.2'.C.I _ . _ _=_ _ . . _~7_7__                                                   C '"

_

                                                                                                                                 .. .. . $ .: ~....~.'l.**l'.$.*_.__4_._____Q.__._.g.,
                                                                                                                                                          .

_ _ .. _m 4_,__. . .

                                                                                                                                                                                                                                                                                .

_

g. __4 .
         ---Q                   =:              '4, -- . 4 =- =. -Q . ._                                 ._       Q;-      -    t--  4    :=;
-- ;;;; =:_ m .f .: _: n -0 = =o rn-e _. :_6 ___._.A3 w _ ._ .wrn_1,.
                                                                                                                                                                                                                                                       ---ee         -  r   -a
                         %-                  - --
                                                                  ,
                                                                                                       --+- 3                                                                                                                                                                                                           =--:f_ == _:                                  .

(aA.am=,.Q q g 9 mM4qy wm p 1950 101

             .
          .

.

                                                                                                                                                                                                                                                                     -

Figure m.2

         '
                                                -                              --- - --- - --                                                     - - ~ ~ - -                                      ~                             - - -                                   --                                        - - -
            *'t-..;;=-!=__..~+._=.___*.__..__._.__.w___.__._.._._.__.__.'~--~--.__:*..____..______=----
                    .._____                                                 .             _
                                                                                                                                    -
                                                                                                                                                  .                                                                                                                                                                   ._.                             . .L_ _1,
                                                                                                                                                                                                                                                                                                                                                      .
                   = = = = _ = =                                                                            _ = -                                                                                  ._
                                                                                                                                                                                                                          -
                                                                                                                                                                                                                                                                  = = = .                                                          =
_ - .: r- 1 rc- - ;____._ _ _.
                    .
                                                                                                                                   *___=.__.__.*                                             --+ - --~ - n r n == = = - r = ._ -                                                                                                   .

m . _---~~'~~~.==_..;.lL

                                                  .. . = = -
~ =_=Z=--.~.--."=*_-----~--!ZE=L
                                                                                                                                                                               = = -                                                       - . = =                                        _-
                                                                                                                                                                                                                                                                                                                           ._

h

                  .-              I~~...                          ~. C "~.~.!~. L~~!---~*                                    !-~~
                                                                                                                                       ~

__.~12 ^*'~-~~~^~!~.~.~~_~^--'.*_..

                                                                                                                                                                                                                                                                                              -
                                                                                                                                                                                                                                                                                                                                     . _ .
                  '
                                          = ,/'                     ..z--rL____-~.-----__                                                                            _ : = z _*- - n. __ - = = _ _ _ _ _ .___.-_==:                                                                                                                                .                        .
                  '              - - '
                                                       . \
                              --.
                                           -.
                                                     . . g{{- . __ . _ -_ _;-]*_..___.__._._.__.
                                                                      .
                                                                                                                                                                      - : --' -'- - -{ =C = -~ Q C = =T Z ; -_ ._ " -- . . _ . ..-

_ .- . . _ _ _ _ _

                                                                                                                                                                                                                                                                                                                                                  ._-
                                                                                                                                                                                                                                                                                                                                                     , _ _ _ _ ,
                                                                                         . _ _ =                                                                      . _ _ .
                                                                                                                                                                                                                        ----
                                                                                                                                                                                                                                                           =                    __.===:=                                                             ..- -

l __. ..- . ..: n\71 \ u\ -s \ \\ =rnanx=:=_____._ _ ___._- _ - - - + - - _._ _ __;L__._ = = _. K 7 ----*--*-~*'-----*~_.-.-* *--- - : _. ____~..__

  • M T-

_ _ ..-..{ ii_ _:'.a. _ \ ?[N\ _ . . _ _ _ _ _ . _ . - . ' . " _~ _ _

                 . _ _                                                                                                                               _.                     .                                                                                                                                                                                 . . _ .

i : ---.= .. _2\

                  -
                                                   -
                                                              'v.~=. s.'. &. , ' ?. =. . __~_~. .__ __. ._                                               :-
                                                                                                                                                         .
~~__.__._______=--_i.=___=__J.__.:._=_-..
                                                                                                                                                                                                    - ___                                   .                                         -

_. .. E

                                                                                                                                                                                                                                                                                                                                                 --.___ .

_ = = = = . _ = . = . _ = _ . . _ = _ . ._:

                                                                                                           =                                                          =1
                                                                                                                                                                                                                              -
                 ._c_. n.g __:.
                  .

y w__. 4n.j.= = _w. ._ _=.=. . . _ . - _ .

                                                                                                                                                               -                                                                                     ~ ~ - -

V U_T.-m iu .:'._.M,)T...\$,\ - _E- i.-

                                                                                                                                   -
                                                                                                                                                                                                                                            ~22=____~~"-= . . _ . -
                                                                                                                                                                                                        -
                 .                                                                    4                                                                                                                           _-                                                  _                    _.
                                                                                                                                                                                                                                                                                                                                                   .n b
                 .-
                                                                                                                                                                                                                                                                                                                                                 -g.g m

_.

                                                                                                                                  . _ _ _ _ _ .

p.-.o~ M.- .__ _ _ _ _ . _ _ . _ _ . . e = & -- . . q#m =

                                                                                                                                                         -
                                                                                                                                                                                                 =--                                           _s4=-____.___. = _ -

M_ -

-- .. _ .. = = = = = . m . x=N R
1 - no. n =..

tr:n n - . ..xt br .-.kh=__=_. _ r _ . . _ _r--------~ = _ - - r nx_= _.3 ' d e ---- --- - - - - -

                                                                                                                                                                                                                                                                                         - - - : ==
     -           r=~S.Ixx n W -- - - x,_2                                        x .% 24         _ ca;      a g\ .                .                                                              .                     __                                                                                         7=r -                           .r;  - _: O C
    *            : r :T4 nr
                 ..                         __ __      z. .__ . _     .                 4 -\in\     : 4%     r r 4%g\r
                                                                                                                 .
                                                                                                                           .__. r :----" - . .
                                                                                                                                                                                                          . - . r_.__In = = ._                                                                  __                  1- = J
                                                                                                                                                                                                                                                                                                                                                 =n . y*
                                                                                                                                                                            + ---~ - nn _ n = r r- ".
  • rz r = n. = ._ . . _.

