ML20154Q665
| ML20154Q665 | |
| Person / Time | |
|---|---|
| Site: | Comanche Peak  |
| Issue date: | 10/16/1998 |
| From: | Hastings C AFFILIATION NOT ASSIGNED |
| To: | Polich T NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM) |
| Shared Package | |
| ML20138L381 | List: |
| References | |
| CAW-98-02, CAW-98-2, NUDOCS 9810260045 | |
| Download: ML20154Q665 (67) | |
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Caldon,Inc.
1070 Banksville Avenue Piusburgh, PA 15216 412-341-9920 Tel October 16,1998 412 341-9951 Fax www.caldon. net Document Control Desk U.S. Nuclear Regulatory Commission Washington, DC 20555 Attention: Mr. Tim Polich APPLICATION FOR WITiiHOLDING PROPRIETARY INFORMATION FROM PUBLIC DISCLOSURE
Subject:
Responses to NRC Staff Questions Concerning Topical Report,
" Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the LEFM/ System",
Caldon, Inc. Engineering Power ER-80P (Proprietary), March 1997.
Dear Mr. Polich:
The proprietary information for which withholding is being requested in the above-referenced response is further identified in Affidavit CAW-98-02 signed by the owner of the proprietary information, Caldon, Inc. The affidavit, which accompanies this letter, sets fbrth the basis on which the information may be withheld from public disclosure by the Commission and addresses with specificity the considerations listed in paragraph (b)(4) of 10 CFR Section 2.790 of the Commission's regulations.
Accordingly, this letter authorizes the utilization of the accompanying Affidavit by TU Electric.
Correspondence with respect to the proprietary aspects of the application for withholding or the Caldon affidavit should reference this letter, CAW-98-02, and should be addressed to the i
undersigned.
Very truly yours,
}i Calvin R. Hastings President and CEO CRH/ta i
Enclosures 9810260045 981020 ~~"
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October 16,1998 CAW-98-02 1
AFFIDAVIT COMMONWEALTil OF PENNSYLVANIA:
ss COUNTY OF ALLEGHENY:
Before me, the undersigned authority, personally appeared Calvin R. IIastings, who, being by me duly sworn according to law, deposes and says that he is authorized to execute this Affidavit on behalf of Caldon, Inc. ("Caldon") and that the averments of fact set forth in this
' Affidavit are true and correct to the best of his knowledge, information, and belief:
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Calvin R. Hastings, President and CEO Caldon, Inc.
Sworn to and subscribed before me this /64 day of i '
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,1998 f4b hb AdkAh i
Notarial Seal Anhonette L Herbst. Notary Public
- Pritsburgri, Allegheny County
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.-My Commission Experes Mar. 11,2002 Member,Pennsytvense Assocetion of Notarfes
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l.
I am the President and CEO of Caldon, Inc. and as such, I have been specifically delegated the function of reviewing the proprietary information sought to be withheld from public disclosure in connection with nuclear power plant licensing and rulemaking proceedings, and am authorized to apply for its withholding on behalf of Caldon.
2.
I am making this Affidavit in conformance with the provisions of 10 CFR Section 2.790 of the Commission's regulations and in conjunction with the Caldon application for-withholding accompanying this Affidavit.
3.
I have personal knowledge of the criteria and procedures utilized by Caldon in designated information as a trade secret, privileged or as confidential commercial or financial information.
4.
- Pursuant to the provisions of paragraph (b) (4) of Section 2.790 of the Commission's regulations, the following is furnished for consideration by the Commission in determining whether the information sought to be withheld from public disclosure should be withheld.
(i)
The information sought to be withheld from public disclosure is owned and has been held in confidence by Caldon.
(ii)
The information is of a type customarily held in confidence by Caldon and not customarily disclosed to the public. Caldon has a rational basis for determining
- the types ofinformation customarily held in confidence by it and, in that connection, utilizes a system to determine when and whether to hold certain types ofinformation in confidence. The application of that system and the substance of that system constitutes Caldon policy and provides the rational basis required.
Under that system, information is held in confidence if it falls in one or more of several l
types, the release of which might result in the loss of an existing or potential advantage, 2
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as follows:
(a)
The information reveals the distinguishing aspects of a process (or component, structure, tool, method, etc.) where prevention ofits use by any of Caldon's competitors without license from Caldon constitutes a i
competitive economic advantage over other companies.
i l
(b)
It consists of supporting data, including test data, relative to a process (or component, structure, tool, method, etc.), the application of which data secures a competitive economic advantage, e.g., by optimization or improved marketability, (c)
Its use by a competitor would reduce his expenditure of resources or improve his competitive position in the design, manufacture, shipment, installation, assurance of quality, or licensing a similar product.
(d)
It reveals cost or price information, production capacities, budget levels, or
)
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commercial strategies of Caldon, its customer or suppliers.
(e)
It reveals aspects of past, present or future Caldon or customer funded development plans and programs of potential customer value to Caldon.
l (f)
It contains patentable ideas, for which patent protection may be desirable.
There are sound policy reasons behind the Caldon system which include the following:
(a)
The use of such information by Caldon gives Caldon a competitive advantage over its competitors. It is, therefore, withheld from disclosure to protect the Caldon competitive position.
(b)
It is information which is marketable in many ways. The extent to which such information is available to competitors diminishes the Caldon ability to sell products or services involving the use of the information.
(c)
Use by our competitor would put Caldon at a competitive disadvantage by reducing his expenditure of resources at our expense.
l (d)
Each component of proprietary information pertinent to a particular competitive advantage is potentially as valuable as the total competitive l
l 3
advantage. If competitors acquire components of proprietary infomiation, any one component may be the key to the entire puzzle, thereby depriving Caldon of a ce~;rtitive advantage.
(e)
Unrestrict ed disclosuie would jeopardize the position of prominence of Caldon in the world market, and thereby give a market advantage to the competition of those countries.
(f)
The Caldon capacity to invest corporate assets in research and development depends upon the success in obtaining and maintaining a competitive advantage.
(iii) The information is being transmitted to the Commission in confidence, and, under the provisions of 10 CFR Section 2.790, it is to be received in confidence by the Commission.
I l
(iv) The information sought to be protected is not available in public sources or available i
infomiation has not been previously employed in the same manner or method to the best of our knowledge and belief.
)
(v) The proprietary information sought to be withheld in this submittal is that which is appropriately marked in the " Responses to NRC Staff Questions Concerning Topical Report, ' improving Thermal Power Accuracy and Plant S6ty While Increasing Operating Power Level Using the LEFM/ System', as Applied to Comanche Peak, September 29,1998, Proprietary Version" and is being transmitted by TU Electric letter and Application for Withholding Proprietary Information from Public Disclosure, to the Document Control Desk, Attention, Mr. Tim Polich. This proprietary information was initially distributed during the proprietary portion of the September 29,1998, meeting between the NRC, TU Electric and Caldon. This information is submitted for use by TU Electric for the Comanche Peak Nuclear Plants and is expected to be applicable in other license submittals forjustification of the use of the Caldon Leading Edge Flow Meter (LEFM/) to increase reactor plants' thermal power. (A separate document
" Responses to NRC Staff Questions Concerning Topical Report, ' Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the 4
LEFM/ System', as Applied to Comanche Peak, September 29,1998, Non-Proprietary Version" is also being submitted which extracts the non-proprietary elements of the proprietary responses, and which non-proprietary document may be made publicly available. Note that the non proprietary document contains the responses to questions 1,2,3,5,6,9,12,14 (relevant portions), and 29.)
This information is part of that which will enable Caldon to:
(a)
Demonstrate the design of the LEFM/ and accuracy of the LEFM/ flow and temperature measurements, as well as the improved calorimetric thermal power accuracy based on the LEFM/ measurements.
(b)
Demonstrate the reliability of the LEFM/ based on design features and on compiled field experience data.
(c)
Establish technical and licensing approaches for the application of the improved accuracy of this method toward increasing thermal power.
(d)
Assist customers in obtaining NRC approval for increases in thermal power based on appropriate use of the LEFM/ for calorimetric power measurement.
Further this information has substantial commercial value as follows:
(a)
Caldon plans to sell the LEFM/ and use of similar information to its customers for purposes of meeting NRC requirements for operation at increased thermal power.
(b)
Caldon can sell support and defense of the technology to its customers in the licensing process.
Public disclosure of this proprietary information is likely to cause substantial harm to the competitive position of Caldon because it would enhance the ability of competitors to provide similar flow and temperature measurement systems and licensing defense services for 5
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l commercial power reactors without commensurate expenses. Also, public disclosure of the information would enable others to use the information to meet NRC requirements for licensing documentation without the right to use the information.
The development of the technology described in part by the information is the result of applying the results of many years of experience in an intensive Caldon effort and the expenditure of a considerable sum of money.
In order for competitors of Caldon to duplicate this information, similar products would have to be developed, similar technical programs would have to be performed, and a significant manpower effort, having the requisite talent and experience, would have to be expended for developing analytical methods and receiving NRC approval for those methods.
Further the deponent sayeth not.
I l
6
Responses to NRC Staff Questions Concerning TOPICAL REPORT: Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the LEFMv' System as Applied to Comanche Peak September 29,1998 NON-PROPRIETARY VERSION
t Responses to NRC Questions: September 29,1998 Non-Proprietary to Caldon, Inc.
NRC Staff Questions
- 1. Describe Caldon's understanding of the background for 1.02 being ascribedjust for instrument uncertainty in power determination
- 2. On page 5-2 of the Topical Report, explain the justification for the use of PTC-6.
l
- 3. Describe how the LEFM/ is used in calorimetric power determinations.
- 5. Who is responsible and how are Calibration, Maintenance, and Training performed and achieved?
- 6. How will monitoring, verification, and error reporting be handled?
- 9. Clarify that the 0.5% used in the Topical Report is 95% confidence level (2a).
- 12. Does cross flow = transverse velocity?
- 14. Provide the references sited in the temperature correlation uncertainty and an explanation of the field data provided in this analysis. [Non proprietary references provided here.)
- 29. How is the LEFM/ used currently to provide correction factors to the venturis? Is the correction determined on the basis of the absolute accuracy or the repeatability of the LEFM/?
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Responses to NRC Questions: September 29.1998 Question 1:
Describe Caldon's understanding of the background for 1.02 being ascribed just for instrument uncertainty in power determination.
Answer:
l
' Caldon proposes to increase current licensed power by 1% for plants using Appendix K evaluation models without any requirement to reanalyze ECCS performance if the plants utilize a new technology for determining thermal power. The new technology provides on-line verification ofinstrument accuracy and is capable of accuracies sufficient to ensure that there is a higher level of certainty that 1.02% of the current licensed power will not be i
exceeded than is currently being provided, and, hence, a higher level of certainty that the criteria of 10 CFR 50.46 (b) will not be exceeded.
As set forth in the Opinion of the Commission in the ECCS rulemaking proceeding, RM-3 50-1, December 28,1973,Section I.A. of Part 50, Appendix K, specifies the following for the initial conditions to be used in Appendix K evaluation models:
For the heat ' sources...it shall be assumed that the reactor has been operating continuously at a power level at least 1.02 times the licensed power level (to allow for such uncertainties as instrumentation error), with the maximum peaking factor allowed by the technical specifications. A range of power distribution shapes and peaking factors representing power distributions that may occur over the core lifetime shall be studied and the one selected should be that which results in the most severe calculated consequences for the spectrum of postulated breaks and single failures analyzed.
The question has been raised as to what the phrase "such uncertainties as" implies and whether operating at a power level 1% higher than the current licensed power could have any effect on the continued validity of the current Appendix K analyses of ECCS performance. A review of the regulatory history, including the interim acceptance criteria, the record of the ECCS rulemaking proceeding, implementation of Appendix K, and operating experience, has turned up nothing that would suggest that anything other than the need to account for the uncertainty of determining the thermal power at which the reactor is operating led to the adoption of 1.02 times the maximum licensed power for an initial condition for Appendix K ECCS evaluations.
The NRC staff, in its concluding statement, had recommended essentially the same initial conditions as were adopted by the Commission. However, the staff had recommended "that the reactor shall be assumed to have been operating continuously at a power level no lower than 1.02 times maximum licensed power level (to allow for instrument error)..."
Concluding Statement of Position of the Regulatory Staff, RM-50-1, at 40,109.
Regulatory Guide 1.49, Rev.1, issued in December 1973, concurrent with the issue of the Commission's opinion in RM-50-1, recommended the use of an assumed power level 1.02 1
i Responses to NRC Questions: September 29.1998 l
{
times the proposed licensed power for analyses and evaluations of all normal, transient and accident conditions necessary to evaluate the adequacy of the facility. The staff explained the purpose of using 1.02 times the proposed licensed power as follows:
... analyses in support of the proposed licensed power are made for a slightly higher power to allow for possible instrument errors in determining the power level. The regulatory staff has concluded that a margin of 2% is adequate for this purpose.
I Nowhere in the Commission's opinion is any reason given for the addition of the words "such uncertainties as."
The record shows that the initial conditions of Appendix K had their inception in the ECCS evaluation models approved with the issuance of the interim acceptance criteria. 36 l
i Fed. Reg.12247, June 1971. See for example WCAP-7422L, Westinghouse PWR Core Behavior Following a Loss-of-Coolant Accident. Id at Appendix A, Part 3. Here.1.02 times the licensed power was used to account for uncertainties in determining the operating power level and the worst possible power distributions and maximum peaking factors were determined. The maximum peaking factors for which ECCS performance were found to be acceptable were placed in technical specifications for the plants.
The manner in which the initial conditions have been applied since the promulgation of Appendix K is also instructive. Initially, when Appendix K was issued, reactors then O
operating under the interim acceptance criteria were required to perform ECCS evaluations using approved Appendix K evaluation models. Since the worst possible power distributions and maximum peaking factors allowed by the then current technical speci0 cations were used, unless, of course, the Appendix K evaluations supported different values. (As specified in 10 CFR 50.36, the technical specifications must be derived from the analyses and evaluations a the safety analyses reports and amendments thereto. Hence, the maximum peaking factors allowed by plant technical specifications must be consistent with the maximum peaking factors used in the ECCS evaluations which demonstrate that the ECCS performance satisnes the criteria of 10 CFR 50.46(b).
In general, in applying initial conditions for the interim acceptance criteria and those required by Appendix K.Section I.A., the following were incorporated in approved ECCS evaluation models:
1.
Reactor power assumed to have been continuously at 1.02 times the licensed power (or proposed licensed power in case of amendments) to account for uncertainties in determining thermal power.
2.
A cosine curve representing the power distribution shape resulting in the worst consequences (normally the highest calculated peak clad temperatures).
The cosine curve is worse than any other power shape occurring at any time
' p in core life. This shape can only occur during a return to power and for a G
2
Responses to NRC Questions: September 29.1998 l
(N short time thereafter and is not possible in continuous power operation.
b Hence it is an extremely conservative assumption; and 3.
The maximum peaking factor in the technical specifications (or proposed to be placed in the technical specifications);
These three assumptions have then been used in the Appendix K evaluation models as inputs to calculate the initial stored energy in the fuel, fission heat. and decay heat from actinides and fission products. None of these input assumptions are affected by increasing the operating power provided that the operating power does not exceed the 1.02 times maximum licensed power assumed in the evaluation of the ECCS performance showing that the criteria of 10 CFR 50.46(b) will not be exceeded. This is consistent with the objective stated in the opinion of the Commission in RM-50-46 dealing with conservatism:
(1)
Stored Heat. The assumption of 102% of maximum power, highest allowed peaking factor. and the highest estimated thermal resistance between the UO: and the cladding (calculated using the above input assumptions) provides a calculated stored heat that is possible but unlikely to occur at the time of the hypothetical accident... Opinion of the Commission, RM-50-1, December 28,1973 at 27, A-4.
Thus, it appears that the approval of the Caldon proposal resides solely in demonstrating y
F that there is a sufficiently high probability that the power level assumed for evaluation of V
ECCS performance in existing Appendix K evaluations will not be exceeded in operation at a 1% increase in licensed power level with the proposed improved technology for determining plant operating power.
A review of the Standard Review Plan (SRP) was also conducted to identify references to application of the 2% margin to initial conditions for accidents. The results, summarized in Attachment 1, indicate that the 2% margin for initial conditions is required for analysis of 12 accidents in SRP Chapter 15. Of these 12 accidents, the license is permitted to use less than 2% margin in 9 cases provided the lower margin can be justified by the applicant.
Attachments:
- 1. Summary Table of Review of Chapter 15 of Standard Review Plan.
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Responses to NRC Questions: September 29.1998 Attachment I to Question I l
Section of Chapter 15 Reference to 102% initial Permission to use power level condition below 102% if justified 15.1 1 throut;h 4: Decrease in Yes Yes Feed temp etc.
15.1.5 Steam sys piping failures No in and out of containment 15.1.5 A Rad Consequences No 15.2.15 Loss of Load etc Yes No 15.2.6 Loss of Emergency AC to Yes Yes Station Auxiliaries 15.2.7 Loss of Normal Feed Flow Yes Yes 15.2.8 Feed System Pipe Breaks No
-PWR 15.3.1-2 Loss of forced reactor Yes Yes coolant Flow 15.3.3-4 Reactor coolant pump Yes Yes motor seizure 15.4.1 Uncontrolled Control rod No withdrawal-suberitical/ low power
- g.,
15.4.2 Uncontrolled Withdrawal No
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at Power 15.4.3 Control Rod Malfunction Yes Yes 15.4.4-5 Startup ofinactive loop Yes No and flow controller malfunction -
BWR 15.4.6 CVCS reduces boron Yes No concentration PWR 15.4.7 Inadvenent Loading of No fuel assembly 15.4.8 Spectrum of rod ejection No accidents - PWR 15.4.8 A Rad Consequences of No Ejection 15.4.9 Spectrum of rod drop No accidents-BWR 15.4.9 A Rad consequences No 15.5.1-2 Inadvertent Operation of Yes Yes ECCS that increases inventory 15.6.1 Inadvertent opening of Yes Yes PWR or BWR pressure relief valve 15.6.2 Rad consequences of the No failure of small lines carrying l
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Responses to NRC Questions: September 29,1998 Attachment I to Question 1 iO Section of Chapter 15 Reference to 102% initial Permission to use power level condition below 102% if justified primary coolant outside containment 15.6.3 Rad consequences of No steam generator tube rupture -
PWR 15.6.4 Rad Consequences of No Main Steam Line Failure Outside containment - BWR 15.6.5 LOCA resulting from Yes Yes spectrum ofpipe breaks within
- RC pressure boundary 15.6.5 Apps A, B, C, D: Various No rad consequences of LOCA 15.7.3 Rad releases due to liquid No containing tank failures 15,7.4 Rad consequences of fuel No es.
handling accidents
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15.7.5 Spent fuel cask drop No accidents
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Responses to NRC Questions: September 29,1998 Question 2:
O On page 5-2 of the Topical Report, explain thejustification for the use of PTC-6.
l Answer:
The context of the reference to PTC-6 is repeated here from page 5-2:
l "Immediately after it is calibrated, a flow nozzle is capable of providing measurement accuracies in the 10.5% range, providing the differential pressure and fluid temperature measurements are made with laboratory grade, calibrated instruments (see for example the discussion of turbine heat rate testing in ASME-PTC-6, Reference 9)."
PTC-6 is referred to for purposes ofillustration only and does not apply to the use of the LEFM/ for thermal power measurement.