__.

                 .-                                  _.._ ...._. _ .,

y __ ;,_ . g_._ _ _. _ _ _ _ _ . _ _ . _ . _ .- _ 4s

                 ' ==. c : = _ _ _
                 . - - -
                                                                                                            -

n- -

                                                                                                                                                                                                                                            . == : ._ . =. :_ = - -
                                                                                                                                                                                                                                               -                                                                          --_.                     .. .,
                 .= nh. . -- _=__.                                  : = = 1 __           =-\r..g ._             = +. . :\.w=:\ _= ~t ~K \ A:._

g - u- _-_.- ._. --- - - - - - - - _2_ = = _;; - r- n Q = g =.. - ..._pt--

                 ._                                                                                  .-_
                                                                                                                          .p.     \t_.                                                        -

__.__._:____. ._ _ ..___: - - :_- r . g _9- _ _. _ _ .__ _

                                                             -                       _
                                                                                                                                                                                                                                                       .                      __.                                 . . _ .

r . V=( . == 1 c =-& 1._ a. ..._.. 1 ,%._ _. _ _

                                                                                                                                                                                                     --

_,--- _

                                                                                                     .                                                                      . _ . .                                                         :-                                                 -- 1:                                  -
                                                                                                                                                                                                                                                                                                                                                                          .
                 ;==_ ..a=                     :=- ~= _.. $ ==== A= _:m_g===-Lgw_. ._
                                                                                                                                                                    -------,-_:--,=_=x...
                                                                                                                                                                            .

_=--. -

                                                                                                                                                                                                                                                           =--                  = = = .                                      --
                                                     . _;_ w       3 _. .

_ . e .,

                 -_                                                           ..
                                                                                                   . . _ _ .1-_h-                                                                                                                                            - - - - - - - --
                                                                                                                                                                                                                                                                                                                                                    % h

_j_;=:Qu(=t'4t4p:s:  % --- n--=---- - .- : -- - -- __n.__.;=------- - -- . ._ t: Lax: __ ___ g =2. _ =- - _ .. 1.Lr:=r = = =%g = ==_ : .- --

                                                                                                                                                                                                                                                                                    = = = = .                                                 =
                                                                        ==                ; n - n\-       ===\=\====_m\;s                             t 1\=- : _- ._ _ _ _ _: _ __                                                                                                  n --- :- : : - -                                             r_. -
                                                                                                                                                                                                                                                                                                                                                ---

w: r2-rm ..=z == ==r y==4: um_w_._.4=.=g --- 5 _tex=tntt. . w --- :===.=n:-- =- .

                                                                                                                                                                                                                     .                     ..___. _ = _.= - -
                                                                                                                                                                                                                                                                                            - - .                        _r                            n
                                                                         -:-N                    v                                                                                                                                     _ . _ . _ _ . _
                                                                                                                                                                                                                                                                                                                                                                     's
                                                                                                                                                                                                                                                                                                                                                                          ~
                                                                                                                                                                                                                                           + - - - - u- __ _. . _ r u - - - - - -
                ;- .:rn :-Q.t; rn1bg==22: ==i:

t= =- r- t-\r=h=\ \--\ -t:% .tX r _ ---+- -- - -- - - - - - - - -

                                                                                                                                                                                                                                                                                                                                       ._

_9 0 t == = = :_

                                                                                                      , ----- nt__.V                             v +--              q;t a-                                                                                                    ._: r - - - ; _. __ = -
                                                                                                                                                                                                                                --
                                                            .
                                                                                                                                                                                                                                                                                                                                                 -3r.
                                                                                                            -~ ---
   -

t ==u ==_ .Q.===. rq . G_.=  : Q =__

                                                                                                                                  . _ .
                                                                                                                                                          . _. - _ \. n;                                                                      -------_:---=2.
                                                                                                                                                                                                                                                                  .__ . . _ . . _ .
                                                                                                                                                                                                                                                                                                                                                                  - m,a
   .            g
                - .      . _. __.   - . _A___.

7 J, _ . __ . . g=_ = m -Wr__.: . ._._-- .._.p_....g_=__:__-_-____.__.__ g_ ..__t=_t.,- .g

                                                                                                                                                                                         ._.                .. .

_. _ ._._ . :1__.__. .

                                                                                                                                                                                                                                                                                                    .

r - - S.

   -'           ' -- - b C*d . 1._. . . . M _ g -~=!7 -- ~~-" "--* *h~g\ T T A : S.. :--,2- --_**_2:(ri_--.Y._1____                                 ~
- : *; - --

e ... _. . _ __ ___-:---- nn;. C * ,_ _ . . _ . - - -- ;_ . _ _ V

=x 1.g= nr . __:- _- r_ -
                                                                                                                                                                                                                                                                                                                                                          --Q
   .'  ;

tt ==rg: =a.g :--==D. g = ~ 4'4 =- ---~ =W.g==:.t x tb\ =- : := =:==== =x __r 1. -

                                       .
                                                               .._                                          _x: = ==+ = s _- ;                                                    s= v .y v = r== : ==.. :== r-                                                                                               .
                                                                                                                                                                                                                                                                                                                             - - -
                                                                                                                                                                                                                                                                                                                                                 - %

o

   *:                                                                                                                                                                                                                                                                                                                                            .m
_ r g =.- S r - M.u 4 m .r---- P Q\ \?%2:=t - xid
= _. =.==$ - - v, . . - - ~ t------ -

y _ . _ _ . ---\. 3: \n\. - --------. . -._____ -

                                                                                                                                                                                                                                                                       - . _ ,_::                 _ __._. _
                                                                                                                                                                                                                                                                                                    -
                                                                                                                                                                                                                                                                                                                         =, . _ .
                                                                                                                                                                                                                                                                                                                                     . . __n-          .-...
                                                                                                                                                                       ._.~a...
                                                                            . ,g.q.                                                                    -
                . . _ . . .                                                      .                                 _.
   <

p p a--.$:- .n_C.

                                      .m                _. ,,-._                             . . . .
                                                                                                                   ---
                                                                                                                          .._._...__.____n__g_...._.s..._.
                                                                                                                                                        . ..

g\rny-  :._.___:=...=._-=..---.-.-

                                                                                                                                                                                                                     . _ _ ..                                    ._                 ..                                                               -.-

g sM  %=r==z s =- ===w -

   -
   -'
       .
=1uJmg-r--
                       -
V 2==w.

n = - MQ3==-::=r_ s

                                                                                          =n =-                    r=;r;mwe~..                  _ . =. .=_x =,\ =.\.        .v =
                                                                                                                                                                                        =.       -   d          h=. v:
                                                                                                                                                                                                                                   - -
                                                                                                                                                                                                                                           ===        r- :_2_ =_ :- -- -
                                                                                                                                                                                                                                                                             ===                                                  =

_. g--

                                                                                                                                                                                                                                                                                                                                                        -.

9 y  : = 4: r=- y _;"_cP a =___._ -~ : ot_. nn -- ---- :=_ _=.r --- g21 2

                                                                                                                                                                               ._y -L\        = nq\=._.d;:\ : \::r--

ur

                                                                                                                                                                                                                                    .__ u = :_

n---- -- - - ... _ e _ ._.

                                                                                                                                                                                                                                                                            - :--- .
  • r - . . 2. .
= h&W ms=e-g=mgman=== =w=
               - ._ . _._. m -                                                                                  ._= =_. _= _ ._ ._ = .:_.=                                     __ . ,\_nN:                      =2_ xb= % :                                                                                         .
               =                              .=                    =            ===-.;.2=====.                                                                                               :
                                                                                                                                                                                                                              . %. , . _ _ _ _ . _ _ _ _ _

7____ .. _ e._,;__.....x...g......._

                                                                          . .-.                _.                          .                                                                                .                                                    .._.                   .
               ._.._.-_..
                .__.

_

                                                                   . . _ . . .
                                                                                                   . - - . . . . . _. __. __ . . _ . _ __.
                                                                                                       ,
                                                                                                                                                                                        .                                                                                                            . . . _ . .                 . . _
'
               ,---.                                                                                                          n ;. . . . _ = .                                                                                . ?g . . a '-                                                                                                          --
                                                  =..--_...=_                                               _.                                      = = . . _. 1 r._. 4 :&c:=t ra. ._1.                                                                                 : . ._ =.
                                              .   . . . . _ . . .                                                                                                   . . _ ,                                                                                                             . _ _ _ _ .
                                                                                                  ==.                                                                                     .                                                                                                                                               .
                    =-                                         "

_,--- ~ggi id=Q [=-J : - $-pj~].j Q--- 9= - .

                                                                                                                           -5 E: i ;r;
                                                                                                                      -                                                              -                -

b i \ M1 @h Q.f- r . ._ . .

                                                        -

1.

                                                                    ,                -: j. ,                                                     _
                                                                                                                                                                                              ;
 -
              .
                                             -            -
                                                                                        ,=:sy s=s=====v= - e.74=g= swww= r- -                                                                                                                                                                                                                 ;=                            ,
                         .

k _._.. ..s T: __. j r

                                                                                                                      .=.

_..2:_..=.,a

1: :
                                                                                                                                                           .

_ _. :

                                                                                                                                                                                .
                                                                                                                                                                                            ,.-.r=c=.w m _.v.o_._,o._----.__._

_- g ;-- no _ _. _.g: - ~

                                                                                                                                                                                                                                                                                                                             ..= _                        ..

_ _. . y . s - .2

                            .

4_. - -. _ . . , . . _:

                                                                                   -

4..4:..=_i- y = w .9 rs -. ._ g a. _=_qm.= m, - g, _r_.: .m 4-: r,_j. r.

                                                                                                                                                                                                                                                                                                                                                          .
                                                                                                                                                                                                                                                                                                                                                                      -

syg.>p~.2 n a ~a-w mw.e 1950 10,

 .           s.-
                   -

. . Figure A-3

             .
                 -
                                - ' -
                                           '---2

_. _

                                                                            -------.-----:--}--

__ __ _

                                                                                                                                                        -----~..._._..------.-*---
                                                                                                                                                                                                                          -- - - -
                                                                                                                                                                                                                                                                        . _ . _ _                            ._                      =.                                             - ~ - -

__ ~ --_ = 7 T~~__...__.__.

                                                                                                                       ~^
                                                                                                                                                                                                                                                                                                                                                                                              ~~                                    ~
                         * = ~ ~ ~ ~ ' = ~ ~ ~ ~ ~ . :-T~~
                                             -                                  - -                                                                                                                                                                                                                                                                       --
                                                                                                                                                                                                                                                                                                                                                                                                                   %~
                        .i- .__ .y" - - ' .-_ - . . _ _-.__

_.

                                                                                      --                  --
                                                                                                                             -t=                                                                     -- __.._._

_

                                                                                                                                                           .__                                         _ . _ . _ _ . _ _ _ _ . - .                                         = _ = _ _ . - _ _ - _ . _ _ . - - _ _ . _ _q_+
                                                                                                                                                                                                                                                                                     -                         -

4

                                                                                                                                                                                                                                                                                                                                                                                                                                 ._=.___
                                                                                                                                                                                                                                                 = ' =;' -- E " C I C '. " ' Z ~~ #
                                                                                                                                                                                                    ---
                        '_.                                                                                                                                          T ---                                                                                                                                                                                                                                                       >
                         =__ ~=_. - _. .= "'i;. E_ F.r2 . =_= { H_ 1_.=___._.-._'~._'___.-._--'_.2C--
._ .