Attachments:
None.
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Responses to NRC Questions: September 29,1998 Question 3:
Describe how the LEFM/ is used in calorimetric power determinations.
Answer:
The proposed use of the LEFM/ is for direct measurement of feedwater mass now and temperature, and indirect measurement of feedwater enthalpy, for the thermal power determination. This determination would be used directly to calibrate the nuclear instruments in lieu of the existing instrumentation. At the discretion of the licensee, the LEFM/ may also be used for calorimetric calculation of reactor coolant flow, and for setting non-safety-related setpoints for which thermal power is an input. The increased accuracy as compared to the existing instrumentation would be beneficial in these applications.
At Comanche Peak, the LEFM is currently used for the secondary calorimetric calculation only. The secondary calorimetric is used as input for the daily calibration of NIS > id the cross-correlation N16 system.
In some plants, feed, water flow and/or temperature instruments are used as direct inputs to the reactor protection system or another automatic safety function. In these cases, those instruments are classified as safety-related, and would continue to be used for these functions. The LEFM/ is not being proposed for these functions. Its use would be O
limited to power determination and the non-safety-related uses of calorimetric power discussed above.
Attachments:
None.
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l Responses to NRC Questions: September 29.1998 Question 5:
Who is responsible and how are Calibration, Maintenance, and Training performed and ach,eved?
i l
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Answer:
Calibration and Maintenance Calibration and maintenance is performed by I&C using site procedures. The site procedures are developed using the CALDON technical manuals. All work is performed in accordance with site work control procedures.
Routine preventive maintenance procedures include physical inspections, power supply checks, back-up battery replacements, and internal oscillator frequency verification.
Ultrasonic signal verification and alignment procedures which involve digital oscilliscopes with the LEFM will be replaced by automatic set-up in the LEFM/. Signal verification will still be possible by review of signal quality measurements performed and displayed by the LEFM/.
Training G(d I&C personnel must be qualified per the I&C training program on the LEFM system before work or calibration may be performed. Formal training from Caldon was provided to site personnel. Formal training on the LEFM/ system will be provided by Caldon.
Attachments:
None.
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Responses to NRC Questions: September 29.1998 Question 6:
How will monitoring, verification, and error reponing be handled?
Answer:
Though this application is not safety-related, the LEFM/ system is designed and manufactured under Caldon's Quality Control Program, which provides for configuration control, deficiency reponing and correction, and maintenance. Specific examples of quality measures undertaken in the design, fabrication and testing of the LEFM/ system are provided in the Topical Report, Section 6.4 and Table 6.1. Table 6.1 lists the error bounding, validation and verification procedures planned for the LEFM/
system.
At Comanche Peak, the LEFM system is included in the System Health Plan and the preventative maintenance program. The system is monitored by the System Engineer for reliability. As a plant system, all equipment problems fall under the site work control process. All conditions that are adverse to quality are documented under the ONE/ SMART form program. The software falls under TU Electric's Appendix D QA
. program with a software QA plan in place. The current software was verified and validated and is under Caldon's Verification and Validation Program. Caldon's Verification and Validation Program provides procedures for deficiency reponing for
- engineering action and notification of holders of V&V software.
O The Comanche Peak LEFM/ System will likewise be under Caldon's V&V Program, and procedures will be maintained for user notification ofimportant deficiencies.
Attachments:
1 None.
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Responses to NRC Questions: September 29,1998 Question 9:
Clarify that the 0.5% used in the Topical Report is 95% confidence level (2a).
Answer:
The 0.5% mass flow uncertainty stated for the chordal LEFM and the LEFM/ is a 2 standard deviation (2a) uncertainty; that is, it represents a 95% confidence interval. This is intended to be a bounding approximation. This subject is discussed further in response to Question 13.
Attachments:
None.
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Responses to NRC Questions: September 29,1998 Question 12:
I Does cross flow = transverse velocity?
Answer:
I, Yes. For the purposes of this report, the terms are used interchangeably.
b-Attachments:
None.
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Responses to NRC Questions: September 29,1998 1
I Question 14:
Provide the references sited in the temperature correlation uncertainty and an expla of the field data provided in this analysis.
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j Speed of Sound in Water by a Direct Method' g[ji Martin Greenspan and Carroll E. Tschiegg m4 I' 3 The speed of sound in distilled water was mes.sured over the temperature range 0* to iii 100* C with an accuraev of 1 part in 30.000 The results are gwen as a orth-degree polt-nomial and in taetes. The water was contained in a cylindncal tant of SIed length. term'i.
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nated at each end by a plane transducer, and the end-to.end time of Sight of s pulse of sound e. l, was determined from a rcessurement of the pulse-repetJtion frequency required to set the
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f 1, Introduction I as the two pulses have different shapes, the accuraev $ I with which the coincidence could be set would b'e 1 M
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The speed of sound in water, c, is a physical very poor. Instead, the oscillator is run at about M i pmperty of fundamental interest; it, together with ' hall this frequency and the coincidence to be set is 7 ld
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the density, determines the adiabatie compressibility, l' that among the 6rst received pulses corresponding to z
and eventually the ratio of specific heats. The vari-a particular electrical pulse, the Srst echo correspond-N r o auon with temperature is anomslous; water is the ing to the electrical pulse next preceding, and so on.
W only pure liquid for which it is known that the speed Figure 1 illustrates the successive signals correspond-1 pK, of sound does not decrease monotonically With ing to three electrical input pulses. The input pulses temperature.
fsIl halfway between the pulses for which the coinei-i=
5 There is also a practical interest in e in that water dence is set, so that ther do not tend to overload E is used as a standard liquid for the calibration of the ampliSer or distort tlie oscilloscope traces. The '
instruments that measure the speed of sound in period of the oscillator, when properly set. multi- :-
liquids automatically, both in the laborntory and in plied by twice the length of tne tank, is the speed of i figure 4,}
the 6 eld. In fact,it was in connection with the cali-sound m the sample.
h 2 that our interest The oscilloscope trace actually looks like that u
bration of such "velocimeters" (1)In the first place,shown in the inset (Sg.1). The first cycle corre-E
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in this work was first aroused.
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maries (2, 3] clearly show. In m'any cases, the dis-of the transducers, whereas the succeeding cycles 6 i 3- '.
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crepancies far exceed the claimed accuracy or at correspond to sound redected one or more times from M r
least the precision of the methods, even when the an outer face. Therefore, the coincidence is set bv 4A s based k methods compared are the same. In the second maximizing tue peak on either the first or secon'd p 4i place, there exists no set of data that gives a smooth but the se;cond half cycle is easier to use because it -
J balf cycle the same result is obtained in either case variation with temperature over any considerable I
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is bigger. What we are measuring here is the s
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nondispersive liquid this is the same as the phase
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Ef ducers, quartz crystals in this case. If the left-hand J
]
blocking osc. is excited by a short, pulse from t.he crystal, say,Ilator, the oscilloscope, waien measures r,
y c.-
I i
- m. Soc. I the voltage on tne right-hand crystal, will show a n
acceived pulse and a series of echoes, as indicated H
l l
l l
~
'h Nas,.
in idealized form on the line below (fig.1). The g l I
pulse repetition frequency of the blocking oscillator 0
l l
l L
y
'h NBS is controlled by a sine-wave oscillator, and if this sh NB5 { frequency were adjusted so that each blocking oscil-l 4
lator pulse coincided with the first received pulse of
[
' J the next preceding cycle then the oscillator period 0
l l
l would equal the ttme of fli,ght of the pulse. However, I
Fiocaz 1.
SeAemanc el nWAod.
i Ty y ea. securied h set bv the once et Naved ham.,cb ander w,,,,,,,,,
,,g, u,,,
- ~~
v=
, r e.
a a,.
.~4.c e.
249 1
v i
I
time o ie-fourth or three-qu:rters of the tunsducer period later than tne time of Erst arrival, by wnich The elect time there is opportunity for sound traveling by art, conve:
pr,tns other th.n the shortest to afect the location h
oulse-formt: l of the maximum. Ilowever, the results are inde-n
~-
t itter., In i
,O pendent of wnether the Erst or second half evele is i
th nne (;
used; thev are also not afected by substituting ervstals o' twice the thickness, or bY changme the b(
within the
- f t must be diimeters of tne tuk, or of the hot electrodes. These Sange dur-s resulta lead us to believe that the error introduced by,
- ce count c this maximization technige is n ligible.
The bloc!
The question has been enmhic also in another hs;b and way. Suppose a coincidence to have been made at by a large, frequencyJ; others can then be mele at submultiples of f. At the frequoney f/2 for iratance, the first
{uon of a sq received pulse corres ading to a particular input Faucss 2.
Detsy Inne, duassembled.
wave gener pulse coincides with e second echo bot the first, An=
- m.k u. ca. Spea o uw name now.. 4.t in.,,4,,,,
y means o as before) correspondin to the electrical pulse next "7JG'J."T."A.'flgg" * "" "' "6'" *** " "'* *== me The reec th of 1 preceding, and so on.
frectively, the soteid pulse is timed over a path twice as long as before. It is ic,in this high-free found that ttte measurementa atf and nearf/2 are 5
6
' ast sweep substantially identical, so that the error in question scillator t is less than", or at most comparable to, the experi-elay time mental ermr of the time measurement.
2 33l'*
E
- 3. Apparatus
{
h I
ee r
3.1. The Delay I.ine The disassembled delay line is shown in the photo-h
$irrers' al 31 4
U L[.
A[
A,,, 't graph, figure 2.
The length of the tank is about
,,to a srn h
.the water -
J 200 mm, and the bore about 13 mm. The filling
\\ V L
S h
? power inpu holes are scaled by plugs having Teflon askets; a f
L L
istures arco i
small hole in one I g provides pressure re case.
iThe tempe The tank is of e uumium steel 2 which, after heat t
fwithin less treatment, takes a good optical 6nish. Because 3uired ic this steel is not so corrosion resistant as the nickel-s chromium stainless steels, the bore of the tank was j
T25 C, or 70.03* C; a 1
heavily gold lated.
cm sj Lj The ends e the tank are optically flat and parallel
-- ~
ithermal co-
[ther low,
~
to within less than 1 u.
To these ends are carefullt The terc wrung the 0.8-mm thick x-cut quartz erystals, which also are optically flat. The caps, when bolted on, twith a plat clamp the crystals through neoprene 0-rings. A riavn 3.
scAe-out,t ue <=d ef,A,4 ant,,A,
.,4Ac crp, /
eBrid *- A 6
coaxial cable passes through a sealin cach cap, and sad cop assembly.
Mionanthe the center conductor makes contact mth the outer,1 g g g a,, g ging,c g me mengg
$he platint (bot) clectrode of the crystal through a li ht spnng ma,
...,, m. 3. mtm. o.not;.
,w..
pressure ri 3
The outer electrode is a 9 mm etrele of ummum-gading ser l
backed ressure-sensitive adhesive tape. The inner was the tank and heat treated together with n.
n ater are i (gmund electrode is of fired-on gold and is about From these data, the length of the souud' pnth i-1reme l
12 mm in diameter. Contact is made through a known to better than 2 parts in 102 at any tempera-0.01' Ltures).
'I light gold-plated helical spring which touches the ture between 04 and 100* C.
It is, of cour n electrode around the edge and bears on a shoulder necessarv that the crystals be wrung down wdh hination w machmed into the bore. The inner electrodes and great ca're so that the fringes disappear all amund ces a springs are unnecessarv if the sample has high cou-the pe ' hery, to achieve this accuracy. The clarut-g er,so t -
ductivity or a high liielectric constant; ther are in g ets must bear directiv over the contartu dings e<
- usually omitted for water and aqueous solutions of su ace and not spread out over the unsuppor
- M salts. Figure 3 is a schematic drawing of one end area, else the crystal will bend. With these prr of the assembi.
cautions, the defav line ma be disassembled and
.The me The length i the tank was measured at 20* C.
reassembled repen'tedi wit reproducible reaulv i
If the cr en propert wrung on and
-dinarv$
and the coefficient of thermal expansion of the steel clamped,ystals have they cannot be remove by hand afM was measurvd on a sample cut from the same bar as several days,'but must be soaked off.
.ki,'*J,",,,*.'
. nrm.e===sini p u.
1e h.=*--
- ne==.
b
/
y.
9 b
q O
- I 3.2. The Electronies nnd poured, while stdl hot, mto the preheated tank.
I Although dissolved air has a neghgible etfect on the V
.i.ne electronic circuits (fig.1) are. for the most speed of sound in water [4), it is desirable to exclude g -
pa :, conventional.. However, the osed. iator and the atr and so prevent possible bubble formation on the i
- nd e-formmg circuits must be excepuonally free of transducen.
p tt er. In addition. the oscillator must be provided The other two samples were vacuum distilled di-
'*i uthm, fine frequener control. so that it can be set eth rectiv into the tank. The tank was phteed in an ice the required sensitivity of measurement, and bath' and connected to a flask of distilled water.
a must be, so stable that the frequency doe = not I
change dimag the counung time by enough to alter l The system was then evacuate
-d water alloweil to distill over at about 50* C.
iI The results of the three runs were the same within Thebloc t r pr duces a pulse about 100 ng o hg*S$,2 measuz_ement data e, therefore, p
l c high and 0.05 to 0.25 usec wide. It is best driven g
hv a large, fast pulse such as is gotten by differentia-1
.h a
V.
1" don of a square wave dedved. in turn, from the sine-3.5. Technique
- l wave generator.' The jitter mar be reduced further g;
a ui. %
hy means of a narrow band Siter after the oscillator.
The water bath was cooled to just above 0* C, y
=== e ca. -
The receiving circuit consists simpir of a short and the heaters were operated at low power to sta-leugth of low-capacitance cable, a wille band (3.5 bilize th.e temperature. (Beinw roont temperature
' M:.
.\\le. tu this case) amplifier of gain 100 to 1,000, and the refrigeration ma-hine was run contmuously.)
I a high-frequence type oscilloscope equipped with After the reachngs were taken, the power mput to
@7 X
Inst sweeps. The ' sweep is triggered from the the heaters was merensed, and so on until the tem-n oscillator through a variable delav; the necessarv perature was just below 100* C.
When the tem-1 '"
delay time is about half the oscillator period.
perature was stabilized, as indicated by the con-
- 4
~
stancy of the Mueller bridge reading and the near 3.3 Temperature Control and Measurement zero reading of the thennocouple galvanometer, the
'q coincidence was set, on the osedioscope by one ob.
-d.I The delay line, suspended from its cables, is server and the frequenev (doubled for convenience)
- -~
deepir immersed in a 27 gal, well-insulated, water was measured bv counting eveles for 10 sec (about S
batul The bath is provided with 2 pump-type 75.000 counts) by means of'an electronic counter.
6 stirrers. 3 heating coils, and a cooling coil connected At the same tinie, another observer balanced and 2
g-to a small refrigeration unit. The temperature of read the Mueller bridge and rend the thermocouple
.- 5 f-V the water adjusts itself so that the losses equal the galvanometer deflection.
- 7
(
power input to the heating coils, nad various temper-While the temperature readings were being made, atures are obtained simply by varying the power input.
the coincidence was independently set and the re-i !.1 The temperature is, by tius means. easily held to sulting frequency measured three times or more.
4 othin less than 0.005 deg C for the interval of time The various readings were alwavs within the 1
.y.
required for the measurements, except that above count inherent error (even for different observers) p r
a, C. or so, the variation may become 0.02* or and the modal value was recorded. This, divided W
75 gd 0.03* C; at the higher temperatures, however, the bv 20 and multiplied by the length of the tank at f l-therms) coef5cient of the speed of sound in water is the particular temperature, was taken as the speed W
f['
mther low.
of sound. e, corresponding to the temperature, T, il T
The temperature of the bath water is measured obtained by calculation from the 1,
mometer and the thermocouple readm, platinum ther-M' b
Bridge. platinum resistance thermometer and Mueller with a
?
A differential thermocouple has one june-sociated calibration data. All temperature calcula-(([
tA crywat 5 le in the delay line, and one tied to tions were made to the nearest 0.001* C and the final tion en the sam $ermometer; it passes through the m
[ %c.
the platinum t result was rounded cff to the nearest 0.01* C.
m -::
"""'"'".3 pressure release tube (fig. 2). The thermocouple In order to insure that the comeidence was set on r E
(
reading serves to indicate when the sample and bath the proper evele,it was first set approximately, using
- - h. r with it. i,
water are substantially in thermal eqtu'h'brium, and the coarse frequency control at a moderate sweep
,} +f psth is>J measurements are made when the discrepancy is less speed and low oscilloscope g,ain, so that the entire q
empera-v than 0.01* C (somewhat greater at the high temper-pulse was visible on the screen. The sweep speed h
- h course,1 atures). The thermocouple and galvanometer com-was then increased while the delay was readjusted u r n with >i bination was calibrated for small temperature dif-to keep the proper cycle centered. Next, the gain
. L around.
ferences against the platinum resi. stance thermom-was increased while the base line was moved off the
" 9 e clamp-eter so that small corrections to the temperature screen to keep the point of extreme deflection cen-b readings could be made, tered, and the amplitude was then adjusted to a
)
itse - "
ppo 9
maximum using the fine frequency control J
a se pre /{
3A. Samples
- o results. 3 The measurements here reported were made on
- 4. Resuhs j
ed and three separate samples of water. One sample was 0
?
a en and f~
ordinary laboratory distilled water. This was boiled From readings taken at 83 temperatures between F p'.
d aftera 0.14' and 99.06* C, the calculated values of the 4@gC#"p%F"@',,MM,@lLM'*
speed of sound were fitted by the electrnnie com-1 t'
3 l
251 M
w v,.
p y
ir
- l' h
q
i
]
I
~~
M l
l r
.o.
(*c m,
e
.os >,
y 2
=.
c_.
q 9.j p
r
- 3 i
a l -on j l 28
- o. - -
ll l l
,g h
.o.
t i
o io ao so
.o so ao to so so ioa j
u st hy f ewennme,'c h
"s i
I Enocu 4.
Deviations, r, of epation i from the data, e
i uter SEAC by the method of least squares, to a significant figures, so that on account of roundin.og UfS gfth-degree polynomial, errors, the tabulated differences in some cases differ i; )i. 5l E
by one unit m the last decimal place from the dit-a b.Ell si e-E a,T'.
(1) ferences of the tabulated values of c.
It is believed I
(see section 5) that the systematic errors do not i
- 4.
s ".,,,'
exceed 1 part in 30,000. The tables should, there.
The reduction in the residual sum of squares over a f re, be used in the followmg manner. In table 2.
fourth-degree polynomial, due to fitting the fifth.
linear interpolation should be performed to the 4
I degree term, was stattstimlly significant at a prob-nearest 0.01 m/s and the final res it rounded oH to i
abilitt level less than 0.005, and the deviations of the nearest 0.1 m/s. The error will then not. exceed the data from the fifth-degree polynomial showed no pne half unit i,n the last place, i. e.,0.05 m/s. Linear statistically significant indication of lack of random, mterpolatton m table 3 will vield errors that do not
./
l r
ness. The deristions are plotted against tempera-exceed 2 units (0 2 fps) m the last place. tun. in figure 4.