_ _ _ _ _ _ . . _ _ _ . . _ _ ,

                         ~-                      =_ E1_. =_a_ _ -                  _

o w.. _ ___..._-=__. ,=. a., m)_ e. =-=.==_a_=._=._..=n.--- .

                                                                                                                                                                                                                                                                    -                                        -
                                                                                                                                                                                                                                                                                                                                                   . - - - - -
                                                                                                                                                                                                                                                                                                                                                                                                                                                           -
                                                  ':_?-
                                                                    '^
                                   --
                                                                                 *}                                                                                                      ~~~--^T.~~                                    .--y_;.~_.-._                                                                                   _____ y
                                                                                                  '.'~_~_---'-*~
                                                                                                                                                                                                                                                                                                                                                                          - - - . . - -

_ _ _

                        -

_ _ - . M-._

                        ====___=-____                      __                         __--_~                                                                                                                         ___ v
                                                                                                                                                                                                                        -

_ , __ . _ . _ . .

       -                                                                                                              .                                                                                                                                                                                                                                                            __.

n _=

                                                                         -- -. n _-__l-                                                                                                      _ _ . - . . _ .,                             . . _ _ - _ _ . . _ . _ . . . _ _ _ - - _ - _ - - - - .                                                                                                                               -                        -
                        ==

i = .=. ,==m=g wm=-a .

                                                                                                                                                     -
                                                                                                                                                                                            ====s _. __ - 16
                                                                                                                                                                                                                                          = = == = =w ==-
                                                                                                                                                                                                                                          -.=m.__=_.._.____==._-==
                                                                                                                                                                                                                                                                                                                                                                      =u=_
                                                                                                                                                                                                                                                                                                                                                                                                      -

Ti

_ --
                        ===--.-
                                                                                                                                                       . . _                                                                                                                                                             _
                        --
                                                                                                           ,_1                                   .                                                               -- m                                                                                                                                                                                               ss %- ' " "
                                                                                  -- % '_ a _._g-__.-_.__--_..-___.__:.                                                                                                                      . - _ - _ . - . . . - - . - . _ - _ . . . - . - - _ . . - _ _ . .

_-=__..-__.a=~.-a_ =_%~_------ -- - - - - - --

                                                                                                                                                                                                                                                                                                                                                                                              =^               - ~ ~
                                                                                                                                                                                                                                                                                                                                                                                                                          .

___ . _. ._y _ ,_. _, s...

                                                                                                                                                                                                                                                     .-_.-..._.---.

_. -_ =L

                                                                                                                                                                                                                      W ~ - ~ _ " ' - ' - ~ ~ ' ' ' - ~ ~ ~ ~ -.r --%r._ _r-~_ ~ ~ - - -

Q

                                                     -
                                                                                           .-
                                                                                                                                                                                                                                                                                                                                          ~~~ .

E;$C_ _.-A _ l _ _. .

                                                                                                                                                                                          . - . - . - _ .
                        'cr- _ .E=-
                                                                                                                                                       '
                                                                                                                                                                                                                                                                                                                                                                            ~ ' ' '
                       ==? 3- -q                                                           A-- \=.g,4                                                                                                  _== :p == ;= == . .. ,._. --                                                    -

_ . ;=E' = 3 j --~ o m---

                                - . . _ _                                 _-_.-..._s_y__                                                         ,

g _ . _y ,.

         .
         .                                                                . . _ . _ ._._ V._W                                                 s              . . _ . . . . _ . _ _                              --- ;_ ;                    _ . . _ . _                                                          _ . _ _ . . _ _ . ._ _ . _ .                                                                  -%3--

__ _ .-

                                                                                                                                                                                                                                                                                                                                                                                                                              -

________-_h ___

         *"'

o $ -~-~; _ _ _ _ -__ c __ \_.._..-..____.---.N.--__..___-.-.___-

                       -.

__.

         ,e           g.
                                                                       -

__ e . < _._ _.______-___ _ _~ _ q-._ ;.

                                                                                                                                            .

s ___ ._ _ . . - .

                                             . __m_ "1____.
                                                                                                                                              .                    _

_.- M.._._._.-.

                                                                                                                                                                                                                                                                                                                                                                                                                                            ._
                                                                                                                                                                                                                                                                                            - - -_

_.

                                                                , ._____.._                                                                                  \                                                                                                                                                                                                                                               4..-___--.

w _ _. .

                        .

m. a .-.=. - _ os= __ u._== v= x-. _-..=_-.r-- _+w _ _ .

                                                                                                                    . _ _ _
                                                                                                                                         =                                                                   . _ _ _ . . _ _                                                    . _ _ _ - -                                                  __-____-...-                                                    =_ s =. .
                       =m
                      , _ . . .                              _ . _ - _ . .                                                              x _ r _-.

_. _ -_ _____. m _. - - - . .

                           ^                                             --

7_--~' '

                                                                                                                                        '"~Q                                          _.___,__.m                                                                                                  _ _ _ . _ . _ . _ . _ , _ , . _ . _ _ . _                                                                     -D                             '
                      ._.--!= d _~~ -                                                                               7='                 5j d ~-~iF_Dr==-I--     -
                                                                                                                                                                                                                                " - ' - ~* - - -                                                  - - ~ ~ ~ ~ " - - - - " ' " - ' ~
                                                                                                                                                                                                                                                                                                                                                                                                         .   =    Q5 .5
                      = .s =C=- a == -                                                                                                                                                                                                                                                                                                                                                                       w
                                                                                                                                      -
                                                                                                                                                     =t.mch                                                          -e r==                                                        _ =. . _ _ __ _r=_r; ZG              -                                                                                                                 =E
     \

EM~ - * =_ _'~.Z _

                                                                                                                                     --
1. . l_ .-A~Y% : _.- . . _ __ _. _ . - _ _ . . __ _ _ _ , .
                                                                                                                                                                                                             .-
                                                                                                                                                                                                                                                                                                                                                -

___y FMG2. .

                                                                                                                                                                                                                                                                                                                                                                                              -
                                                                                                                                                                                                                                                                                                                                                                                                                                    -

___________..t 9 n

                                                                                                                                                                                                                                      -
                                                                                                                                                                                                                                                                                .-
                      .                           __

_=___m pa_=m ___s-1_1- -N.__.._.__..______ _ r= ,4_. _. _ _ . . _ 5_4 _.g ==_ :- --- - _= g ===r n:_=y_ p -- - - - - - - - -

                                                                                                                                                                                                                                                                                                                                                                       = - - -

__q_ =;

       >
                      = =_;
                      .

(~ w .__ m _- c w_.m_=._ -_ - _ --

       -

r== -- --

                                                                                                                                                                                                   ,-._w                                                                                                                                                  _ _ _._ _

_

                                                                                                                                                                                                                                                                                                                                                                                                               = r. .=_-. - % =;
       <
       -              a =.m,               g --z ._ . .._                                                               _ =
                                                                                                                                =-
                                                                                                                                                     -_4_ _

_.

                                                                                                                                                                                                        \ _1_A __ _ _
                                                                                                                                                                                                                                    .
                                                                                                                                                                                                                                                                                . _                               _ _ -                                                           .__=
                                                                                                                                                                                                                                                                                                                                                                                                   =            == .3c,    :
           ,
                                            @N __ _ . -. 3 E~Yt-zm= N=S $x--~                                                                                                                                                                                                                         - - - - - -                                                                                -
                                                                                                                                                                                                                                                                                                                                                                                                            ?=                            =

g g=.w u

       ="                                                                                                                                                                                                                                                                                                                                                                               _- +- . 4 .4.=_-
                                                                                                                                                                                                                           .
                                                                                                                                                                            --                  c aqm:      % g: . A
                      ._                                                                                                                                                                                                                                                                                                                                                                    --
       -              . _ -
)== -: Q ._- - 1.-.t- s _ __
                                                                                                                                                                                                                                                                                                                                                                                                                                              -

S _~~~~.. - _ k . .Y . . _YY Y--' ~

Ti. .
       .C,                                                      n - =.

g . _. p. . g yy_ _ c. ._:.._._w

                                                                                                                              . . .
                                                                                                                                                                                          -                        .
9. _y_ . ..m.m . __g =_ _ g m__-- _ =. . ._ _ ._

s 2 M F- q b' :~~ -' '. ._-. -_- g.,m_ rt, _: 2 D 1-_ _- t) i .. . _- =. .k=-.o W S_~~ N. .'s~iE. ~c' _~ ~._--*_ _-- _-- - - "--_ = :' =. l , fs ' ~ ~ "

                                                                                                                                                                                                                                                   -                                     --
                                                                                                                                                                                                                                                                                                                           .                                   -
                                                                                                                                                                                                                                                                                                                                                                               ._-
       %             w ~~ q z. :% - - - ---- Q l _.- L. _.- O ' ~ - - n                                                                                                                                              "D ;z Jbyy'a="'"'\                                                                ---                                  -                        - - - - -
                                                                                                                                                                                                                                                                                                                                                                                                               .Q = :_=:-~ - ~ ~ ~

Ce - ' 2 0** a'r-

                                                                                                                                                                                                                  '.=. _ EM    . 9 _ 2 -..y__ ~M_--_--__________-__-.>___.
                                                                                                                                                                       -

C4Q . _1- ~ ~1- _ ___ - e . . _ . - t _=_c g . _ _ . . . .g--_..;_ ..

                                                                                                                                                                                                                                                                                                                                   .
                                                                                                                                                                                                          .
                                                                                                                                                                                                           ,
       ~-            :_ -.-6r .z=                                                                                                                                                           s                                    _

_ _ _ _

       =
       "e .
                     . . -
                     " ~ '

i t_.,.__ \=nr_= \ -- 4,__ _

                                                                                                                                                                                                                                                                                                                                                  ._               ---=1==                                           __

__ _ - - . . . - . _ . __g g - N -._- _ =__=i. = . _ . _-_,=_ ._ - - __=_c_=, _= _= r._\r.r _= - . _ _- \=:r.___h_..=._- =___=__ = rr _r o

                                                             --
                                                                                                                                                                         .                                                                                            _                                            _

_ g C==2

                                                -._.:E 55___. =-a.____, -TA__ g,__u - $-- _ _ ,__._{RE __ =1__ ; ___.

_ _  ;  ? 4 --i == w_=.-..=_.._u._=..=_..___

                     ,_                    .-                                            ..                             _ . . . _.. _ _ _ _ _

___ _ , _ __ . _ _ . _ , _ _ ._ ___g__.____ _ -_, ==\ _ _ _ - - _ _ _ _= _=- == _

                                                                                                                                                                                                                                                                                                                                        .
                                           .

_ .E.== -

                                                                                                                                                       = cau.= r ==_g== w=                                                                                                                                                                                                                                                                 ,
                                          .--             ='#.                           M 5 ~ 5 NT=_I5 "-i"---5'N. _ _-N1.i'~~~-~Y-'-3EE5- i' _ n - J _i5
=. == _ g 7.= ;_= - - - -

_ _- 4.==. _=\ ; ; g =:3=_._g __ . n - 7 =-

                             - . . _ - _ . . . _ . = = .._==;_,=
                                 . . .
                                                                                            =                        =. = -                                           . _ _ . ___ -7 _.,_ -,,, _ - , + - _ __ _ - + _

_

                                                                                                                                                                                                                                                                                                .

_

                                                                                                                                                                                                                                                                                                                                     --....n._                                       . _ . - -
                                                                                                                                                                                                                                                                                                                                                                                                           ---
                                                                                                                                                                                                                                                                                                                                                                                                                             -.._.
                                                                                                                                                                                                                                                                                                                                                                                                                                --

_ . . . . . _ _ .