I
- /
dI The values of c,in eq (1), for e in meters per second S. Discussion
- ~ *
(m/s), and T in degrees C, are: a,- 1,402.736 : a,==
E 5.03358 ; e,= -0.0579506 ; ae3.31636 X 10-*: a.== -
i error an{ ts a list of the knon possible sourcesj U *.*.
a 1.45262 X 10-*
and c3=3.0449X10-'. The stand-an estimate of the upper limit of each ard deviation 'of the measurements is 0.0263 m/s, or i
3 shout,17 ppm. Estimated standard deviations of S.I. Frequency g-i f.\\.he values of e predicted by eq (1) were calculated for five representative temperatures. The results As already stated, the frequener was measured hv 4
I are given m table 1.
counting cycles for 10 see; the total count was
.9 gi about 75,000. The inherent error is -::1 count,bui p
g; Lat.: 1.
E.nimera sisaderd denation (s. d.) of rotwee of e tn all cases the mode of at least three independent r
gedwed 6y.patiosi t readmgs, of which, at worst, two were the same aint H
the third diferent by one, was taken as the observed g
{.remii,.r sw.
- s. a.
value. The countmg error can thus be as great as the effect on I part in 75,000, but as it is random,d in section 4.
L
.c
.i, n.
the final results is negligible, as indicate
'3 h 'a j
!y U
I' ;i
- ,=ss The 10 see time base was obtained by division from 2s a
a 1.Mc crystal oscillator which is stalile to 2 parts in 1
j M
i from WWV or from a local precision standard. gnals g
10' per week, and which was compared with si I
The 4.
y Table 1 and fi ure 4 make it clear that eq (1),
errors due to maccuracies m the time base arr-3 together with the listed constants provides a satis-therefore, also negligible, g
factore interpointion formula and the errors intro-duced' by its use are small r' elative to the possible S.2.14neh of Path
- [ tank is abot 4 mperature systemane errors of measurement (see sectiou 5).
ven in tables 2 and 3 were calculated The length of the tank across its polished end* ai yg] and c i i
The values h'y SEAC.
20' C was determined within lu, i. e.,5 ppm. Ther H
from eq (1) mal expansion measurements were made at 20". 00;.
quest Table 2 gives the speed of sound in meters per of the soum second for each degree C from 0 to 100, and table 3 and 100* C; the lengths at mtermediate tempera-between the tures were caleu!ated by quadratic interpolaho"-
inntes to th l g',ves the speed of sound in feet per second at inter.
The maximum absolute error in the thermal expan-Jwhich the vals of 2 deg F from 32' to 212*. In each case, the differences, which are listed for convenience in inter-sion coeficient is estimated at 0.2 ppm; this arr"l fdevelopmen polation, were calculated from a table having more mulates to 4 ppm at 0* C, and to 16 ppm at 100'
.IL
- bly were 252 g
\\
=.
5 TA91.E 2.
SPetd of send an mater, metrse un Is t
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Thus, the total uncertainty in the length of the attention to avoidance of clamping pressure too near [
tank is about 5 ppm at 20' C, and increases with the unsupported areas of the crystals, the crystals i' temperature both wan; at O' C it becomes about might deflect. enough to cause very sizable errors. Lj dysat*.o 9 ppm and at 100* C,'about 21 ppm.
The present design makes it possibfe to disassemble The question arises as to how closelv the length and reassemble the delay line repeatedly without
> 60 of the sound path in the sample, i. e.,'the distance rHecting the result by a detectable amount; this H
'"'"* d.
between the inner faces of the transducers, approxi.
holds true when the crystals normally used, which 9 M **
(Pan. '
rnstes to the length of the tank across the ends to are 0.8 mm thick, are replaced by crystals 1.6 mm %
trhich the crystals are wrung Experience with thick. It, therefore, appears that errors produced #
%'.e.
developmentafmodels showed that unless the assem.
by, mis lacement or deformation of the crystals are bly were very carefully made, with particular matam cant.
=
s4c.
b 253 3
.-iiif S.3. Sett t hs Coine.dsnee l constant at this vr.lue out to 70* C, and nses to
- ome;e2-a about,35 ppm at 100' C.
It is upon these considers.
As explained in section 2, it is believed that no tions that the recommendations for the use of the measurable error is introduced by the technique of tables in section 4 are based.
Pa maxumzauon of the accond half cycle of the received The values of e here reported are lower than thow pulac. However, a word should~be said about the of most other workers, m particular the value at (Q_ g effect of personal bins on the part of the operator. ' 30* C is about 0.4 m/s below that of Del Grosso The operators report, to varying degrees, tendencies Srnura, and Fougere (31, whose work with the ultu-to adjust not only for maxuuum height of peak, but sonic interferometer is pernaps the most enrefulb v
also for maximum symmetry and sharpness of peak.
Long experiment has convinced us that any of the ' planned, executed, and analvzed work of this type to date. It. was, therefore, felt desirabic to perionn three entena lead to sensibly the same result, so an independent expertment using an apparatus and that althourb different operators weigh the three a method as different as possible from those of both c*
enteria differently, ther reproduce each other's Del Grosso, et al., and ourselves. An apparatus settings so well that the discrepancies are negligible was constructed with which a is possibic to measure.
i l,
relative to other sources of error. The assumption as a function of distance, the phase on the aus of a
't.
[ is implicit that the errors of bias do not much exceed heam of progressive waves emitted bv a small pisten-the discrepancies among individuals.
like radiator. If the wave were plaine, the pnase,
- ( The radia would varv linearly nith distance z, and the phase mtennas has S.4. Temperature speed c would be 2r/r/, where f is frequener. In
@Nroblem ears ll-6}.
the present case, the wave is not plane and the slope The Mueller bridge with which the resistance of of the curve 3rf: versus, depends on z and on tne 9n wh2ch the the platinum thermometer was measured has a least geometrv of the arrangement. However, the theort kdequatelv count of 0.0001 ohm correspondine for a 25-ohm enables 's to se!ect a distance 7. of the receiver froth hose radius u
thermometer, to about 0.001* C. 'The bridge was the source such that for r>i the departure of calcurvatu calibrated internally so that the indiented resistance 2r/ds/de from e is as small as desired.
formal 5 in terms of the internal standard is correct to about
'Five runs were made in distilled water nt tempera-
. assical har 0.0002 ohrn aside from temperature effects and slow tures between 15' and 25' C.
The priccipal uu-tegral ord drifts in the arm ratio and in the zero. Allow'ng certninties are thought to be first, one of c. bout 40 ery poorly for these, it is estimated that the bridge error does ppm corresponding to a possible enur of 0.0l* C in mpared te i not exceed 0.005* C; crrors in the calibration of the the temperature, and second one of nhout 50 ppm own alter platinum thermometer itself and those due to heating related directiv to the innecuracies of the screw with 7which can }
by the bndge current are much smaller. More im-which the receiver displacement, was measured.
Jn the illumi portant is the error that aries from thermal gradients These are independent. However, m the worst case goptics is mot m the bath. On the assumption that this does not of the 5. the result differed from the value gotten the ngorous execed half the readine of the differential thermo-from table 2 bv oniv 27 ppni. The value of Del e rapidly c couple wluch, it will Ge recalled, measures the dif-Grosso, et al. [3] disagrees with thnt of table 2 by 272 The ca!ct ference between the temperature of the platinum ppm.
] mounted
/S element and that of the sample, an upperlimit to the This work will be reported in detail elsewhere.
ighoshadov
(*) corresponding uncertainty m the speed of sound, j eathergeome e, was enleulated at various temperatures from th i
The nuthors are grateful to the g ormer case Enjincering Metrologv Section anfersonne gould ac u knowu thermal coefficient of e.
This u er limit of the Leneth tter case is zero at 74* C, where e is stnuonary an mercases 3,c ion, m whose Laboratones the length of the taink stenctdv in both directions reaclun shout 25 ppm at 0* C, and about 14 ppm at 100g C.
and its thermal expansion, respectively, were meas.
g espite, e,
':*o g y l1 ured. Thanks are particularly due to Joseph 31.
$. sde Cameron of the Statistien! Eup,neenng Section who S.S. Punty of Sampl*
ndvtsed the nuthors on problems of data procesmc.
f"re2 f *** *,e Because the results ohtamed on onlinary laboro-and who performed the curve-fitting computation <
"F on SEAC-D tory distilled water were i2whstmsruishable from those j
obtained on the same water redistdled in vacuum
- 6. Reletwees directiv into the apparntus,it is felt that the remaiu-
[t] Martm Greenman and Carroll E. Tsclue:g. Ses.srmnal
[
y ing idipurities do not have a measurable effect.
unre.onue velocimeter for bquids, Rev. Sea. hurn s
- n, {
Several measurements made on local tap water gave
'2) n[.Nconnell and W. T. Mruk. Microneenstic irm l Imfinite len l results about 30 ppm higher than for distilled water.
t,iomem u.mg 30 Mc puw J. Acoust. Soc..On" (sidered bec 27, 072 (1953).
eradist. ion fit S.6. Over-all Acmacy (31 V. A. Del Grosso, E. J. Smura, sud P F. Fougere. Acek-
, is and coax acy of ultrasonic snterferometer determmations. S p
j%h[a)' vo From the foregoing discussion it appears that the g rt g S.,,%*,g*j) h * * " -
major sources of error are the uncertainties in the N Marun Greenspan and Carroll E. Tschaegg. Effect of gg 7)
- length of the path and in the temperature. Both of diesolved aar on the speed of 80"nd m irater, J. Acon
({ terms of a l these are temperature dependent their sum is an Soc. Amer. 28. 501 (1956).
upper limit to the total error. This is about 35
,,_ m l ppm at 0* C;it falls to 15 ppm at 40' C and is almost
%suixarov, March 27,19m,,,.
214 E.
Q( 3 -
O THE OURNA_.
OF THE ACOUSTICAL SOCIETY OF AMERICA M
Volume 31 l
Number 8 u
AUGUST 1959 Speed of Sound in Distilled Water as a Function of Temperature and Pressure 1
Wawa D. Wasow
- v. s. Meest ont=ana u reury, ws oak, sa.a sp.se, xw (Received January 26,1959)
An ultrasome pulse type apparatus was used to measure the speed of sound in distdled water over the pressure range 14.7 to 14000 paia and the temperature range 0.9 to 91.2*C, The temperature where the maximum sound speed occurs shifts to a higher temperature when the pressure is increased. At atmospheric l
(
pressure the computed maximum speed was 153336 m/sec and occurred at a temperature of 74.164*C, The isotherms of sound speed, plotted as a function of pressure, are concave upward below 20*C, concave down.
1 I
ward above 20*C, and are approsuantely linear near 20*C for the pressure range of 14.7 to 14000 paia.
These curvatures have a maximum value of 1 part in 300 compared to the estimated accuracy of mensare-raent which is I part in 10000. 'De resalts are pressated in tables and also la the form of a fourth degree equation 6tted to the czperimental data by the method of least squares.
L INTRODUCTION to determine sound speeds in water within the tem.
A distilled water is important for the computationPRECISE knowledge of the speed 14 7 siaSP$14 000 psia. The present paper is con-P of many thermodynamic quantities. Numero:s meas. cerned with measurements in distilled water. Numerous urements have been made of the speed of sound but systems have been designed for sound speed measure-only a few measurements have been made of sound ments but the fixed path double crystal "velocimeter" speeds as a function of temperature and pressure. was selected by NOL as most suitable for measure.
Greenspan and Tschieggi and also Del Grosso have ments under pressure.
2 published accurate tables of sound speed as a function of temperature at atmospherte pressure. The efect of U. EUMEN MGEM l
pressure on sound speeds have been explored by The method used in this work is similar in principle Holton,8 Smith and Lawson,* and by Litovitz and to that developed by Greenspan and Tschiegg at the i
Carnevale,* and others; however, diferences exist be. National Bureau of Standards. The water sample is tween these data. Consequently, measurements have contained in a tubular housing, each end of which is been made at the Naval Ordnance Laboratory (NOL) terminated by a 5 Mc quartz crystal for the transmis.
sion and reception of sound pulses. A knowledge of the i M. Gesenspaa and C. Tachiogg J. Research Natt. Bur.
S N 59, 249 (1957); also J. Acoust. Soc. Am. 31, 75 repetition rate of the pulses when echoes are super.
imposed is suflicient to determine the time required for s v. 'A. Del Gesano, Natannal Raearch Laboratory Rept. No.
a sound pulse to traverse the length of the velocuneter.
4002 (19521.
\\
8 G. Hoiten. J. Appl. Ph. 22,1407 (195 t).
An accurate determination of this length then allows
- A. H. 5auth and A. W.
weos, J. Chem. Phys. 22. 351 (1954).
the ve1ocity of sound to be computed.
5T. Litovits and E. Carnevale, J. Appl. Phys. 26. ?,16 t1953).
l'he main diNerences between the veloctmeter used 1067
/ c.oritene o im nr as am.am.: s, w a.or e. /
m - ___ _. - _ _.. _. _ _._
__m..._..__.
1068 WAYNE D.
W I t. S O N i
Figure 2 presents a block diagram of the electronie
[
,m,
- ""*Q-j s
( ;
- i instrumentation required for the sound speed measure.
r J
ments. An interpolation oscillator equipped with a sne f
Orb.
f 5-
frequency control is dltered electronically and used to m'
'I v
W' N C*
control a pulse generator. The pulse from this ;;enerator
\\Y~
is shaped by a blocking oscilhtor to furnish a pulse of
\\'
180.v amplitude with a duration of 0.03 acc to one N
crystal in the velocimeter. The second crystal receives the pulse after it has traversed the water sample and Fic.1. Schematic of velocmeter: A. test chamber: A quartz crystal: C. 0-nns seal: D compression ipnne: E. eiectrical land: feeds it into preampliders prior to displaying the signal E bed "
on an oscilloscope. Coincidence of the sound pulses in the velocimeter is adjusted by observing the signal by Greenspan and Tschiegg and the velocimeter used trace on the oscilloscope while varying the oscillator at NOL are as follows: (a) the National Bureau of frequency. It is this frequency which determines the Standards (NBS) instrument was 20 cm m, length as time required for the pulse to traverse the liouid in the compared to 12.7 cm for the NOL instrument; (b) the velocimeter. The pulse repetition frequency is doubled NBS instrument used 3.5-Mc crystals and the NOL and displayed on a frequency counter with an accuracy instrument used 3.0 Mc crystals; and (c) the NBS m.
of 1 part in 100 000 for the computation of sound y,g,y strument used crystals which were wrung to the ends of the tube without electrode plating at the contact Figure 3 shows the general arrangernent of the com-area while the NOL instrument used gold plated plete instrumentation for monitoring and accurate crystals. The NOL velocimeter, shown m Fig.1, is a control of the physical environment of the velocimeter.
stainless steel tube with a bin. bore approximately The pressure vessel containing the velocimeter is placed i
4 5 in. long. The two ends of the tube were machined in a 110-gallon constant temperature bath regulated plane parallel and perpendicular to the axis of the tube by a mercury thermoregulator. Three stirring pumps to an accuracy of 0.00003 in. To each end of the tube are used to circulate the water in the bath to assure a is attached a cap containing a 3 Mc gold-plated X-cut constant and uniform temperature. The absolute tem-crystal backed up by a Mycaler insulator and a com-perature of the bath is measured by a platinum resist-O pression spring. The springs are used to force the crys-ance thermometer to the nearest 0.001*C. Temperature tals against the ends of the tube when assembled. A vadatirs and tersperature gradients are recorded by
\\._/
neoprene 0-ring located between each crystal and the the action of a thermistor placed in the bath near the tube provide leakage seals. This O.rmg is designed t pressure vessel. The thermistor acts as the resistance in compress fully under the force of the spring and allow one leg of a Wheatstone bridge; the unbalance of this the crystal to make uniform contact with the ends of bridge is observed on a recording potentiometer and the tube. One end cap contains the electrical leads for variations in temperature of 0.0003*C are easily de-tected.
the communication of sound pulses between the crys-tais and the external electronics, and the second end In Fig. 3 a single meter is shown as the device used cap has a bellows attached for the purpose of m to measure pressure. Actually, a manganin resistance mitting the pressure to the water sample toside the gauge, a sensitive Heise gauge, and a dead weight tube. The bellows was carefully designed to tnsure a tester were used to determine the absolute pressure.
negligible pressure differential between the hydrostatic Greatest reliance was placed on the dead weight tester pressure 6 eld outside and the pressure inside the veloci-since the manganin cell was unstable at low pressures; meter. The velocuneter is placed inside a heat treated this cell was used however to detect changes in pressure steel pressure vessel capable of withstanding 1,00 000 as small as 4 psi for higher pressures. It is estimate psia. This vessel has steel end plugs, one of which ts used that the absolute pressures were known to within 7 psi to tranarnit pressure to the inside of the vessel and the or, when referred to velocity coordinates, the pressure other to bring out the electricalleads. A medium grade was known approximately to 1 part in 20 000.
oil is used to convey pressure from the pressure gener.
III. METHOD OF MEASITItEMENT ator to the pressure vessel Sound speeds were measured by drst adjusting the bath to a particular temperature and then by varying i===
4",,,,
M"".d-the pressure over the desired range. Since an adiabatic
.m.
~*
increase in pressure of 2000 psi will change the tempers-m L.2eSL l~~~%
ture inside the velocimeter nearly 1*C it was necessary o
~
I to wait until thermal equilibrium was reestablished m-maprum,.
before a measurement was made. The thermistor used I """ !
=cem
- 2 to measure temperature was located outside the pres-j Fic. 7 Illoca diagram of instrumentation, sure vessel and was not sensitive to changes inside the
_m__._
___m SPEED OF SOUND IN D I S T I L I. E D WATEf1 1064 O
I eta i
i
.u
.<ar. i j
q'a-*'"j a
aorr.rma te.
.oa ;
stafsaJae etsstasa;g
.ogsma.t routeess970 f*(ansansETE.
Frc. 3. Schematic of esperi.
84tl.L8BC L840-e
= iry mental setup.
!g.
~<'oca'rt" l
1 i
p t*f
/.
NW W.h t -
f.R.
{
- - = =-
j' y
- g :
7co'= raat,,rv=parwr g
es ni,
=s
=_
gi f f, gj l.
d - l.%;
J n
e a
ir
+
.ws,
s mm
- mm,.m m m mmm m m m m m
_, m m,, _
velocimeter. Hence the sound speed measurement itself tion obtained to describe the coefficients of Eq. (1).
was used to determine when thermal equilibrium ex.
The speed of sound in distilled water is therefore given isted. That is, the measurement of sound speed over a by peric,d of time (approx 1 hr) was used as a thermometer C= a.+a T+a:P+a:T8+a.T*,
(1) to determine when thermal equilibrium was estab-lished. After thermal equilibrium was reached ten measurements of the pulse repetition frequency were
,,,,{ (gpf recorded and averaged to give the time required by g
the pulse to traverse the velocimeter. The pulse repeti.
tion frequency is obtained by superimposing on the T is the temperature ('C), P is the absolute pressure oscilloscope the peaks of the first half-cycle of all echoes (psia), and the computed (bdf values are given in A
in the "docimeter.
(
Table II. The parentheses indicate a set of 6 values 4
associated with each a4; for example, Table II gives a.- 1402.859+ 1.050469X 10-2P+ 1.633786 The measured values for the speed of sound as a function of temperature and pressure are presented in X 10-'P'-3.889237 X 10-L*P8, etc.
Table I. These values are plotted in Fig. 4 with tem. An IBM computer was used to compute sound speeds perature as the abscissa and in Fig. 5 with pressure as from these equations and the results are tabulated in the abscissa. In the determination of the sound speeds Table III. The standard deviatioca of the differences recorded in Table I, corrections for the change of between the computed curves an.1 the measured curves length of the velocimeter due to changes in temperature for four pressures are given in Table IV.
and pressure have been applied. The results of Table I were used to obtain empirical equations for the speed Sm M Ts of sound as a function of temperature and pressure.
It may be noted in Fig. 4 that the muimum sound Equation (1), a fourth degree equation, was first ob-speed shifts toward higher temperatures as higher tained by the method of least squares for each ci the pressures are considered. This behavior agrees with the eight curves shown in Fig. 4. The coefficients of the results obtained by Smith and Lawson, and also by dght equations were tabulated and a third degree equa. I.itovitz and Carnevale.' The temperature for the peak TAS12 I. Meamared values of the sp.ed of sound in distilled water.
Te.o.rstar.*C
- 7 o.vi' 2.77*
80.20' to.es*
29.ts
- J'.e2 *
- J 7*
so se' e*.es*
ts.fo*
- t.2 7' 14.7 1407.41 1416.35 1449.05*
1481.61 1509.37 1528 36 1542.60 1551.01 1555.02 1554.90 1549.80 2000 1429.25 1438.06 1471.46 1504.34 1532.67 1352.03 1567.11 1576.21 1581.13 1581.&3 1578.03 4000 1431.66 1440.13 1494.17 1527.34
!$55.87 1575.72 1591.22 1600.96 1606.58 1607.97 160$J1 6000 1475.J7 1484.42 1517.28 1550.49 1579.04 1599.16 1614.92 1625.21 1631.44 1633.35 1631.75 8000 1499.72 1508.50 1540.99 1573.79 1602.12 1622.17 1638.22 1648.91 1655.69 1657.95 1637.36 10 000 1524.61 1533.29 1564.78 1596.90 1625.06 1645.14 1661.28 1672.30 1679.34 1682.13 1682.18 e
12 000 1549.93 1558.00 1588.75 1620.25 1647.88 1667.72 1684.00 1695.13 1702.55 1705.65 1706.39
(
14 000 1575.22 1583.15 1612.66 1643.41 1670.58 1690.4 t 1706.31 1717.68 1725.28 1728.69 1730.02
. p.
e w
e.
m_.
1070 WAYNE D.
WfLSON O
TAsl.r. !!. Coetlictents m the sound velocity equatsons for distilled water.
4)s 16.)..i 4),
4 6.),
a.
1402.859 1.050469 X 10-'
t.633786X 10-'
-3.389237 X te-o
~
4, 5.023859 6.138077 X t0-*
- 1.080177 X 10-*
1477679X to-u 4
-5.690577 X 10-'
- t.071154 X 10-*
1215786 X 10-*
- 3 088886 x 10-'s as 2.884942 X to-*
1.582394 X 10-*
-2.420956X 10-n 5.086237X10-"
4
- 8.238863 X 10-'
- 6.839540X 10-"
9311687 X 10-
-1.345198X 10
==
TAuta IIL Sound velocity in distilled water computed from Eq. (1).*
Pre-are Temperature *C
_=
ps o.oo*
10.00*
- o.co' Jom*
44m' som*
oo.co*
- o.oo*
so.oo*
90.oo.
ico oo.
14.7 14Q3.01 1447.85 1482.92 1509.66 1529 30 1542.88 1551.26 1555.06 1554.74 1550 34 1542.5I 2000 1424.49 1470.03 1505.66 1532.92 1553.11 1567.34 1576.47 1581.14 1581.77 1578.58 1571.54 4000 1447.24 1492.88 1528.68 1556.21 1576J9 1591.51 1601.25 1606.65 1608.10 1605.80 159930 6000 1470.93 1516.15 1551J9 1579.37 1600.17 1615.26 1625.49 1631.47 1633.62 1632.10 1626.88 8000 1495.36
!$3936 1574.97 1602.41 1623JO t638.M i649.23 1655.68 IM8.40 t637.57 1653.20 10 000 1529J6 1563.60 1598.17 1625.33 1646.19 1661.68 1672.54 1679.36 1682.54 1682JJ 1678J8 12 000 1545.72 1587.60 1621J8 1648.15 1668.90 1684.44 1695.48 1702.56 1706.13 1706.47 1703.73 14 000
!$71.28 1611.66 1644.56 1670.88 1691.44 1706.96 1718.10 1725.38 1729.26 1730.10 1728.17
- V.hmoty gives in m/sec.
=
atmospheric velocity can be obtained by diferentiating Eq. (1) and equating the resulting cubic equation to temperature exceeding 74.17'C (see Fig. 4). A change zero. When this is done it is found that the peak sound in curvature of the isotherms in the vicinity o speed at atmospheric pressure occurs at a temperature has been obserwd. Below 20*C the isother of 74.164'C. Linear interpolation of the results of cave upward, above 20*C they are concave downward, b
Greenspan and Tschiegg yields a corresponding tem-and in the vicinity of 20*C they are nearly line perature of 74.178'C. Later work by Greenspan.and Additional measurements at NOL on sea wate with the sing-around system placed this that the general effect of pressure on sound speed i V
Tschiegg8 maximum speed at 73.95'C. The sound speeds meas-essentially the same as that for distilled water. Thi f>ehavior is in contrast with the results predicted by ured at NOL at atmospheric pressure agree well with Kuwahara in his sea water table and by3fatthews'in f
the results of Greenspan and Tschiegg. The standard tables of pure water and sea water which show the deviation of the diference between the NBS and the therms plotted against pressure to be concave dow NOL results for all of the atmospheric pressure data is 0.15 m/sec.
at all temperatures.The soundspeeds computed bythese The characteristics of the isotherms shown in Fig. 5 authors depend on an empirical equation dev nmin require comment. At high temperatures it is seen that e for the mean compressibility of sea water.
some curves intersect; this is to be expected, however, This equation was derived from Ekman's measure-since the sound speeds at low pressures decrease for ments on sea water and from Amagat's* specific volume measurements on distilled water. Ekman has suggested that Amagat's specfic volume data is in error below orstaan==m 150 atmos and he applied a correction factor to Amagat's
==.
a_
data in this range. A descriptive analysis of Kuwahara's J""
N computation is given by Beyer." It is shown here that the corrections nman applied to Amagat's data were j""-
=" E in the correct direction although, as Beyer points out, j,,,.
,, z g4-tYj a m re accurate expression for compressibility is still dis at 7
,# ra as a function of tem-desired. Eman's equation is accurate to 1 part in 500 3a" imt"-
3 and this is what limits the accuracy of Kuwahara's 4
i
~ ess m,.,,,
' S. Kuwahara. Hydrographic Rev. 16. 126 (1939).
- D. J. Mattherrs, Hydrogssphic Department Rept. HD 282 (London.1939).
~, e = =.e =.e
.o*
' V. W. Ekman. Pubts. cire, cons. perm. internat. l'erplor.
4 [.-
ta mar. No. 43, 3-47 (1910).
ressresance (*Cl
- E. IL Amagat, Ann. chim. et phys. 29,68-138, 304-374 (1893L
' M. Gnenspan and C. Tschaegg, J. Acoust. Soc. Am. 28, 500 18 R. T. Beyer, J. Marine Research (Sears Foundation) 13, (1956).
113-121.(1954).
l SPEED OF SOUND IN DISTILLED WATER 1071 work. Del Grossou has called attention to an error in TABLE [Y. $tandard deviation of tb4 dditttDCes betwee Ekman's pressure determination which is of sudicient
,Q" * *d """' 2"d * * "'*P"*di"8 "'**"'*d "" ' ""*4 magnitude to explain the 3.0 m/sec diference which exists between the predicted and the measured sound p,,,,,,
speeds at atmospheric pressure. Ekman did not measure a=
==
to ooo pressure himself; instead he used his compressibility 14J 0.16 1.0 measurements to compute his operating pressures from an empirical formula which was made to agree with y
12000 0.19 1.2 Amagat's data for 0*C. The error in Ekman's equation for mean compressibility is only 0.25% but it is sudi-cient to explain the 3.0m/sec discrepancy in sound or subsequent measurements, will be available in th speed. A companson of the sound speeds computed by future to explain this interesting behavior.
Matthews for distilled water and the sound speeds 1
measured at NOL is shown in Fig. 6. It is seen that the VL DISNSION OF mtORS 1
predicted speeds are remarkably accurate in spite of i
the compleaity of the computation. In particular, it An estimate of the accuracy of the sound speed meas-urements is obtained from a summation of the individ.
ual errors. Assuming a random distribution, the expen.
i mental error e, in sound speed that may occur for any otSTILLED WATER one m m m b @ h irso -
'o c
<,'=a*e '+#*ei,*+y er +6*er,
r 1
r..o%
s;Y stoo -
where a,4, y, and i are representative constants for the ve a
T. set changein velocit and pressure. er,y with frequency, length, tempera Wiuo -
.ao c j
f'co' deviation of frequency, length, temperature, and pres-
<r., er, and er represent the standard g,
. [n7 sure from the measured value. Thus, from Table V, the y
maxunum expenmental error in the measurements is U*"
computed to be 0.093 m/sec. It should be pointed out that the " constants" e, #, y, and 3 are not actually ci*oo constants, however, the deviation from linearity of these functions is small except for v. In Fig. 4 it is seen that y varies from 4.97 m/sec/*C at 1*C to 0.00
'*8' COMPUTED FROM EQ (0 "o
acco *ooo sooo 8Eco coco 5000 'acco PRES $URE (PSt.A)
- o-Fac. 3. Velocity of sound in disulled water as a lusction of pressure esto -
may be noted that the present measurements are nearly 3.0 m/sec higher than the predicted sound speeds f
,/
at atmospheric pressure, as first noted by Del Grosso.
Although the second denvatives of Amagat's distilled f
/
/
water data are unsatisfactory for the direct computa-5*
/
~
tion os sound speed, it is interesting to note that sound
,/
oismto wen speeds computed in this manner and plotted agamst j i.co e...c c pressure are concave upward for Amagat's temperature j
gg,,g,,,,,,
range of 0 to 40*C. The curvature (concave downward) scuo u.c.,outmanata oaras noted in Kuwahara's and Matthew's work must result
'"* ~
then from the inclusion of Ekman's work. Although the majority of data referred to above pertains to sea
/
ano water, the same arguments hold true for distilled water
/
and can be used when speaking of general features such i
as curvature. It is hoped that theoretical predictions,
- V. A. Del Groeso. Natl.\\ cad. Sci.. Na:L Researca Council.
Publ. 600 (1959).
Fic. 6. Cosiparison of velocities predicted by D. J. Matthews and measured at NOL.
- - ' ~ - ~ ' ' ' ""
~ ^
~
1072 WAYNE D.
W i l. S O N O
T4stz v.
a time delay during redection in the NOL velocimete-computed in this manner was found to be 0.0001 m,see indmdual error Caer6cient and it is Considered negligible for the purpose of this e.=0.2 cps a=0.127 m/sec/ cps work.
M' M7Y *
$ ~= Nm*#'*N The remaining errors in Table V are computed di.
s.c
,p= 7.5 paa 4 =0.011 m/sec/pua rectly from the references given. The term " shear vis.
cosity" refers to the viscous absorption which occurs at m/sec/*C at 74.1M*C. The above error was computed the tube walls. The eHect of bulk viscosity, radial and at a temperature where y is greatest, i.e., at 1*C er, lateral heat conduction, scattering, and molecular and the error m the frequency measurement, includes the chemical absorption are all absorption phenomena error due to the accuracy of the counter and the error which are computed easily from the references cited.
which results from the abih,ty of the operator to set The arithmetic sum of the systematic errors is seen coincidence. Each value for the velocity in Table I was from Table V to be +0.027. m/sec at atmosoheric obtained from the average of ten measurements of pressure and -0.013 m/sec at a pressure of 14 000 psia.
frequency at each temperature and pressure. The stand-The total error, which is the sum of the random errors ard deviation from the mean of these ten readings is and the systematic errors, is then -0.106 misec or 0.2 cps and it includes a 0.1 cps variation which is
+0.120 m/sec depending on what pressure is con.
characteristic of the counter.
TAstz VL Systematic errors.
In addition to the random errors discussed above, systematic errors resulting from actual physical phe.
" d""
nomena must be added to obtain the over.all accuracy h,"y,,,"3 d
$ oco"p$ I E of the measurements. Corrections may be naade for Redection (time delay)
Neglivble
- a. b systematic errors when they are known, however, since Mnite pulse height
- 0.002
- c. d the tables of sound speed have not been corrected for ty N 15p e j
such errors, they are treated here like random errots. Radial heat conduction Nestigible
- d. I A complete review of systematic errors is beyond the h*'n1 heat conduction Negligible O
Intended scope of this paper; a surnm=ry of these errors c3e.,cai adeo,ptio,s Negligible Molecular scattenn is given however in Table VI for reference. The errors Duperson Nestigible h
se,ii,,sie e
in Table VI have been computed to the first three sig.
nificant figures and errors which are less than 0.001
- $,5s, m/sec are considered as negligible in this report.
g,a.7 g em,e r.ejg jj;s,g
== t i The pressure differentis.1 error is an error which re. A so I.e. u. g, y g g,,
v.a. nso).
suits from the force required to compress the bellows t,/.h M lem. rai."e" T.i.E ft".Me**e*nl.' ', of of the velocimeter. This force causes the pressure inside e.
the veloctmeter to be less thac the pressure outside where the pressure is measured. The error due to the l 7, Wy,%*a,',*y, @l","fR
- s=7,. rgpg,m. nsu.
small pressure diferential listed in Table V is the
)
mazar.um error expected. This error will decrease ap-sidered. The over-all accuracy is then at least 1 p i
10 000, proximately linearly to zero as the pressure goes to atmospheric pressure. It is also conceivable that this VIL ACENOWLEDGMENTS pressure diference may cause a dedection in the crystal The author is deeply indebted to Mr. Dudley Taylor transducers in the NOL velocimeter. If this should occur, the mazunum etter in sound speed produced by for the design and construction of the v the distortion would be -0.030 m/sec at 14 000 psia the pressure vessel, and for the frequ nt cons and would decrease linearly to zero as the pressure is the numerous problems encountered in this wo made to approach its atmospheric value. The third Equally important has been the work of Mr. Walter error listed in Table VI is due to the time delay that Madigosky who contributed snuch thought and e to the choice and assembly of the necessary instrumen-occurs during reflection of the sound wave at the trans-tation for the measurement of sound velocities. The ducers. This additional time delay has been computed by treating the transducer as a damped mechanical author would also like to express his gratitude to the IBM computer stad at NOL for their participation in system which responds to a transient force. Only the the denvation of the velocity equations expressed first half-cycle of the incident wave train was con-herein, and to Dr. T. A. Litovitz, Dr. H. E. Ellingson, sidered in this analysis since this is the portion used to and Mr. A. T. Jaques for their frequent aid and en measure sound speeds. The error in sound speed due to couragement of this work.
THC JOURNAL oF THE \\CoUsTICA1. SOCIETY oF AMERICA Volume Jt. NUMBER $
\\ UGUsT.1954 Resonance Absorption and Molecular Crystals. IL Benzenet LeoNAaD blE9EsMANN linseerruy of Cdifornu, La Ma, Cailornu (Received March 24,1959) mthm each molecule. These two vibrational roodes can ov atomic vibrations leads to lengthy relaxation times marulested as unusually high acoustic ab esonate." This resonance for gromnq single benaene crystals of average linear dimension.
enethod was developed excessively high absorption (10* higher than in crystalline q cm-'. This available molecular constants by a theorv given previously. A partial list of ve y predicted from resonance absorption is predicted to be the dommant absorption mechanism en in which INTRODUCTION A thermal oscillation: those in which each moleculeMOLECU
. selected for initial study because of the wide
- 8 vibrates as a whole about its lattice position, termed vanety of thermodynamic data available for this the acoustical branch, and the internal vibrations of compound. Although benzene is a liquid at roo temperature it has a relatively high melting point the atoms comprising a molecule, termed the optical (33*C) which makes its study in the solid state branch. In many crystals these two vibrational modes overlap in frequency, leading to resonance.
possible wtthout unusual techniques. However, it is
=cessary for acoustic observations to be made on a Previous work,5 hereafter referred to by the designa.
Single crystal rather than on the polycrystalline state tion I, has shown that resonance can result in unusually n order to eliminate contributions to absorption from high acoustic absorption. High absorption results from friction and scattering at crystal boundaries, fracture the relatively slow transfer or exchange of energyand at other imperfections. For this reason a large s between lattice and internal vibrations. Just as in crystal of benzene was grown for the purpose of the wealdy coupled mechanically resonant systems, theacoustic observations. The following sections describe transfer energy at resonance is large, but the rate of the method of preparation of the crystal and observa-transfer is slow, particularly close to resonance. The tions of the acoustic absorption.
phenomenon is some respects resembles the familiar relaxation absorption observed m gases and hquids, but GROWTH OF MON 0 CRYSTALLINE BENZENE the latter arises from transfer of energy by collision, whereas the present phenomenon requires near fre.
As in the case of nearly all organic compounds, quency coincidence of two vibrational states; hence the molecular binding forces in benzene are relati term, resonance absorpion. It should be emphasized (its binding forces are largely van der Waals that this resonance phenomenon is not associated with Consequently crystalline benzene is a fragile s acoustical frequencies but rather with the extremely incapable of supporting severe therma high frequency thermally excited vibrational modes conventional technique for crystal growth in which within the crystal, heat Sows through the external crystal surface intro-duces far too many stresses and could not be utilized It was shown in I that the rate with which energyfor benzene.
oscillates between the two vibrational systems deter.
mines the acoustical absorption; a low transfer fre.
The schematic diagram given in Fig.1 illustrates the quency leads to large acoustic absorption. Stated in method whereby unsupported thermal strains were another rnanner, whenever the oscillator coupling is avoided in crystal growth. Instead of the usual small, or the intermolecular binding forces weak, of crystallization from the liquid, whereby heat is absorption will be high. Conversely, in highly absorbing extracted from the external surfaces, heat is ex crystals the Lennard-Jones molecular constants, e and from within. The coldest exposed region is the tip r, will be found to be small and the intermolecular heavy copper rod on which the seed is placed. Henc s
spacing large.
exterior growing surface is always warmer than the Tables of the Lennard-Jones constants suggest that central region and thermal stresses are compressive
-many organic compounds should exhibit rather than in tension. In practice the copper tip was attached directly to the refrigeration coils and operated resonance t This work received support from the Bureau of Shir* Navy in the vicinity of O'C. The air temperature in the refrigerator was accurately controlled by means of ment n
from the Senops Insutuuon on L. Liebermann, l'hys. Rev. 113, 1052 (1959).
heaters and thermostats at a constant temperature in the vicinity of PC. In addition a small amount of 1073
---w
m.
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TNE JoCENAL oF THE.tcoUsTICAL SoCurrY oF.tMERICA Aco UsT. seet i
l l
_m ga!T. J. sPPt.. PHYS. 1967. vot. 18. PRINTED IN GREAT BRITAIN O
Pressure dependence of the velocity of sound in water as a function of temperature A.1. BARLOW and E. YAZGAN Department of Electncal Ensmeenng. University of Glasgow MS. recetved 28th kne 1966, m ren.redform :Sth November tW Abstrset.