                                                                                                                                                          . ..

_ -. _ _ _ . _.___.--..g-.__.__.,__.__.., .._._._g

                     -_                                  = = . =                                                    .                     -
                                                                                                                                                   --                                                                 .
                                                                                                                                                                                                                                                       .__                                                                                                                 ,=                                   -..
   '
                                                                         =
                                                                                            . . _ . _
                                                                                         ==m. . _ _ _ .m. =E _ m_ m ==
                                                    - h .W?- ~ -51_ E=3E:M ? ^";~;~~- - E l-~~$l
                                                                                                                                                ~

_ _ _ . _ _ . . _ . _ _ . . _ _ _ . . _ . _ . . _ .

                                                                                                                                                                                                                                                                 ~
                                                                                                                                                                                                                                                                         ..

c _ _ m =x..

                                                                                                                                                                                                                                                                                                      ~"^^~T~

__.._____%_....__._..

                                                                                                                                                                                                                                                                                                                                                                                                                                          =
s. _ E .,
                                                                                                                                                                                                                                                                                                      =
                                                                                                                                                                                                                                                                                                                                                              "l- .d $_ __ - 55
                                                                                                                                                                                                                                                                                                                                                                     -
                     *Q r                                    -s.     . =E--;i: E_ . ~. _~=2 W, ,-_ _ x-O= 9. m.
                                                                                           . _ _                                                  _ _ . .
                                                                                                                                                                                                         '_E_E_*..           .          _==__A, .---,._                                                                        7 n._w.__,__.      L t ^ -~.a" ^_. ' ' - . _ _ .
s. w m.m. _m. _. + __ _
                                                                                                                                                                                 .

_-

                                                                                                                                                                                                                   -               -
                                                                                                                                                                                                                                                                                                                 .
                                                                                                                                                                                                                                                                                                                      - -
                                                                                                                                                                                                                                                                                                                                                                                 -___._=.

_

                                                                                                                                                                                                                                                                                                                                                                                                                        .
                                                                                                                                                                                                                                                                                                                                                                                                                                 , = =
                                                                                                                                                                                                                                                                                                                                                                                                                                                  -
                     = :wmm=mm==n =~--        . . . _ -
                                                                                                                                                                                                                                                                                                                                                                                                   =_ =a_=.                  --

_ 1950 iM

O

        ,   e #
  • s
          -

Figure A-4

          .

e

"-- 1*- _. '!-- .7*J
                                                                                                                                                                             *        - - - ' ' ' " - * -
                                                                                                                                                                                                                                           ~. * ;.I._                   -

_ . _ _ . . _ _ . .

                                                                                                                                                                                                                                          = ~y=- ~~ i = =:== : E =.=^ _~~- ~.% _: . -
                                                                                                                                                                                                                    ^

C ^ ^R= . .

                                                                                  ;-                  _

_. _ ~&~ _2-~ q = -. -_ ._ _

                                                                                                                                                                                                                      .T_^.'=                                                                                                                                                                            9

_ . .

                                                                                                ._                          _ . .                                                                                                                                                                                                                                                                       N
                                                                                       -               . , _ . .*                                 -e._                _=

_ . _ . . _ -_ e__.g._wo.-a - - - .*.-=.e_'e.-_a- - =

                     .__ . L -_-.u                                              n h =. ' f =__ i-j =3.=.a.=_:- - _ ; i _ - .. ._ .                                                                                                                .i_:___ :}

_. _ :.g[ ._.____ _

                                                                                                                                                                                                                                                                                                                                                                                                                                                   *
                     = = - - -                                     =
                        - ' : ' . . ' T r - -** --'_' -~~- .L '. : -- _:n--*
                                                                              = - - _. _. . . = - _ . _" *.~~-                                                            _ -. 4_2 ' =.:-u--=====_:
                                                                                                                                                                                          ;'._ : ~ L                           -

yp' -._;. :---- *: =. * - -_ _ = _ __.=__:_.'_

                                                                                                                                                                                                                   -
  • _ : - -~2 :: ---_- 7 _

Eb .3. 5; *- --* --- ~~~_Y. 5-~ ._ ['_._~ i-_ _[  ; __, b -- k g

                     . - - _ _ . .                                    . - _ _                                                      -                                .___
                                                                                                                                                                                                              - _.____ -                                                        - . .                              . _ _ - . - - .                                                                        .                                   .
  <

_ _ . _ _ _ _ _ ___.)- _ _ _ _ _ . ._ . . - - ^ '~

                     *----~----*--:'_.______._.._.
                                                      ._- . _ _.-.._ _ . ___ _ .__ ._ _ . ._

_ . _ . . . _ _ -----._ _ _. _ _ . . _ . _ _ _ . _ _______.%

                                                                                                                                                                                                                                                       .___._-M-
                                                                                                                                                                                                                                                                                 ..__-..___  .
                                                                                                                                                                                                                                                                                                                       .___.__.:____.._.'

___.____ _ __ _ _ -- ; - "

                                                                                                                                                                                                                                                                                                                                                                            -

_---": '_ _ _ _ - H . 5$

                                                                                                                                                                                                                                                                                                                         ~ ^

Gi^E::= - i =55:E EE E '==33 5 " ^f E~ = i= '-~--#=b-~E *i: ^=~-$ f ~~~ =D 2 - f F - - - F '- 3 -~~r r  : ' ___ - ,,= . _ _ _ _ . _ . .-=-)_,_._-.___.._ =-Q T . ;._ . _ _ , . _-- l f_- : p :" '==E g_ _ . _ ___