Measurements of the velocity of sound in doubly distilled water have been made at pressures up to i! 600 lb in-8 in the temperature rense 16-94*c.
The basic expenmental technique and the theory of measumment have been decnbod m detail in a previous paper by Barlow and Yazgan. The nsults are believed to be accurate to withm =0 30 m sec-L at 16*c, the error decreasing to =0 20 m sec-t at about 74*c.
A polynoaual has been fitted to the data to permit calculation of the velocity at any temperature and pressure in the range investigated. The results at hsgh pnssure are generally in agreement with those obtamed by Wilson, although substantial differences at atme.W 4 and low pressures indicate some systematic error in Wilson's results.
The factors involved in making definitive rnessurements of higher accuracy are discussed.
- 1. latroducnoe Several measurements of the variation of the velocity of sound in water as a function of pressure and temperature have been made in recent years. Up to 1959 the accuracy of O
such measurements was rather limited, few investigators claiming a mammum error of b
tess than t 0 1 % (Holton 1951, Smith and I.awson 1954, Litovitz and Carnevale 1955.
Tait 1957). Companson of the values obtained at the same temperatures and pressures shows discrepancies exceeding this limit. In order to obtain more reliabic values. Wilson (1959) carned out an extensive series of measurements of the velocity of sound in distilled water at pressures up to 14 000lbin-8 in the temperature range 0-100*c. A maximum error of 0 01 % is clatmed for these results.
The acoustic system used by Wilson (1959) was similar to that developed by Greenspan and Tscluegg (1957) and used for the determination of the velocity of sound in water as a function of temperature at atmospheric pressure. Essentially their method involved a measurement of the transit time of a short transient sound pulse through a known liquid path length, the pulse being gener-+ed by shock excitation of a piezoelectric transducer.
Recent measurements by Barlow and Yazgan (1966) have shown that although the vanauon of velocity with temperature found by Greenspan and Tschiegg (1957) is sub-stantially correct. their absolute values are high by approximately 0 40 m sec-1 The technique developed by Barlow and Yazgan (1966) is based upon measurement of the total phase shift experienced by a modulated high-frequency pulse propagated through a known liquid path. This method is capable of high accuracy and. under suitable conditions.
absolute accuracies to within = 0 003 % are attainable. The results obtained over the temperature range 23-80*c are in agreement with those of McSkmun (1965), !!gunas, Kubilyunene and Yapertas (1964) and others. In paracular, the value of 1496 58 = 0 04 m sec-1 obtained at 25 000'c is in close agreement with the value of 1496 55 m sec-'
ecently found by Gucker. Chernick and Roy-Chowdhury (1966), using a diferent expert-mental technique of comparable accuracy.
The values of velocity obtained at atmospheric pressure by Wilson i 1959) are consistently higher than those found by Barlow and Yazgan i1966L The diderence increases from a value of 004 m sec-1 at about 74*C, where the velocity of sound in water passes througn i
Q 2 maximum. to approximately Om3 m sec-L at 25 000*c. For companson. the aosolute Q
accuracy claimed by Wilson 1959) corresponds to a maximum error of 0 !$ m sec-'
j
- 3 M5 I
646 f
A. J. Barlow and E. Ya:gan la view of the evidence for a systematic error in the results given by Wilson (1959),
possibly inherent in the type of acoustic system ernployed, there is a need for a detinitive series of measurements of the velocity of sound in water over wide ranges of temperature and pressure.
As a step towards this objective, measurements have been made over the temperature range 16-94*c at pressures from atmospheric to 11000 lb in-2
- 2. Experimental 2.1. Acoustic system and velocity measurement The fixed path acoustic system used to obtain the results given in }3 is similar to that developed by McSkimin (1957). The electronic system and method of velocity measure.
ment are considerably different, and have been described in detail in a previous publication (Barlow and Yazgan 19661 A diagram of the acoustic system is given in the figure.
~' -
k Eiectrical connectens
/
l l
I p
e i
' Seclung sctts i
Y lMh "$8es rocs
'l "r-- X-cut quart! crystel l
(
h o-Fused quertt suffer rod k
l l
n--0-reg seel l
m [
s i
h fbFesed quarts rmt specer l
1- *Terminstmq tud D
!Mi-I-- 5 prog
/
,/
/
/
/
--8ellow s
/
/
l
/
0 7 -tmq stel M
/
/
Acoustic system for measurement of velocity under high pressure.
The length of the liquid path is defined by a fused quartz ring spacer. The end surfaces of the buffer rod are optically flat to 0 1 pm and parallel to 5 seconds of angle. The faces of the ring spaar are similarly optically flat and parallel, and one end of the terminating rod is also optically flat. By wringing the cylinders to the faces of the ring spacer, a known and reproducible separation of the cylinders is obtained. Small radial grooves on opposite sides of the spacer allow the liquid to fill the space between the faces of the fused quartz rods. De effective separation of the two quartz cylinders was determined by rnaking an extensive series of toensurements of the velocity of sound in water at atmospheric pressure and comparing the results obtained with those using precision gauge blocks in place of the i
ring spacer (Barlow and Yazgan 1966). Thus, although the limited space in the high-4 pressure vessel precluded the direct use of gauge blocks to define the liquid path, the effective length of the ring spacer at atmospheric pressure was determined by reference to the previous measurements. By this method the separation was found to be 0 304 588 in., giving an acoustic path length of 1 547107 cm. This value is in excellent agreement with the results s
(
of a series of measurements which have been made by the Metrology Division of the
Pressure dependence of the s;elocsty of sound in water as afuncison of temperature 647 O
Nauonal Engmeeting Laboratory, of the thickness of the spacer at several points.These measurements gave an average thickness of 0 304 580 :: 0 000010 in.
As shown in the figure, the acoustic system was mounted vertically in a holder inside the pressure vessel. A light spring was used to apply a slight axial force to the terminating rod, chie8y to prevent damage should the parts of the acoustic system become separated.
This spring was not such as to cause appreciable compression of the fused quartz ring The water sample was separated from the pressure transmitting fluid by means of spacer.
O% rings, and a bellows allowed compression of the sample.
2.2. High-pressure apparatu.s and temperature measurement A conventional arrangement of the high pressure system was employed. The pressure was generated by a hand pump and rnonitored by a Bourdon gauge. The pressure vessel had an internal working space 11 in, diameter by 10 in. long, which was sufficient to contain the acoustic system and a special thermocouple. Pressure measurements were made by means of a dead weight tester (Barnet Instruments Ltd. type 4540), for which a maximum error of 3 parts in 104 is claimed. This instrument was correctly calibrated for the local gravitational factor of 981 55 cm sec-2, and the readings in bars were converted to Ib in-2 using the relauon 1 bar.= 14 504 lb in-2 A silicone liquid was used as the pressure transmitting fluid.
The pressure vessel was 6tted with a heating jacket, and the temperature was stabilized by a sensitive controller based upon a design by Tempest (1963). A thermistor in the inner shell of the heating jacket was used as the sensing element.
The temperature in the pressure vessel was determined by the use of an iron-constantan thermocouple arranged so that the thermocouple junction was as near as possible to the fused quartz ring spacer, although outside the water sample. This thermocouple was calibrated in the open pressure vessel directly against a platinum resistance thermometer T
certified by the National Physical Laboratory. Measurements were made at a number of points in the range 20-100*c. Checks were made of the temperature variation with thermocouple position inside the vessel and it was found that the variations were insigni-ficant. It is estimated that the overall accuracy of temperature meastatement was such that a maxunum error of i 0 03 desc was possible. For measurements made under pressure.
the readings of the potentiometer used to determine the thermocouple e.m.f. were corrected for the pressure dependence of the e.m.f.
The results of Bridgman (1918) for an iron-constantan thermocouple were used to make these corrections: in general the corrections were small or insignificant.
2.3, Water sample Doubly distilled water was used throughout. This degree of purification was considered adequate in view of the negligible effect of small quantities of impurities on velocity (Weissler and Del Grosso 1951, Del Grosso. Smura and Fougere 1954). No attempt was made to free the water of dissolved air, since the effect on velocity is probably less than 1 part in 106 at atmospheric pressure (Greenspan and Tschiegg 1956). However, care was taken to prevent the inclusion of air bubbles when filling the sample container so that the sample measured was saturated with air at atmospheric pressure.
2.4. Esperimentalprocedure Measurements were first made of the vdocity of sound in water at atmospheric pressure and a temperature of about 20*c. with the sample in the pressure vessel and using the associated temperature measurement and con:rol apparatus. The results at nominal operating frequencies of 10 and 30 Mcis were in a;'reement to within 0 06 m sec-8. after applying a correction for the effects of diffraction. Die value at 30 Mc/s was found to be only 0 02 m sec-2 less than the value obtamed by extra,,olation of the results of Barlow and Yazgan (1966) which were obtained over the temperatcre range 23-80*c. At about
648
(
A. L Barlow and E Ya:gan v
20"c an error of 0 03 desc corresponds to an error in velocity of about 010 m sec-i.
the estimated limit of temperature error given in s 2.2 is therefore substantiated.
A series of velocity measurements was then obtained at a temperature of about 16 6'c over the pressure range from atmospheric to 1000 bars, using a nominal operaung frequ of 30 Mets.
Measurements were made at intervals of 100 bars for increasing and decreasing Although pressure changes were made very slowly, about one hour was required pressures.
for the restoration of thermal equilibrium after each pressure change. Slight pressure readjustments were made during this time to confine readings to exact 100 bar intervals and to allow for the very slight !cakage in the dead weight tester. This leakage was greater at i
the higher pressures and some instability at 900 and 1000 bars was found.
Accordingly, the pressure range was restncted to 800 bars. Only the results of a series of measurements in which velocity values forincreasing and decreasing pressures agreed to within 0 20 m see-L were regarded as acceptable, and the average value was taken at each pressure.
For temperatures above about 30'c it was thought undesirable to make measurements at atmospheric pressure since the expansion of the enclosed water sample could distort the bellows and a slight excess pressure may have given unreliable values of velocity:
A pressure of 100 bars was therefore applied before increasing the temperature above about 30*c and all initial readings were obtained at this pressure.
- 3. Resmita
' Die experimental results are given in table 1.
Except for the six values given for tem-peratutes above about 30*c at atmospheric pressure, each value of velocity is the average of readings taken with increasing and decreasing pressure obtained at a nominal frequency of 30 Mets.
A small correction, equivalent to a maxunum of 0 05 m sec-1, has been applied to account for the change in length of the fused quartz ring spacer with temperature.
O the spacer is compressed by the hydrostatic pressure, a correction amounting to a maxtmum Since of I 24 m sec-1 at 800 bars has also been applied to reduce the apparent velocity to the 1
true value.
This correction has been based upon a value of 5 35 x 10*lbin-r for the bulk modulus of fused quartz obtamed from published elastic constants (American Institute l
of Physics Handbook 1957) and from data given by McSkimin (1957).
This value has been taken to apply over the temperature and pressure range of measurement the amount of the correction is correct to better than 62% over the range (McSbmm 1957).
A correction of 0 02 m sec-1 for diffraction effects has also been applied to the data, following the theoretical results of Bass and Williams (quoted by McSkimin 1961), which have been confirmed experunentally by Barlow and Yazgan (1966). Errors arising from other sources, for example the differential pressure t. cross the bellows, are negligible, and corrections are therefore unnecessary.
- 4. Analysis of exgU results Following the procedure adopted by Wilson (1959) an equation of the form V = ae a a:T - asT: e asT3 -- a4T4 e asT5 m see-t II) where at = bro - b,if - berP2 a besP3 a b,4P4 12) has been fitted to the results. The coefficients of equation (2) are given in table 2.
In these equations T is the temperature in *c and P is the absolute pressure in umu of 10'Ib in-8 The coefficients are valid over the range of measurement 15-95'c. and from atmospheric pressure to just over 108 lb in-8 As a check on the fitting of these equations recalculated values of the velocity at the temperatures and pressures of measurement have been obtained and compared with the original data. The greatest deviation was found to be 019 m sec-4 with an average of O
0 065 m sec-1. the deviations being randomly distnbuted throughout the temperature and p
ressure range.
w U
J.
N b
i
,N Table 1.
Emperimiental values of the velocity of sound (no sec 8) la water as a fiancelon of tesaperature asmi preswre Tempe:ature (T) 16 565 30 680 39 93J 47 990 60 590 71 350 78 850 93-370 h
l*senuse (Ib in 2)
R 107 1471 19 1510 58 1528 66 1540 16 1551 24 1554-91 1554 64 1548 26 k
1450 4 I487 79 1527 81 1546-04 1557 93 1569 83 1574 02 1574 27 1569 01 2900 8 1504 25 1544-52 1563 32 1575 42 1587 92 1592 88 1593 45 1589 12 E'
4351-2 1520 73 1561 58 1580 60 1593 05 1605 83 1611 44 1612 41 1609 20 5801 6 1537 78 1578 37 1597 51 1610 07 1623 37 1629 54 1631 05 1628 23 7252 0 1554 64 1595 30 1614 61 1627 21 1640 87 1647 08 1648 99 1647 18 g
j 8702 4 1571 82 1611-78 1631 22 1644 31 1657- %
1664 66 1666 75 1665 92 10152 11 1589 13 1628 82 1647 94 1660 86 1675 03 1681 99 1684 40 1683 93 h
18603-2 1605-82 1645 35 1664 43 1677 46 1691 75 1699 06 1701-55 1702-40 7
3 Table 2.
CocfNcients of she ceguations as " 64a l-bear i 642P8 I b42F8 I b.eP8f b..
b.:
bas on bs:
j o
1401 968 883-73652 49 69035
+20 51695
-33 83572 I
i5 051718 14 325934
- 10 00579 13 787598 l1-452633 5.
g 2
5 8485264 to
~ 2 029127 x 10 a g.5 478028 x 10 ~8
-3 373606x 10 a i 7 830629x 10 3 k
3 1 3-381084 s10
- I 4 493318 x 10 3 1 290872 x 10 a g 9 460639x 10 3 1 245880): 10 3 E-4 1 484859xto *
--4 498863 x 10
- 1 1 357265 x 10 *
-I-090535 x 10 i 1 984527xto
- 5 13 091069 <10
- I I 674%2x 10 7
-5 229535 x 10 7 14 441468 x 10 7 9-317469 -10 8 4
i l'- u. I air i asT: I a4T3 I a:T4 I asT*m sec-8, where Tis in *c and f in units of 1051b ia-* abwlute.
R J
4 0
A i
+
o E
.. ~ -
6$0 A. J. Barlow and E. Ya:gan
- 5. Discussion 4
The main errors in the results given anse from the uncertainties in absolute pressure and temperature measurement.
The possible error of 0 03 degc in temperature measure-ment corresponds to an error of =010 msec-1 at about 16*c decreasing to zero at about 74*c, where the velocity passes through a maximum. Although the dead-weight tester used is capable of at solute pressure determination to i3 parts in l04, a realistic estimate of the precision obtained indicates that it is reasonable to allow limits of =10lb in-s on pressure readings throughout the rangc. This uncertainty arises from the difficulty found i
in maintaining constancy of pressure at the limit of sensitivity of the instrument.
The absolute pressure is then accurate to 13 lb in-2 overall corresponding to a possible error in velocity of 60 13 m sec-1 As described in the previous account of the experimental technique for velocity measure-ment (Barlow and Yazgan 1966), random errors in velocity arising from the electncal measurements are small and have a maximum of i0 04 m sec-L with a standard deviation of 0 02 msec-1 The sum of the random errors is therefore iO 24 msec-1 at room temperature, decreasing to m0 14 m sec-1 at about 74*c. Examination of the experimental data shows that the values obtained deviate from smooth curves by random amounts which are less than these estimates. Except for a possible uncertainty of about I part in 10'in the length of the liquid path defined by the fused quartz ring spacer and possibly slight errors in the variation of this length with pressure, systematic errors are, by com.
parison, negligible. The results given are therefore estimated to be accurate to within iO 30 m sec-1 around 15*c and to within 60 20 m sec-1 around 74*c. A comparison of the results with those obtained by Wilson (1959) shows significant differences between the values obtained at atmospheric pressure, and diferences in the variation with pressure at constant temperature. At atmospheric pressure the present results are some 0 65 m sec-t lower around 20*c and 0 34 msec-1 around 70*c. These differences become gradually h
less with incstasing pressund are change sign at about 10 000 lb in-8 at 20*c and 5000 lb in-8 w/
at 90*c. Thus, although the values at atmospheric pressure indicate a systematic error in Wilson's results, over most of the pressure range there is agreement within the combined experimental error limits between the two sets of values. It is possible that the systematic error is reduced by increase of temperature and pressure, or that the diferences are reduced by small unsuspected temperature or pressure dependent errors in either the present results or those of Wilson.
In order to obtain definitive values of the velocity of sound in water as a function of pressure and temperature, significantly better than the existing data, further experimental I
work is required. Absolute velocity measurements accurate to about 3 parts in 108 are now possible without undue diflir.ulty. The reduction of errors arising from inaccuracies in pressure and temperature measurement to this level or less would involve considerable l-experimental problems. It is preferable to define the liquid path by precision gauge l
blocks; the resulting increase in the diameter of the acoustic system would entail a larger pressure vessel. Absolute measurement and stabilization of the temperature of the water sarnple to 60 001 desc is desirable, and can only be achieved by immersion of the vessel in a large constant temperature bath and by the use of a platinum resistance thermometer in conjunction with a Smith bridge or similar instrument. The greatest problem arises in absolute pressure measurement. Direct use of a dead weight tester is undesirable since, although the time required for the measurement of velocity is only a few minutes, the slight leakage in this time rnay give some uncertainty in pressure readings. A sensitive secondary gauge is preferable, but reduction of the absolute error in pr. v.ure to a maxirnum of I or 21b in-* at about 1041b in-2 is extremely difficult and is close to the limit attainable at the present stage of development of high pressure measurement.
AC'7 Thanks are due to Professor L !.amb for his encouragement and help in this work and i
for the provision of facilities. The work was supported by a contract with the Nat onal Engmeering Laboratory, Ministry of Technology. The authors are grateful to Mr. A. T. J.
Hayward and the Metrology Division of the Laboratory for their kind assistance.
Pressure dependence of the o elocity ofsowed m water as a timctiort of temperature 65I
['
Refereoces
(
BAmLOW. A. 3.. and YAZoAP.. E., l966. Brit. /. Appl. Phvs.. 17. 807-19 BarocMAN. P. W.,1918 Proc. Amer. Acad. Arts Sci.. 53,269-386.
Det Gaosso. V. A., SuunA, E. J., and Fouctas. P. F 1954. U.S. Naval Res. Lab. Rep., No. 4439.
GassNsPAN. M., and Tsca sco, C. E.,1956. J. Acoust. Soc. Amer., 28. 501.
1957. J. Res. Nat. Bur. Stand.. 59. 249-54: Rev. Sci. Instrum., 28,897-90\\.
GucKen, F.T., CHzaster. C. L, and Roy.Caowowcay, P. 1966, Proc. Nat. Acad. Sci..
HoLTON, G.,1951,1. Appl. Phys., 22, 1407-13.
55.12-19.
It.cuNAs. V., Kvast.YUNENs. O., and YArsnTAs, A.,19(>4 Soviet Phys.-Acoust.,10. 44-8.
Lrrovrrz. T. A., and CAaNtvALs. E. H.,1955.1. Appl. Phys., 26. 816-20.
McSK MtN, H. J.,1957, J. Acoust. Soc. Amer., 29, i185-92.
1%l. J. Acostt. Soc. Amer., 33, 539.
- 1%5. J. Acoust. Soc. Amer.. 37,325-8.
SurrH. A. H., and L4wsoN. A. W.,1954, /. Chem. Phys., 22, 351-9.
TArr, R. [.,1957, Acustica, 7,193-200.
TsunsT, W.,1963, Electron. Entar. 35, 314-4.
Wr tstra. A., and Det Gnosso, V, A.,1951, J. Acoust. Soc. Amer.. 23. 219-23.
Wit. son, W. D.,1959, / Acoust. Soc. Amer.. 31,1067-72.
oO
onti. L sPPt.. PHYS.. (96o. Vol 17 O
Phase chan8e method for the measurement of a
ultrasonic wave velocity and a determination of the speed of sound in water A. J. BARLOW and E. YAZGAN Department of Electncal Engineenng. University of Glasgow MS. received 19th.Vovember i965. m revisedform 15th February 1966 Abstract.
A description is given of a technique for measuring the ultrasonic wave velocity in liquids, based upon the meassarement of the total phase shtft through a liquid path at frequencies in the region of 10 Mets.
A tixed. path acoustic system is employed and the method is suitable for use over wide ranges of temperature and hydrostatic pressure.
i The phase difference between a modulated r.f. pulse propagated through the known liquid path and the incident pulse retiected from a solid-liquid interface is determmed by cancelling each pulse separately asamst a continuous-wave signal adjustable in phase and amplitude.
From two such measurements at slightly different frequencies the total phase shift in the liquid may be calculated.
h technique is capable of very high accuracy and under suitable conditions an absolute accuracy to better than 3 parts in 10' in velocity is obtainable.
Measurements of the velocity of sound in water have been made over the temperature range 23-80*c and the results are presented as a fifth. degree polynomsal. A value of 1496 58 ::: 004 msee-t at 2.5000*c is obtained.
- 1. Introduction Any study of experimental methods for the determination of the velocity of sound in liquids leads inevitably to a comparison of the values obtained for water in view of the many measurements of this basic reference value made during the past thirty years.
A summary of results reported up to 1954 is given by Del Grosso. Smura and Fougere (1954).
The results show considerable scatter, and more recent measurements made by means of experimental techniques apparently capable of high accuracy have not fully resolved the discrepancies. The present situation is shown in table 1.
Only those results are given for which an accuracy to better than 6 003% is claimed. Four of these values are in Table 1.
Values of the velocity of sound in water at 15 00*C Reference Experimental technique Velocity Limit of (m sec-')
error claimed (m sec-')
Barthel and Nolle (1952)
Double crystalinterferometer. 3-25 Mcis.
1496 :t
=0 20 vanable path of a few em Del Grosso er al. (1954)
Single crystal interferometer.1 Mcis.
1497 41:
=0 05 vanable path of a few cm Greenspan and Tschaegg (1957) Time delay, timed path 20 cm 1497 00
=0-05 Brooks (1960)
Time delay. vanable path I-m 149652
=0 34 Neubauer and Dragonette(19641 Time delay. differennal path about I m 149 H 0 20 20 Ilgunas er al.
Single crystal mterferometer.1-12 Mets.
1496 594 20 15 vanable path of a few em McSktmm i1965)
Modulated pulse cancellation. N) Mc.s.
1496 65 20 10 rixed path ofless than I cm
- Extrapolated from 24 76'c: : extrapolated from 2000*c: )extraootated from 17 !0'c. usms data of Greenspan and Tsensegg i19571 m each case.
f.
39 407
308
.L L Barlow and E. Ya:gan agreement within the limits of stated error, those of Brooks (1960). Neubauer and Dragon.
ette (1964). !!gunas, Kubilyunene and Yapertas (1964) and McSkimin (1965).
Two other results, for which the highest accuracies are claimed. those of Del Grosso et al. (1954) and Greenspan and Tschiegg (1957) dirTer considerably.
Several factors may be readily excluded as possible reasons for these differences.
variation of velocity with temperature around 25'c is 2 7 msec-1degc-L (Greenspan and The Tschiegg 1957), thus the variations in the values are too large to be explicable as tem Deviations from absolute purity of the samples of water used are unlikely ature errors.
to be sources of substantial errors.
1956) to increase the velocity of sound in water by less than a few p Small quantities of other impurities have been shown to have negligible effect (Del Grosso et al.
1954. Weissier and Del Grosso 1951).
On the evidence available it therefore seems probable that certain experimental techn including those of Del Grosso et al. (1954) and Greenspan and Tschiegg (1957), are not suitable for absolute measurements of high precision. Systems involving steady-state sinusoidal wave propagation are preferable to those involving the propagation of transient waveforms, or step functions, over distances appreciably less than I metre.
Error estima-tion in the latter systems is difficult since pulses may be distorted by resonances in trans-ducers and by different absorptions applying to each Fourier component of the transient waveforms.
In view of the importance of diffraction of the acoustic wave on observed velocities. the frequency of operation and dimensions of the acoustic system should be so chosen that diffraction effects are small or negligible.
Calculations of diffraction corrections have been given by McSkimin (1960), Bass and Williams (reported by McSkimin 1961) and Del Grosso (1964). Furthermore. experimental techniques requiring only small quantities of liquid are preferable since temperature stabilization is simplified and measurements under high hydrostatic pressure are possible. He choice of a fixed path acoustic system reduces the problems of mechanical alignment and further facilitates the study of velocity as a function of pressure.
s A fixed-path acoustic system based on the design of Schulz (1955), as developed by McSkimin (1957), fulfils the foregoing conditions and has been taken as the basis of the experimental technique used in the present work. However, a new method of measurement based upon a determination of the total phase shift in the liquid path has been devised.
His method gives a differential accuracy comparable with that of the ' sing-around' tech-nique used by Greenspan and Tschiegg (1957) together with a high absolute accuracy.
De method uses a continuous sinusoidal waveform gated to provide a pulse of r.f.
oscillations, which is propagated as an acoustic wave through the liquid path. The pulse duration is sufficient for steady-state conditions to be attained after the decay of the initial transients.
The time taken for the acoustic pulse to travel through the liquid path is determined by phase comparison with the original continuous waveform. Essentially, the method combines the high resolution and accuracy of a continuous-wave interference measurernent with the advantages of a pulse propagation technique. A detailed description of the system is given in the following section.
- 2. Experimental system 2.l.
Mode of operation A schematic diagram of the experimental system is given in figure 1.
A continuous wave signal from the crystal controlled oscillator ai s passed through a buffer amplifier b to a i
diode gating circuit c.
De gate is opened by a pulse of a few microseconds duration to produce a short wavetrain which. after further amplification (d), is used to excite the X. cut quartz crystal transducer of the acoustic system. Longitudinal waves generated by the transducer propagate in the fused quartz rod and are partly reficcted at the quartz liquid interface.
Part of the incident wave propagates through the liquid and, after rerfection from the boundary between the liquid and the terminatmg fused quartz rod follows the
Sound relacity m water by pha.se measurement rechmque 809
'/
- Cout.flC A
. u P=.
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=ou 10..., y '.
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'b 9tFEREnct cuann V U
- cumaum, b W cin.m cm.,
inum.. incu un um. inc..
sill.,seg 49 100 cm 8'H."St if 10 cm Figure 1.
Schematic diagram of experimental system.
first reflected wave in re-exciting the transducer. The output from the acoustic system is passed through a buffer amplifier e and into the receiver f.
The received pulse train is displayed on the oscilloscope. Apart from the transmitter pulse, the display shows two main pulses, the first from the fused-quartz-liquid interface and the second resulting from one double transit of the liquid path by the sound wave. The total phase difference between the high frequency content of these two pulses is a function of the velocity of sound in the liquid.
In addition the display will contain subsequent pulses which have made further transits of the liquid path or the buffer rod. In the present system these t
pulses are irrelevant.
The remaining part of the system provides a reference signal for measuring the phase difference due to the liquid path.
A signal from the oscillator at passes through a buffer amplifier g to a simple uncalibrated phase shifting network h.
This is followed by a precision adjustable delay line j capable of providing a known and continuously variable phase shift. Accurately matched source and load impedances are used to minimize standing waves on the delay line. The output from the line is further amplified (1), con-trolled in amplitude by a piston attenuator m, and passed through a buffer amplifier n into the receiver.
- 2. 2.
Measurement procedure The phase difference between the waveform of the pulse reflected from the interface and that which has made one double transit of the liquid path is determined by cancelling each separately against the reference signal. Initially, the uncalibrated phase shifter and the attenuator are adjusted to give cancellation of the interface pulse. "llie calibrated delay line and the attenuator are then adjusted to give cancellation of the second pulse. The change in setting of the delay line gives the fractional part of a cycle or wavelength ditierence between the two pulses, but does not indicate the number of complete cycles forming the major part of the total phase difference. This number may be evaluated if the measurement is repeated at a slightly different frequency, obtained froni a second oscillator a,.
The two oscillators generate frequenciesfi and fe, differing in frequency only by a few parts m a thousand. Thus a principal advantage of the system is that it is essentially a narrow-band technique. The electronic circuits can therefore be designed so that the variation in overall phase shift on changmg frequency is negligible, elimmating the possibility of errors arising on this account. Furthermore, the mean frequency of operation can be chosen to comcide with the resonant frequency of the transducer. or with odd harmonics
810 A. J. Barlow and E. Ya:gan of this frequency. ensuring a high signal-to-noise ratio in the received pulses.
Previously developed systems usmg pulse cancellation techniques generally involve determination of several cancellation frequencies over a comparatively wide bandwidth. The present system
'-)
avoids the experimental difficulties inherent in this procedure and virtually eliminates the possibility of errors arising from frequency-dependent phase shifts in the electronic appara-In addition, the need for the sound wave to make only one double transit of a short tus.
liquid path makes this system particularly suitable for the measurement of highly a liquids.
The high precision of the technique arises from the separate evaluation of the number o complete wavelengths in the liquid path and of the remaining fractional part of a wave.
length.
De former, typically 50-300 with the frequencies and liquid paths used in the present work, is determined exactly.
The fractional part of a wavelength is determined to an accuracy governed by the measurement of the phase shift, given in turn by the chang in the delay line setting.
His measurement can be made with an accuracy to better than 3*, givmg approximately 3 parts in 108 overall.
Changes in velocity of this magnitude can therefore be detected; the absolute acc depends also on other factors discussed in s6.
- 3. Descripden of apparate Two completely separate sets of apparatus have been constructed and used in the measure.
ment of the velocity of sound in water.
One of thesesets operates at frequencies of 30000280 and 29 932800 Mc/s, the other at 10 011780 and 9 912014 Mc/s. These fre-quencies are measured by an electronic counter checked against standard frequency trans.
missions.
De use of a continuous wave reference signal, controllable in phase and amplitude, necessitates particularly thorough screening of the basic oscillators and of all units preceding the receiver. In addition, stability is of prime importance. The following descriptions give the relevant details of each unit.
3.1.
Oscillators Standard circuiu have been used for the two crystal controlled oscillators required in each frequency range.
Colpitts circuits using resonant quartz crystals operating in the fundamental mode are satisfactory at 10 Mc/s; at 30 Mc/s third-overtone crystals operating in a Butler circuit are preferable.
The crystals used are AT cut quartz designed for zero temperature coefficient around 25'c, and temperature stabilization is therefore not required.
Each oscillator provides an output of approximately 1 y r.m.s.
5 3.2.
Bufer amplifiers b andg Dese buffers eliminate any possibility ofinteraction between the ' acoustic' and reference signal channels. Each consists of a single broad band stage with tuned output, having a voltage gain of about 3 and a bandwidth of at least 25% of operating frequency.
- 3. 3.
Diode gating circuit c This unit consists of a balanced four-diode switching network and is operated by a positive pulse of 100 v amplitude. During the application of the pulse, typically of 5*sec duration, an output of 0 6 v peak to-peak is obtained. In the 'off' condition the output is less than 10-5 of this value. This rejection ratio in the gating unit is sufficient since the overall rejection ratio of the transmitter channel is improved by class C operation of the following ampli8er.
3.4.
Transmitting amplyfer J The transmitting amplifier consists of two broad band class A stages followed by a class C push-pull output stage. The circuit is aligned to give a substantially tlat response around the nominal operating frequency, to ensure negligible variation m the overall phase shift between the two slightly differing actual operstmg frequencies, in the 'on' state of 1
r w-r c
e- - - -
Sound celocity m water by phase measurement teciumque 811 l
r the gating unit a minimum of 25 v r.m.s. is generated across the transducer crystal. m the
\\
'off' state the output is less than 2u.
v
- 3. 5.
Bufer amplifer e This buffer serves to isolate the acoustic system from the continuous wave signal present i
at the receiver input. A single untuned pentode stage is used and the gain of the circuit l
is approximately unity.
3.6.
Phase shift channel The uncalibrated phase shifter h consists of a conventional series RC circuit supplied from a low-impedance balanced transformer of 1.1 : I ratio. A switch preceding the transformer permits 180* phase change. and adequate variation of phase within this limit is given by values of R = 0-SkQ and C = 5-100 pr.
This circuit is followed by a single stage amplifier, the primary function of which is to provide a source impedance equal to the characteristic impedance of the calibrated delay line. Since the impedance of the delay cable is almost entirely resistive (7170) a ' wire-in' triode of very low output capacitance is used with a non-inductive anode load resistor of 72 0.
The cable is connected directly to the anode lead of the valve in order to minimize wiring capacitances. Series capacitors of appreciable reactance in the line are avoided by supplying the line drive circuit from a negative h.t. supply, ne delay line consists of precision coaxial cable (Uniradio 21) with the lengths in circuit joined by s.h.f. connectors (Plessey CZ70157 and CZ70159). By arranging the cable in two series of lengths, successive lengths in the first decade differing by '100 cm and in the second by 10 cm. only four pairs of connectors are in circuit for any setting. De design of these connectors makes it possible to adjust the length of each cable to i 01 cm. A constant-impedance telescopic line, having the same characteristic impedance as the cable, is used for fme adjustment of the overall delay. This line has a maximum variation equivalent to 12 cm length of the cable.
V The line is terminated by a matched resistance at the input of a single-stage wide-band amplifier with a gain of approximately unity. As in the line drive circuit, considerable care is necessary to minimize stray capacitance and inductance; a ' wire in' pentode of very low input capacitance is used.
3.7.
Piston attenuator m and compensating amplifer i The line termination stage is followed by a wide band amplifer having a gain of some 40 da. His amplifier compensates part of the insertion loss of the piston attenuator.
The second stage of the amplifier is tuned, the coil forming the launching coil of the attenu-ator. The attenuator is a circular tube of 0 750 in. internal diameter; operation is in the H (least attenuation) mode. A Faraday screen is fitted to eliminate other modes and to assist in ensuring the absence of phase shift along the waveguide. His essential require-ment is also ensured by maintaining sufficient spacing betweert the launching and pickup coils to give a minimum insertion loss of 50 da.
He signal from the attenuator is passed through the buffer amplifier n and added to the output of buffer e at the input of the receiver. nese two buffer amplifiers are the only active circuits in the system in which the signal level varies between initial and final measure.
ments. By making them identical any variation of overall phase shift with signal level is automatically balanced since the signal levels in each are identical at cancellation.
3.8.
Receiver /
The receiver is a conventional fixed frequency tuned amplifier having a variable gain of 80 da maximum and a bandwidth of 1 Mc/s. The circuit is designed for rapid recovery from overload so that maximum sensitivity is restored less than 10 sec after the high-voltage transmitter pulse. The receiver output is displayed without demodulation on a wide band oscilloscope (Tektronix 545A).
814 A. L Barlow and E. Ya:gan s
Table 2.
Specincntion of gauge blocks Type Supplier Thickness Stated max.
Exp. coett < [0*
CO*c) error (degc-')
(parts m 108)
Chromium carbide C. E. Johansson Ltd. 0200000in.
=10 75 Quality AA 0 300000in.
= 067 75 Fused quartz E. Leitz Ltd.
3 00000mm
=3 53 0 43 Class O 5 50000mm
= 2-02 0 43 6 50000mm
= l 74 0 43 The length of the liquid path was defmed by precision gauge blocks. Table 2 gives the specifications of these blocks. Three identical blocks were optically wrung on to the buffer rod, well clear of the path of the ultrasonic beam, and the surface of the termination rod was in turn wrung on to the blocks. This process required considerable care, but was found to give values of velocity repeatable within experimental error, although the system was assembled and dismantled several times. Only a slight axial pressure was applied to the assembly, chiefly to prevent damage in the event of the system coming apart. Errors arising from compression of the blocks are therefore negligible.
The acoustic system was placed horizontally in the liquid sample to permit free circulation through the gap between buffer and termination rods. A holder similar to that described by McSkimin (1965) was used to support the system and to enclose the transducer end of De axis of the acoustic path was approximately 10 cm below the water the buffer rod.
level.
1
- 4. 2.
Water sample and temperature measurement Doubly distilled water was used throughout the measurements, this degree of purification being considered adequate in view of the negligible effects of dissolved air (Greenspan and Tschiegg 1956) and of very small amounts of impurity (Weinier sud Del Grosso 1951 Del Grosso et al.1954). The specunes was contained in a small tank surrounded by a large bath.
Conventional controls were used to stabilize the temperature of the water bath to a few millidegrees, ne specunen was gently stirred and precautions were taken to minimize cooling by evaporation. He temperature of the specimen was determined by a platinum resistance thermometer situated close to the acoustic path. This thermometer was calibrated, by the National Physical Laboratory, shortly before making the series of.
Resistances were determined by means of a Smith Bridge to a precision measurements.
corresponding to i 0 001 desc. No variations in temperature around the acoustic path could be detected and the temperature of the specimen remained constant to better than 0 002 desc during a velocity measurement at a given temperature. The average ofinitial and final readings was taken as the temperature of measurement. As a check on the thermometer calibration, a second platinum resistance thermometer was used, the tempera-tures given by the two thermometers being equal within the accuracy of measurement.
The absolute accuracy of tenvrature measurement is estimated to be better than 0 003 desc. This figure corresponos to a velocity error of s 0 8 cmsec-1 around 25'c. reducing to zero at 74*c where the velocity in water passes through a maximum.
I
- 4. 3.
Efect ofdgraction on observed velocities The excess velocity due to diffraction has been calculated, for each frequency and liquid path length, by three distinct methods. These calculations are based upon the empirical curve given by McSkimin (1960), the theoretical results of Bass and Williams quoted by McSkimin (1961) and the tabulated phase errors given by Del Grosso (1964). The results are shown in table 3.
{
Del Grosso has computed phase errors as a function of:
2 Ala, where : is the path length and a is the source radius, for values of 2ra/A up to 100w. For the source radius of 0 625 cm
.___________m_._
Sound relocity m water by ph'ase measurement technique
$15
(
Tab 6e 3.
Excess velocity resulting from diffraerion Values calculated for a beam diameter of 12 3 mm Frequency 1.iquid Calculated excess velocity (msec-')
path Bass and Williams. McSkimin Del Grosso see McSkimin (1961)
(1960)
(1964) 30 l3mm 0 019 0020 0-028 30 1I mm 0 021 0421 0 030 30 6mm 0028 0028 0444 30 0 6 in.