                                                                                                                                                                                                                                                                                                                                      -._=_____                                                  y_ _ _g

_- . - _ _ . _ _ _ ..__.L_____._-__.- _ . . - __ _ _ . _

                                           ..                         . _                                                                                                      .-                             . . _ . ..                                                           _ _ - - . _ . _ _ . . _ _ . - _ _ .                                                                                                                        -
                    .i..i..._.g,,

l-._'..---*---_----.= ..- . }

                                                                                                                                                                                ,m--                     ,         ~[,,.
                                                                                                                                                                                                      ~*----____.:,..*_--Q--

g_

                                                                                                                                                                                                                                                                                                                   --__.-__.__:'

_ . _ _ _ . _^ . . I

                                                                                                                                                                                                                                                                               ,,--------"-----------]--._:.._.                                                                                       -. . % -5
                                                                                                                                                                           -                                             --
                               --      . __. - - - _ _ . _
                                                                            . _ . _
                                                                            ,

y..---__w... _ _ _ ..L-

                                                                                                                                                                                                                                 . . _ .- ~ n: _;._ g             -_.                                                                           . _ _ - .
                                                                                                                                                                                                                                                                                                                                                                                                     ._,
                                                                                                                                                                                                                                                                                                                                                                                                                                          -
                                                                                                                                                                                       - - = :. ; -==.---;..---~_---'
                                                                                                                                                                                                                                                                                                                                                                                          -

[ :=';;r =="- Ef - .T_f]E i=:==f :=. ---

                                                                                                                                                                                                                                                                                                            -- 1*_ , __ g___;.

_ _ f = % ==i o -- . _ _ - _

                                                              - ._                                                                                        . . _ . _ _ _ . . , - - . _ _ _ _ _ - . . _ . . _ _ . _ _ . .
                                                                                                                                                                                                                                                                                 =rr --~ z____ _ . _ _ _ _ _ _ _ _ - . _ - -

p- u t-- ._.y__ _ _ _ . . _ _ ..=1 r=2 -rd. :: -. n --- --~. r::=r-- r . _r

                                                         -                                                                                                                                                                                                                                                                                                                                                                             --
    -

It) m p._. __-._..--%.__.._

                                           .

_ ___ ._, _ _ . _ . - . . . . . . _ . _ _ . . _ _ . _ . . . - . _ . . _ _ . . _ _ . _ . _ _ .

                                                                                                                                                                                                                                                                                                                                                                                                                           .. D ---2
    @                                                                                                                                                                      --                                          -
                                                                                                                                                                                                                                       --~_.-                              - - - -                            -                *---

w t-~.___ _ = n' ..,.= _ _ . _ _ _ ._.

                                                                                                                                                           -___                         _                            - - - _ .                                                                                                   -                           --                                          ._

g _ . =__.__--_law = . __ _ _ _- _=__= _=._==_w__.__=_.- --_-=_g_ _ . _ _ n_ g z_.

                    . _ . . _

_ _ - . . _ - .

                                                                    ..

_ _____ _ _ _

                                                                                                                                                                                                                                                                                                                                                                                                   ~_ _y__._
                    ~--'_.__T---:-                                                                    _                                                                         _
                                                                                                                                                                                                                                         - - - - '

_ _ _ . _..M.'.--* tr_. _ MF_j ! i _ _ . _ - . _ - . _ _ . _ _ _ .

                                                                                         .

__ y.s., _v v_ .m _ _ _ _ . . . _ _ _ _ _ _ _ _ . _ _ _ . _ . _ _ _ ___ _ ___ _ _ _ _ _ _ _ _ _ h

                                                                                                                                                                                                                                                                                                                                                                                                = _ _ _ _ ___ - .

p_ E_=. _== ==%_ = %= ,.W____. __ ___- ___- _9 = ~R u m._ .;_._1+

                    -

______._ w p__ __ .- . . =u yn

                                                                                                                                                                                      =_:=.=:---------____:-
                                                                                                                                                                                                                                                                                                                                      .-
                                                                                                                                                                                                                                                                                                                                                                . _ _ __                          rn
                                                                                                                                                                                                                                                                                                                                                                                                  - ._ .

3.,s 4 E 2~-f # E'- . __ ._.J - N _._.__.__.

                                                                                                                                                                                                    .
                                                                                                                                                                                                                                                      .__
                                                                                                                                                                                                                                                             , _ _ _ _                            _
                                                                                                                                                                                                                                                                                                      ,.__.___._r_                  .

___,.-

                                                                                                                                                                                                                                                                                                                                                                                                  ~~=-
                                                                                                                                                                                                                                                                                                                                                                                                                .4 F -
                   . .=m.         = a._. =_..f3

____-.a

                                                     =

T :_-- _ . . . _._q.=----- 3 _._ - y__ - a a -r=._=_

                                                                                                                                          - - _. -M4..____.___._.__..
--------------------
                                                                                                                                                                                                                                                                                         .                                                  _ . _
                                                                                                                                                                                                                                                                                                                                                                                     -
                                                                                                                                                                                                                                                                                                                                                                                                 -

b :- -=Eh-5 N

                                                                                                                                                                        --]                                                                                                                                                                                                                      f 3,_                             p-
                                                                                                                                                                                                                                                                                                                                                      - - - - -
                       .
                                                         .q -                                                                                                                       .
                                                                                                                                                                                                            .

_ j E==_ y g=Ei $_ _ _._ ._- =:- - - 1 M_._ _=-

                                                                                       -

_

                                                                                                                                                                                                                                                                                                                                                                  -
                                                                                                                                                                                                                                                                                                                                                                                                 - . W E --

b_.__- __ n ,

   "                                                   $                          bt(               ~_":.c          -'*+ * - * -

L .- _ _ _ _ N.g_-_. ._. _.

  ',                          1_~~-.~-   . - _

r2.._ _ _ . _ . _ . - - - - , _ _. . _ . . _ _ _ _ . _ _ _=. _ _ __i. _$.

                                                                                                                                                                                              . . .

_ _y;s _ __ _% _ _ __..- _ -_ _ _ _ _ _ .. _ .. _ _ _ _ _ . _ . s . 4:. V

                                                                                                                                                                                                                                                                                                                                                  - - - _ _ u. _ )
  ,
  ;               ;        mr ; r ;2 r_

_ . __ . :"\ r n.