0 017 0-019 0026 30 0-4 in.
0 021 0422 0 031 10
- 13 mm 0 101 0 143 0 144 used in the present work, the values of 2waiA are 133w and 249w for frequencies of 10 and 30 Mets respectively. Although Del Grosso (1964), confirming the earlier work of Williams (1951), states that for 2wa/A > 50 the phase error is substantially independent of this parameter, there is some indication that for values of:A/a2 < 01 the phase error decreases slightly for values of 2wa/A exceeding 100w. The results in table 3 have been calculated assuming 2wa/A = 100w; it is therefore probable that the true values are slightly less than those given in the table. Accordingly, in the present work the excess velocity caused by distaction has been calculated using the theoretical results of Bass and Williams, quoted by McSkimin (1961). Table 3 shows that at 30 Mc/s the diferences between the correction calculated from the experimental results obtained by McSkimin (1960) and the corrections calculated using Bass and Williams' theory are negligible.
4.4.
Errors arising from phase change measurements Errors in the measurement cf the fractional part of a wavelength in the acoustic path may arise in three ways: from the uncertainty in the lengths of cable, from the setting of i
cancellation points, and by deviations from linearity of the phase characteristic of the line.
The length of each cable was adjusted to i 01 cm; the maximum possible error on changing from one pair of cables to a second pair is therefore 04cm. At 30 Mc/s the corresponding phase error is t 0 22*.
It was found possible to determine cancellation points to about i t' of phase angle; the maximum possible error between two settings is therefore t }'.
Deviations from linearity of phase change on varying the length of the line arise from standing-wave effects caused by mismatching at the termination and source of the line.
To a first approximation, the error e associated with a phase change e is given by (A. J. Barlow 1959 Ph.D. Thesis, London University) 4 e = s 2r. rte (14) where r, and ri are the magnitudes of the reflection coefficients at the source and ioad re.
spectively. Redection occurs mainly as a result of reactive mismatch. The maximum error occurs when # = 180'. For the delay system used (Barlow 1959 Ph.D. Thesis),
2r ri < 001 at 30 Mc/s; the maximum phase error is then less than = 18*.
The total maximum possible error m a particular determination of e is therefore approxi-3 mately i 2 7'.
For the three longest liquid paths and a frequency of 30 Mc/s this figure corresponds to a maximum possible error in velocity of about = 0 05 msec-5 Errors in the determination of the length of cable equivalent to one wavelength are negligible. since several measuremenu were taken at each frequencyfi andf, using different pairs of cables, and the average value was calculated.
- 4. 5.
Experimental results Typical results for the values of the velocity of sound in twice distilled water are given in table 4 Each value represents the average, given to the nearest 001 msec-5. of the l
two results obtained from measurements made at the slightly differing frequenciesfi ndfi.
a j
in general, the two results differed by less than 003 msec-8 The values shown have been
= =.
D 816 b
A. J. Barlow and E. Ya:gan Table 4.
Experimental values of the velocity of sound in distilled water (a) Frequency 30 Mc/s,6 5 mm gauge blocks Temperature velocity A
Average A Temperature Velocity A
Average A
('c)
(m sec-')
(m sec-')
(m sec-')
('c)
(m sec-')
(m see-')
(m sec-')
23 503 1492 49 0 41 45 127 1536 46 0 43 24-037 1493 94 0 46 49 966 1542 43 0 40 24 905 1496 34 0-40 55 105 1547 36 0 43 25 125 1496 90 0 40 64 980 1553 35 0 40 25 380 1497 59 0 43 70050 1554 75 0 38 25 707 1498 43 0 43 0 40 25 812 1498 73 0 41 71 160 1554 89 0 40 25 910 1498 99 0 40 72480 1554 98 0 39 0 42 73450 1555 42 0 42 27 570 1503 24 0 37 73 900 1555-07 0-40 27 935 1504 10 0-40 74 200 1555 09 0 38 29 920 1508 84 0 41 75440 1555 42 0 43 l
29 323 1507 49 0 39 76 220 1555 00 0 41 29 985 1509 02 0 38 77 030 1554 92 0 39 i
35 420 1519 72 0 44 8 310 1554 70 0 42 l
39 990 1528 78 0 38
'/9 115 1554 61 0 39 80445 1554 39 0-41 0 40 (b) Frequency 10 Mc/s,6 5 mm sause blocks Temperature Velocity A
Average A Temperature Velocity A
Average A
('c)
(msec-') (msec-8) (m sec-')
('c)
(m sec-')
(m sec-')
(m sec-8) 23 340 1492 40 0 44 55446 1547 36 0 39 g
j 25 307 1497 37 0 44 62 780 1552 33 0 47 v
25 425 1497 72 0 40 0 42 25 562 1498 03 0 45 70 950 1554 88 0 38 25 705 1498 45 0 41 74 220 1555 48 0 39 0 43 78 130 1554 73 0 43 34 990 1319 73 0 37 0-40 46 131 1537 77 0 46 corrected for the effect of diffraction, and the expansion of the gauge blocks with increasing temperature has also been taken into account. Table 4 also shows the amount a msec-'
by which these values are lower than those calculated from the results obtained by Green-span and Tschiegg (1957). The rate of variation with temperature found by Greenspan and Tschiegg is generally regarded as being substantially correct (McSkimin 1965). De average values of A for temperature arouno 25 and 74'c and for the intermediate range are also given.
- 5. Analysis of experiseestal results in an analysis of the experimental results it is convenient to distinguish between three groups of variables which may give rise to errors. The first group consists of those factors which either give constant errors throughout the whole series of measurements or cause random variations which are negligible compared with other random errors. This group includes temperature, specimen purity, pressure and frequency. The second group com-prises those variables purpos:ly changed during the measuremenu; these include differences between acoustic path length, operating frequency and diffraction corrections. In the third group are the main random errors.
For the present measurements the spread of random errors in velocity should result Q
entirely from the uncertainties of phase measure nent and therefore be a max 2 mum of Q
s 045 msec-5 This is confirmed by the experimental results, the values of a varying by not more than this amount for a given frequency and path length.
e Sound celocury m water by phase mea.ruremerst techmque 31 **
The results obtained using the 6 5 mm gauge blocks at frequencies of l0 and 30 Mc.s f
4, (
are in good agreement. as may be seen by a comparison of the average A figures for cor.
responding temperature regions. Essentially this agreement substantiates the diffraction j
theory, since the diffraction correction of 0101 msec-1 at 10 Mets is appreciable. It can therefore be assumed that any errors in the diffraction corrections applied at 30 Mcis are i
negligible.
}
The average A figures in the region around 74'c show that the results at 30 Mcis obtained i
with the 6 5 mm. 0 3 and 0 2 in. gauge blocks, for which the highest accuracy is claimed.
are in precise agreement. with A., = 0 40 msec-5 The 5 5 mm blocks give A., = 0 42 l
msec-1 and the 3 0 mm blocks give A., = 0 39 msec-5 These averages are correct to the nearest 0 0! msec-5 These differences have been confirmed by an extensive series of 1
measurements made using a sample of water taken directly, without purification, from the
{
public supply.
An average velocity consistently 005 msec-L higher than that for distilled i
water was obtained over the range 23-80'c. but the relative differences between the five sets of blocks remained the same. It follows that the average thicknesses. taken over each i
set of three blocks of the 6 5 mm. 0 3 and 0 2 in. blocks are within 0 7 parts in 105 of their nominal values, since this i: th - stated accuracy of the 0 3 in, blocks. The average deviation from the nominal value fs the 5 5 mm block is then probably between - 0 6 and - 2 0 parts in 10', the corresponding figures for the 3 0 mm blocks being - 0 7 and
- 14 parts in 105 These deviations are well within the limits specified by the manufac-i turers.
l Considering only the results obtained in the region of 74'c at 30 Mc/s, the average value of a for the 6 5 mm,0 3 and 0 2in. sets of gauge blocks is 0403 msec-1 This figure is 1
unchanged if the results obtained with the other two sets of blocks are included, the value i
of a being decreased by 0 02 msec-5 for the 5 5 mm blocks and increased by 0-01 msec-L for the 3 0 mm blocks.
The standard deviation is 0014 msec-1 and the distribution of the 1-A values around the mean is very close to a normal distribution, as may be expected from 4
the random nature of the phase measurement errors.
Applying the same procedure to the results obtained at 30 Mc/s around 25'c, the average value of a is found to be 0 412 msec-5, with a standard deviation of 0020 msec-8, De I
slight increase in standard deviation is probably partly due to the uncertainty in temperature measurement.
The small difference in a., between c. 74'c and c. 25'c is somewhat larger than could be i
expected from the estimated possible error in absolute temperature measurement, itis i
probable that this discrepancy represents a slight difference between the variation of velocity with temperature found by Greenspan and Tschiegg (1957) and that found in
}
the present work, but it would be unrealistic to regard the difference as significant. In j
general it is seen that the present measurements confirm the variation of velocity with temperature found by Greenspan and Tschiegg (1957), but the actual values of velocity are I
approximately 0 40 msec-1 lower.
j A fifth degree polynomial has been fitted to the experimental results by means of a com-j puter, the fit being such as to give a minimum mean-square error. The data for all five sets of blocks were used, those for the 5 5 mm and 3 0 mm blocks being modified as indicated previously. De resulting equation is V = 1400 7873 - 5189939T-6 394257 < 10-8TS
- 4 4060241 x 10-*T8 - 2 399801 < 10-*T*
- 6 214865 x 10-'T* msec-5 (15) where Tis the temperature in 'c.
The standard deviation of the data from this curve is less than 0018 msec-5 The maxi-mum deviation of any single measurement from the curve is 0 041 msec-8. and the deviations of the data from the curve are apparently random and are substantially in accordance with a normal distribution. This scatt:r is adequately accounted for by the possible errors in phase measurement; the extent of the scatter is approximately two-thirds of that obtained
m 818
.4. J. Barlow and E. Ya:gan by Greenspan and Tschiegg (1957) using the ' sing-around' technique.No significant reduction of these values is obtained by usmg a polynomial of higher order.
4 Equation (15) has been used to calculate the velocity of sound in water at i degc intervals from 23 to 80*c. the range over which this equation is valid. and the results are given in table 5.
Following Greenspan and Tschiegg (1957). the increase for each I degc interval is also given to facilitate interpolation.
Table 5.
Velocity of sound in water, values calculated using eouation (15), together with the increase in velocity per deg C T
V Increase T
V Increase T
V increase
(*c) (m sec-')
(m sec-5)
(*c) (m sec-') (msec-')
(*c) (m sec-')
(m sec-')
23 0 1491 06 43-0 1533 47 1 51 63 4 1552 50 0-49 24 4 1493 86 2-80 44 0 1534 91 1 45 64 0 1552 95 0-45 25 4 1496 58 2 72 45 0 1536 31 1 39 65 4 1553 35 0-40 264 1499 "
' 64 46 0 1537 64 1 34 66 0 1553 71 0 36 27 0 1501 79 2 57 47 0 1538-93 1 28 67 4 1554 42 0 32 28 0 1504 28 2 49 48 0 1540 15 1 23 68 4 1554 30 0 27 29 0 1506 70 2 42 49 4 1541 33 1 17 69 0 155453 0 23 30 0 1509 04 2 34 50 0 1542 45 1 12 70 4 1554 72 0 19 31 0 1511 31 2 27 51 4 1543 52 1 07 71 0 1554 87 0-15 32 0 1513 52 2 20 52 0 1544 53 1 02 72 4 1554 97 0 11 33 0 1515 65 2 13 53 0 1545 50 0 97 73 4 1555 44 0 07 34 0 1517 72 247 54 4 1546 42 0 92 74 4 155547 0 03 35 0 1519 72 240 55 4 1547 28 4 87 75 0 1555 45
- 0 01 364 1521 66 1 94 56 4 1548 10 0 82 76 4 1555 40
-005 37 4 1523 53 1 87 57 4 1548-87 0 77 77 4 1554 91
-049 O
38 0 1525 34 1 81 58 0 1549 59 0-72 78 0 1554 78
-013 39 0 1527 08 1 75 59-0 1350 26 0 67 79 0 1554 61
-0 17 40-0 1528 77 1 69 60 4 1550 89 0-63 80 4 1554 41
-0 20 41 4 !$3039 l 62 61 0 1551 47 0 58 42 0 1531 96 1 57 62 0 1552 01 0 54
- 6. Discussion Measurements of the velocity of sound in water show that the experimental system de-scribed here is capable of extremely consistent results. He scatter of the data is small and follows a normal distribution. Since most of the scatter can be attributed to imperfect matching of the delay line, further developmest of the system could probably reduce the scatter by a factor of two. Here is no evidence of any systematic errors arising from the use of different acoustic path lengths or diferent operating frequencies. During a separate series of measurements investigations were made into the effects of varying the amplitude and duration of the transmitted pulse and of changmg certain critical components of the system. including the buffer ampli5 cts and piston attenuator. Such changes gave no differenen in the measured velocities. Results were also obtained, using the 3 mm ).ocks at a frequency of 30 Mc/s, on pulses which had made two and three double transits of the liquid path. Again no variations in the values of velocity were found.
It follows that the results obtained represent true values of the velocity of sound in the liquid measured. h relating such values to the absolute value for the velocity of sound in water those factors which may give errors constant throughout the.vhole series of measure-ments must be considered. At 25'c the possible error of ::- 0-003 desc in absolute tempera-ture measurement gives a possible error of i 0-008 msec-' in velocity. At 74*c, where the velocity passes through a maximum, the error is negligible. De effect of hydrostatic pressure on velocity causes the values obtained to be high by 0002 msec-5, due to the head of water above the acoustic path. Errors resulting from the variation of atmospheric pressure are negligible. He attenuation in water g:ves errors ofless than i part in 10*:
V errors in the determination of operatmg frequencies are also negligible.
Dissolved air was probably the principal impurity.m the sample of water investigated.
._m m....
~
m -- _ _. _ _ _. - _.. _. _ _ _.. -. _ _. _ _ _ _. _... ~. _ _.. _ _...
Sour;d velocuy m water hy phase measurement techmque 819 Greenspan and Tschitgg (1956) conclude that uissolved air increases the velocity in water by less than i part in 1(P. and around 30*c the increase is possibly of the order of I part in 10*.
This latter figure is negligible; even if the ditTerence is significant. it would seem preferable to regard the velocity of sound in water saturated with air as a standard for j
reference, since this is the normal state of water in contact with air.
It may therefore be deduced that the only significant sources of possible error in the results are the uncertainties in acoustic path length, in the determination of temperature, and the standard error of the data. The sum of these possible errors is = 0 024 msec-1 at 74*c and = 0038 msec-L at 25*c. From the present measurements, the velocity of sound in water to the nearest 001 msec-* is found to be 1496 58 = 0-04 msec-L at 25 000*c and 1555 07 = 0-03 msec-1 at 7440*c. The accuracy of these values is believed to be the j
highest yet attained. The results are in close agreement with the values found by McSkimin 1
(1965). ligunas et al. (1964), Neubauer and Dragonette (1964) and Brooks (1960).
Acknowledgments
- The authors wish to thank Professor J. Lamb for his constant help and encouragement in this work and for the provision of facilities. Thanks are also due to Dr. E. A. Bruges for the use of the Smith Bridge and the authors are grateful to Mr. A. T. J. Hayward for his interest and assistance. The work was supported by a contract with the National f
Engineering Laboratory, Ministry of Technology.
j References BAaTust., R., and Not.1.E, A. W.,1952, /. Acoust. Soc. Amer., 24, 8-15.
Bacons, R.,1960, /. Acoust. Soc. Amer., 32,1422-5.
Det. Gaosso, V. A.,1964, U.S. Navel Res. Lab Rep. No. 6026.
Det. Gaosso, V. A., SMumA, E. J., and Foucsar, P. F.,1954, U.S. Naval Res. Lab. Rep. No. 4439.
GREENSPAN, M., and Tscunoo, C. E.,1956, /. Acowt. Soc. Amer.,28,501.
1957 Rev. Sci. Instrum., 28,897-901;/. Res, Nat. Bar. Stamt., 59. 249-54.
II.cUNAs, V., Kuma.yuNaNE, O., and YAPERTAs, A.,1964, Soviet Rhysres-Acoustics,10,44-3.
MC$KIMIN, H. J.,1957,1. Acoast. Soc. Amer., 29,1185-92.
1960, /. Acourt. Soc. Amer., 32,1401-4.
[
l961, J. Acowt. Soc. Amer.,33,539.
A 1965, J. Acowr. Soc. Amer., ";7, 325-8.
NeusAusa, W. G., and DaAoowens, L. R.,1964, /. Acourt. Soc. Amer.,36,1685-90.
Schutz, A. K.,1955, Z. anrew. Phys.,7,144 Watsstan, A., and Dst. Gnosso, V. A.,1951, /. Acoust. Soc. Amer., 23,219-23.
Wn.uAMs, A. O.,1951, /. Acoust. Soc. Amer.,23.1-6.
WtuoN, W. D.,1959, /. Acoust. Soc. Amer., 31,1067-72.
V
- - - - - = -. ---
Speed of Sound in Pure Water V. A. Du. Gaosso ao C. W. MAcca Namel Rmenk Laborosoey, Waskinpen, D. C. 20190 (Received 26 May 1972)
A sound 4 peed equation of 6fth order in temperature is 6t with a standard deviation of 0.0028 m/see to 148 observations between 0.00l*C and 95.126*C on the Tu scale. The accuracy is believed to be 0.015 minec, and the reproducibility over replications is 0.005 m/sec.
Sen7scr CtaastFICAnow: 13.3.
INTRODUCTION with emphasis about this tempersture but extending In the course of obtaining a satisfactory sea water the to range doser to both 0* ard 100*C, are now sound-speed equation based on laboratory measure-yPo ments,' data were obtained in pure water with an 8
apparent reprodudbihty of better than 4 ppm. In this L EXPERIMENTAL METHOD latter reference, it was demonstrated that by compari-Sound-speed measurements were made indeectly by son of results of reputable observers, the speed of means of the ultrasonic interferometer whose construc.
sound in pure water could be speedied to better than tion and operation have been di-=ad etelier.88
(
0.05 m/sec. Mention was also made therein of indica-Briedy, acoustic wavelengths are measured by electron-(
tions of an anomaly near 4*C. These measurements, ically noting some characteristic of a quartz crjsta!
TAata L Sound speeds meneered in pure water for temperatures on T. scale.