                                                                                                                               - - - - -

an-i n gxu& ---- -

                                                                                                                                                                                                                                                                                                                                                                                                 .r;g
  -;              r                                                                                                                                                                    _ =br\7 4rVN ._ . .                                                                                                            _ _ . _                                                              .
                                                       .x g . ::p.x ; =---= m                                                      eu r -- :-
                                                                                                                                                                                                                                                                                                                                                                                                                                           ,

p l -- ; = u--- -__ ru_. g

  ..              .
                                                                                                                         == - . =a =- _ -nu                                                    t =k.h3h: ._%. n- - - - -===.:=-_=._=_..:===:===-

_ e

                  , . *                                             ..?                                     ^
                                                                                                                                     -~ : ^                              _              _q             -
                                                                                                                                                                                                                                 $                           55                              ?--                    -                   -
                                                                                                                                                                                                                                                                                                                                                             ' ' - = -

3 P =-

= h==d=_= 7=g= - s= ==,= -c=~ , t1

_ _ _ _-.--\- .w= _W _ .T _ . . . n, = . .\ _ _ _=1 mE

                                                                                                                                                                                                                                                             ~= N
      ;                            .      . . .                     .__w__._._.____._._                                                                                                                            _ _ _ _ -                  3                                                                                                                                                               __.          .v          . _ ,

_ _ _ . . _ . _ _ . _ _ _~ ~ ' - - ~ ~ f E D ! W _ _ .__ _ _ _ . ._ ._ . _ --1 -! : - =\M ____.___n . _ _ . . . _ . . - + =

                 .__=_ ==-- Q 4 _ - -
                                                                                                                                                - - - - - - -
                                                                                                                                                                                      ;=g_- y _;Q, _\-_,__ y.y                                                                                                                              - -- - .:=                                           __-,%__.

A [---

                                                                                                                                                                                                                                 .                                                                                                                                                                                                 _

_,

                 ,                                                                                                                                                                                 3_______g.__.___                                                                                                                                      __ ____.                                 _ _ . , , _
  ;-.            c_Q _
                                                                                                --
                                                                                                                                                           --*---t=1,_.                                                                       y-                        .
                                                                                                                                                                                                                                                                                                    .
                                                                                                                                                                                                                                                                                                          -
                                                                                                                                                                                                                                                                                                                                                                      -=                         g _ y3: . __
                ?~'                                                  ?.% _G*ii-E2 ~-{ . .~ * ~~52-fi- ; -W-:'                                                                                                                                                          1=k=                                       .? ri-~=i-5_?                                                                     n ' ?

n- umra;;M =Q=eMMur -

  .

g v% r1=nc_.  % = =: *-= = r- - ====

                                                                                             , _ _ _ .                             g_.                                       =W E-1= ==g                                                      .p.N=E==tss N-:A ___.=- g =                                                                                                                          -
                                                                                                                                                                                                                                                                                                                                                                                                                           =-.

6

                                         . =. = z =!=n".                                                                        J=Z = _: '. - .=-                                     " Q-{hWi=Eih=i$.=$=== =h=-                                                                                                                                                                          - - - ---

5s: =f E9ih=E=f= -i=5-F=5M C- -l=$==ER=Mi=3E== - o e .si m  : - < c=e== =i ==w s m m m EM =hMA=1m ~ =.

                                                  =E =E= xy _;:=.:Ep. __r; 77 ._- 1;_.,__;- r=_
                .               _.                   .._m_..                                         ._____ __                                                                         __..

1 ___m. _g. g __ . -Y _ ;L, .g= A_-g== z. r c => _y . _ ._

                                                                                                                                                                                                                                                                                                      .._._g- --Q____3_.__

___ _

                                                                                                                                                                                                                                                                                                                                                                                                                                       ._
                ~---r----=-n__.___.---_=.._=-r___                  . - . _ . . _ _ _ . - - - - - . _ .                                                                                                                                                       ..__.n-.__.._=__.                                                                          _-                    _ . _

_ _ .. .-- __

                                            - ' ~
                                                                   ~-~'^^-j___._*i**-^._:'.f.j.~_7.-E---
                                                                            ' ..                                                                                  ..____..__.___-____-....._____k-*--"**^-~~~*
                                                                                                                                                                                                 .                                                    L_                                                                                           _
                                                                                                                                                                                                                                                                                                                                                                               --                - - - ~ ~                                      *
  '

_ _ . ,.3 - --f ~i_ IE~_E'j EEiO _E C  ;~=-#rr'r-~ E~21.E-U_E-- -- ' ._[-% d-T" ~-- ~~ -

                                                                                                                                                                                                                                                                                                                                                                                  ~~                           --
                                                                                                                                                                                                                                                                                                                                                                                                                            ~d 7-7_~m = nV__--oo                         u                              r-=_ : _P m_ .n ==_-N
                                                                                                         --                  . .                    -

_- r__-- ._ G. E=4 r_ x_W. _M=_ , . E__-. =. _k=__ ._="i. _= - (".___ _

                                                                                                                                                                                                                                                                        .
                                                                                                                                                                                                                                                                                                                                =_r'*- E_     .               . . =d.=._-E=?                                         tv Z_        E_--      _ -

_.-._--_._.___.

                                 ,                           ,

ryu__ ._a ,._.__.a. g___..___. __

                             --- ==                                                 ..                                 ._ ..__._                                      -_ - . _ ,-- _..._ e ---- .                                                                         _ . _ _ _ . _ _ _ . _ __.                                                                                          = = _ _ =
                                                  -                   .-_.x__._.-                              .

b

                                                                                                                                                                    .. f.h _. -                        . - - - . _ . - - . . _ _ . .   .

__ __. .W:_ _ _~._ _.. . $_.5_ Y. .' ~. 5_'- 5?. -

                                                                                                                                                                                                                                                                                                                                                                                                                         .

1950 104}}