Temperature Sound speed Temp *erature Sound speed Temperature Sound speed Temperature Sound speed
(*C)
(m/sec)
( C)
(m/sec)
(*C)
(m/sec)
(*C)
(m/sse) 0.0010 1402J95 3.4933 1419.287 1.0035 1407.384 7.9894 1439.089 0.0020 1402J98 3.7972 1420.702 1.0035 1407.384 7.9904 1439.094 0.0030 1402.404 3.7982 1420.6M 1.0045 1407J92 7.9904 1439 096 0.0030 1402.406 3.7992 1420.700 1.0045 1407.386 7.9904 1439.094 0.0110 1402.M5 3.8002 1420.707 1.0055 1407.391 7.9914 1439.102 0.0120 1402.448 3.8002 1420.707 1.0095 1407.412 9.9537 1447.087 0.0130 1402.456 3.9911 1421.584 1.0175 1407.451 9.9537 1447.087 0.0130 1402.453 3.9911 1421.587 1.0235 1407.482 9.9547 1447.094 0.0140 1402.459 3.9921 1421.590 1.0305 1407.316 9.9547 1447.091 0.0520 1402.649 3.9921 1421.589 2.0490 1412.468 9 9547 1447.089 0.0520 1402.652 3.9931 1421.595 2.0560 1412.501 39.9657 1528.809 0.0520 1402.649 4.2160 1422.620 2.0620 1412.527 39.9777 1528.831 0.0530 1402.654 4.2170 1422.624 2.0650 1412.543 39.9887 1538.847 0.0530 1402.654 4.2170 1422.622 2.0680 1412.354 59 9924 1550.900 0.1979 1403.383 4.2170 1422.622 2.0720 1412.574 60.0034 1550.986 0.1979 1403.383 4.5269 1424.032 2.4868 1414.533 60.0124 1550.994 0.1989 1463.390 4.5279 1424.639 2.4868 1414.556 60.0204 1550.998 0.1989 1463388 4.5279 1424.040 2.4898 1414.573
$0.0294 1551.004 0.1989 1403388 43279 1424.Q39 2.4918 1414.582 70.!!90 1554.819 0.4878 1404.829 5.4935 1428 364 2.4928 1414.585 70.1210 1554.819 0.4898 1404.843 5.4935 1428.365 2.9736 1416.861 70.1240 1554.819 0.4908 1404.848 3.4945 1428367 2.9746 1416.864 70.1340 1554.824 0.4988 1404.888 3.4965 1428.378 2.9766 1416.875 70.1500 1554.824 0.5008 1404.894 5.9892 1430.543 2.9766 1416.876 90.0858 1550.4J0 0.5018 1404.901 5.9902 1430.548 3.4913 1419.279 90.0868 1550.430 1.0005 1407 3 65 5.9902 1430.551 3.4913 1419.277 95.1214 1547.096 1.0025 1407.377 5.9922 1430.559 3.4913 1419.277 95.1224 1547.100 1.0025 1407.382 5.9952 1430.572 3.4923 1419.200 95.1264 1547.095 1442 Veemme 52 Nember 5 (Port 21 1972
_ - - - - - - -. ~. _. _ _ _ _ _ _ _ - - - - - _. _
SPEED OF SOUND IN PURE WATER
=_
Tasu II Previous sound. speed measurements in pure water with temocratures converted to T. scale Temperature Sound speed Temperature Sound speed
} Temperature Sound speed Temperature Souna soeec
(*C)
(m/seci
(*C)
(misect t
PC) imisect t'Ci smisee
~
0.0560 1402.673 29 9816 1509.081 9.9917 144 7.234 49 995o 1542.543 0.0610 1402.695 29.9 &36 1509 089 9 9957 1447.249 50.0126 1542.50 0.0640 1402.705 34.9710 1519 752 10.0027 1447.276 50 a360 1542.591 0.0600 1402.726 34.9810 1519.768 10.0117 144?J07 50.0466 1542.602 0.0720 1402.747 34.9870 1519.781 19.91 %
1482.091 60.0194 1550.999 4.9887 1426.!!$
39 9727 1528.8 0 19.9206 1482.096 60 0124 1550.999 4 9917 -
1426.126 39 9747 1528.82.3 19.9216 1482.102 73.9957 1555.144 4 9927 1426.129 39.9777 1528.827 24.9815 1496.636 74.0117 1555.144 4.9937 1426.131 39.9847 1528.837 24.9855 1496.646 74.0218 1555.145 TABLE IU. Coed 1Qents for Eq. I for sound speed in m/sec.
A Tabic 16t Table U 6t Combined 6t 0
0.140238689X 10' O 140238749X10' I
O mam8X105 0.503609148X10' O.140138754X 10' 2
-0.58085h99X 10-'
-0.580268889X 10-'
O.503711129X105 3
0.334817140 X10-8 0.331767408X 10-8
-0.580852166X10-'
4
-0.149252527X10-*
-0.14073838 X 10-5 OJ34198&34X10-8 i
3 0J2391J472X10" 0.298M1057X 10-*
-0.147800417X 10-*
0.314643091X10-8 on Te scale with standard denauon of 0.0a3 m/sec.TaaLa IV. Speed of sound in pure water in m/sec. Ca l
l
\\
To
- C 0.0 0.1 0.2 OJ 0.4 0.5 0.6 0.7 0.8 0.9 0
1402388 1402.891 1403J93 1403.893 1404.393 1404.892 140$J89 1405.885 1406J80 1406.874 1
1407J67 1407.859 1408J49 1408M8 1409.327 1409.814 1410.300 1410.784 1411.268 1411.751 2
1412.232 1412.712 1413.192 1413.670 1414.147. 1414.622 1415.097 1415J71 1416.043 1416.515 i [
3 1414 985 1417.454 1417.922 1418 309 1418A55 1419.320 1419384 1420.246 1420.70R 1421.168
\\'
4 1421.628 1422.086 1422.543 1422.999 1423.454 1423.908 1424J61 1424.813 1425.264 142.5.71J i
5 1426.162 1426.609 1427.056 1427.501 1427.9 % 1425J09 1428.831 1429.272 1429.712 1430.151 i
6 1430.589 1431.026 1431.462 1431.897 1432331 1432.764 1433.1%
1433.626 1434.056 1434.485 7
1434.912 1435J39 1435.764 1436.189 1436.612 1437.035 1437.456 1437.877 1438.296 1438.715 8
1439.132 1439349 14J9.964 1440J78 1440.792 1441.204 1441.615 1442.026 1442.415 1442.843 9
1443.231 1443.657 1444.062 1444.467 1444.870 1445.273 1445.674 1446.074 1446.474 1446.872 10 1447.270 1447.666 1448.062 1448.456 1448.850 1449.243 1449 M4 1450.025 1450 415 1450.803 j
i 11 1451.191 1431.578 1431.964 1452 349 1452.733 1453.116 1453.498 1453.879 1454.259 1454.638 12 1455.016 1455J94 1455.770 1456.145 1456.520 1456.893 1457.266 1457.637 1458.008 1458J78 i
13 1458.747 1459.115 1459 482 1459.848 1460.213 1460.577 1460.940 1461J03 tel.664 1462.025 14 1462J84 1462.743 1463.101 1M3.458 IM3.814 1464.169 1464.523 l # 4.876 IMS.229 1465.580 15 1465.931 1466.200 1466.629 1466.977 IM7.324 1M7.670 1468.015 IM8J59 1468.703 1469.045 16 1469.387 1469.728 1470.067 1470.406 1470.745 1471.082 1471.418 1471.754 1472.088 1472.422 17 1472.755 1473.087 1473.418 1473 3 48 1474.078 1474.406 1474.734 1475.061 1475J86 1475.712 18 1476.Q36 1476.359 1476.682 1477.003 1477.32i 1477.644 1477.963 1478.282 1478.599 1478.916 19 1479.231 1479.546 1479.860 1480.174 1480 3 )
1480.798 1481.104 1481.418 1481.727 1482.035 20 1482J43 1482.649 1482.955 1483.280 1483ao4 1483.868 1484.170 14H.472 1484.772 1485.073 21 1445J72 1485.670 1485.968 1486.264 1486.560 1486.156 1487.150 1487.443 1487.736 1488.028 22 1488 3 19 1488.610 1488.899 1489.188 1489.476 1489.763 1490.049 1490.335 1490 620 1490.804 23 1491.187 1491.469 1491.751 1492.032 1492 3 12 1492.591 1492.870 1493.147 1493 424 1493.700 24 1493.976 1494.250 1494.524 1494.797 1495.070 1495.341 1495.612 1495.882 1496.151 1496 420 r
25 1496.687 1496.954 1497.220 1497.486 1497.751 1498.014 1498.278 1498.540 1498.802 1499 063 26 1499323 1499342 1499.HI
!$00.099 1500.356 1500.612 1500.868 1501.123 1501 377 1501.630 27 1501.883 1502.135 1502 386 1502.637 1502.887 1503.136 1503384 1503.632 1503.878
!$04.124 28 1504370 1504.615 1504.858 1505.102 1505.344 1505.586 1505.827 1506.067 1506J07 1506.546 29 1506.784 1507.022 1507.258 1507.494 1507.730 1507.964 1508.198 1508.431 1508.664 1508M6
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35 1519.80s 1520.005 1520.201 1520.396 1520.591 1520.785 1520.978 1521.171
!$21J63 1521.554 i
36 1521.745 1521.935 1522.125 1522J14 1522.502 1522.600 1522.877 152.3.063 1523.249 1523.434 i
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38 1525.428 1525. 0 6 1525.783 1525 959 1526.135 1526.310 1526.484 1526.658 1526.132 1527.004 j
39 1527.176 1527.348 1527.518 1527.689 1527.858 1528.027 1528.195 1528.363
!$28.530 !$28.697 i
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DEL GROSSO AND MADER f
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15J7.74 1137.877 1538.007 1538.137 1538.266 1538J94 1538.522 1538.650 1538 376 1538.9Q1 47 1539.023 1539.154 1539 278 1539.402 1539.526 1539 649 1539372 1539.894 1540.015 1540.136 48 1540.256 1540J76 1540.495 1540.614 1540.732 1540.850 1540 967 1541.0&3 1541.199 1541J15 49 1541.4J0 1541.544 1541.658 1541J72 1541.885 1541.997 1542.109 1542.220 1542.331 1542.441 50 1542.551 1542.660
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1547.878 1547.959 1548.039 1548.119 56 1548.199 1548.278 1548.J56 1548.434 1548.512 1548.589 1548.665 1548J41 1548J17 1548.892 57 1548.967
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4 60 1550.986 1551.0M 1551.106 1551.165 1551.224 1551.282 1551.340 1551J97 1551.454 1551.310 61 1551.566 1551.622 1551.677 1551.731 1551.786 1551.839 1551.892 1551.945 1551.998 1552.049 62 1552.101 1552.152 1552.202 1552.252 1552.302 1552.351 1552.400 1552.448 1552.4 % 1552.543 63 1552.590 1552.637 1552.6&3 1552.729 1552.774 1552.818 1552.863 1552.907 1552.950 1552.993 64 1553.Q35 1553.078 1553.119 1553.160 1553.201 1513.241 1553.281 1553 3 21 1513J60 1553.398 65 1553.437 1553.474 1553.512 1553.548 1553.585 155J.621 1553.656 1553.691 1553J26 1513J60 66 155JJ94 1553.828 1553.860 1513.893 1553.925 1553.957 1513.988 1554.019 1554.049 1554.079 67 1554.109 1554.138 ~ 1554.167 1554.195 1554.223 1554.250 1554.277 1554J04 1554.330 1554.356 68 1554.381 1554.406 1554.430 1554.454 1554.478 1554.501 1554.524 1554.5 % 1554.568 1554.590 69 1554.611 1554.632 1554.652 1554.672 1554.691 1554.710 1554J29 1554J47 1554.765 1554.782 70 1554.799 1154.816 1554.832 1554.848 1554.863 1554.878 1554.893 1554.907 1554.920 1554.934 71 1554.947 1554.959 1554 971 1554.983 1554.994 1555.005 1555.015 1555.026 1555.Q15 1555.044 72 1555.013 1555.062 1555.070 1555.077 1555.0&5 1515.091 1515.098 1515.104 1555.110 1555.115
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74 1555.146 1555.147 1555.147 1555.1M 1555.1 %
1555.145 1555.143 1555.141 1515.139 1555.136 s
75 1555.133 1515.1J0 1555.126 1555.122 1555.117 1555.112 1515.107 1515.101 1515.095 1555.088 76 1555.081 1555.074 1555.066 1555.058 1555.050 1555.041 1555.031 1515.022 !$55.012 1555002 77 1554.991 1554.980 1554.968 1554.956 1554.944 1554.931 1554.918 1554.905 1554.891 1554.877 78 1554.862 1554.847 1554.832 1554.816 1554.800 1554.784 1554.767 1554.750 1554.732 1554.714 79 1554.696 1554.677 1554.658 1554.639 1554.619 1554.599 1554.578 1554.557 1554.536 1154J14 80 1554.492 1554.470 1554.447 1554.424 1554.400 1554J76 1554J52 1554J27 1554J02 1554.277 i
81
!$34.251 1554.225 1554.199 1554.172 1554.144 1554.117 1554.089 1554.061 1554.032 1154.003 82 1513.974 1553.944 1553.914 1553.883 1553.852 1513.821 1553.789 1513.758 1553.725 1513.693
&3 1553.660 155J.626 1513.592 1513.558 1513.524 1513.489 1513.454 1513.418 1513.313 15133 M 84 1513J10 1513.273 1513.235 1513.198 1553.160 1553.121 1513.013 1513 044 1553.004 1552.964 i
85 1552.924 1552.884 1552.843 1552.802 1552.760 1552.718 1552.676 1552.634 1552.591 1552.547 86 1552J04 1552.460 1532.415 1552J71 1552J26 1552.280 1552.234 1552.188 1552.142 1552.095
)
87 1552.048 1552.001 1551.953 1551.905 1551.856 1551.807 1551.758 1551.709 1551.659 1551.609 88 1551.558 !$51.507 1531.456 1551.404 1551.352 1551.300 1551.248 1551.195
!$51.141 1531.088 89 1551.Q34 1550.980 1550.925 1550.870 1550.815 1550.759 1550.703 1550.647 1550.590 1550.533 90 1150.476 1530.418 1530 340 1550.302 1550.243 1550.184 1550.125 1550.065 1550.005 1549.945 4
91
!$49.884 1549.82J 1549.762 1549300 1549 638 1549.576 1549 513 1549.450 1549 387 1549.323 92 1549.259 1549.195 1549.131 1549.066 1549 000 1548.935 1548.869 1548.803 1548.736 1548.669 i
93 1548.602 1548.534 1548.M7 1548J98 1548J30 1548.261 1548.192 1548.122 1548 053 1547.983 94 1547.912 1547.841 1547370 1547.699 1547.627 1547.555 1547.483 1547.410 1547.337 1547.264 95 1547.190 1547.116 1547.042 15M.967 1546.892 1546.817 15 4.741 1546.665 1546.589 1546.513 96 1546.436 1546.359 15M.281 15M.204 1546.126 1546.047 1545.969 1545.890 1545.810 1545.731 97 1545.651 1545.570 1545.490 1545.409 1545.328 1545.2 %
1545.164 1545.082 1545.000 1544.917 98 1544.834 1544.751 1544.667 1544.583 1544.499 1544.414 1544.329 1544.244 1544.159 1544.073 99 1543.987 1543.900 1543.814 1543.727 1543.639
!$43.552 1543.464 1543J76 1543.287 1543.198 100 1543.109 f
3 operated in a continuous wave iterative redection leads to a specification of accuracy of 10 ppm or 0.015 technique and counting these iruposed characteristics m/sec.
as the redector-source separation is varied. The path
/
change for some 300 acoustic fringes at 3 MHz is IL DATA measured by a laser interferometer. Consideration of Some 112 new data points for the speed of sound in all sources of error, including theoretical predictions" pure water were taken in 1970 and are reported in i
1444 Yeeene 52 Number 5 (Port 2) 1972 i
SPEED OF SO U N D IN PURE WATER Table I, with temperatures on the Tu scale. In Table II, Tmt V. Re
"""'I ***"gression curve deviauon averac and sc.atter tor 2
O the previous measurements are repeated with tempera.
- 'I"*"**"'*5-tures converted to the same scale. The results of these
()
calculations are given to the nearest 0.0001*C, although M
C the measurements wer made to only 0.001*C, to facilitate conversion.
5" "
d 5" 0.01
- 0.002 0.003 0.05 0.000 0.000 III. EQUATION DEVELOPMENT 0.2
- 0.001 0.000 0.5
- 0.001 0.004 To ascertain whether these two data sets are compat-30
+0 001 0 006 ible, separate least-squares 6ts were made* at the f!
j$
j$
Naval Undersea Research and Development Center 3.0 0.006 0.002 (NAVUSEARANDCEN). A 6fth-degree polynomial f3 j$
jg g
was found satisfactory for both, vtz:
4.0 4.002 0.002 4.2
- 0.002 0.002 i
4.5
- 0.004 0.002 C = E k.T*.
(1) 5.5
-Om 0.m2 6.0
- 0.003 0.004 8.0
- 0.003 0.004 10.0
- 0.001 0.004 The 36 carlier observations in Table II over the 40.0
- 0.004 0.002 temperature range 0.056*Cf Taf 74.022*C were fit
+jg j$
with a standard deviation of 0.0025 m/sec and coef5-90.0
- 0.004 0.000 cients as given in the third column of Table III.
95.0
+o.002 0.004 The least-squares fit to the 112 data points of Table I nrst data net over the larger temperature ~ range 0.001*Cf Tm 0.06
+0.001 0.006
$95.126'C, but with emphasis between 0* and 10*C 5.0
- 0.001 0.006 has a standard deviation of 0.0026 m/sec and compar-jy jg able coef5cients as given in column two of Table IIL 25.0
+0.002 0.000 Because of the close agreement between these expres.
gj jg jg sions, Tables I and II were combmed, and a hast-O squares fit was obtained to all 148 observations with a 50.0 0.000 0.002 40.0
- 0.001 0 002 O
standard deviation of 0.0029 m/sec and coef5cients as (j
j j$
given in the last column of Table III.
tabla YI. Temperature scale converson T.
To Tar-Tu T.
T.
TcTm T.
T.
T.-Ta T.
T.
Ta-T.
(*Q
(*Q
(*Q
(*C)
(*Q
(*Q
(*C)
(*C)
(*C)
(*Q
(*C)
(*Q 0
0 0
26 25.9913 0.0087 51 30.9897 0.0103 76 75.9932 0.0068 1
0.9995 0.0005 27 26.9911 0 0009 52 51.9897 0.0103 77 76.9934 0.0066 2
1.9990 0.0010 28 27.9909 0.0091 53 52.9898 0.0102 78 77.9937 0.0063 3
2.9986 0.0014 29 28.9908 0.0092 54 53.9899 0.0101 79 78.9939 0.0061 4
3.9981 0.0019 30 29.9907 0.0093 55 54.9899 0.0101 80 79.9941 0.0059 5
4.9977 0.0023 31 30.9905 0.0095 56 55.9900 0.0100 81 80.9944 0.0056 6
5.9973 0.0027 32 J1.9904 0.0096 57 56.9901 0.0099 82 81.9946 0.0054 7
6.9969 0.0031 33 32.9902 0.0098 58 57.9902 0.0098 13 82.9949 0.0051 8
7.9965 0.0035 34 33.9901 0.0099 59 58.9903 0.0097 84 13.9952 0.0048 9
8.9961 0.0039 35 34.9900 0.0100 60 59.9904 0.0096 85 84.9954 0 0046 10 9.9957 0.00 0 36 35.9899 0.0101 61 60.9906 U.0094 86 15.9957 0.00 0 11 10.9953 0.0047 37 36.9898 0.0102 62 61.9907 0.0093 87 86.9960 0.0040 12 11.9950 0.00$0 38 37.9898 0.0102 63 62.9908 0.0092 88 87.9963 0.0037 13 12.9946 0.0054 39 38.9897 0.0103 64 63.9910 0.0090 89 88.9965 0.0035 14 13.9943 0.0057 40 39.9897 0.0103 65 64.9911 0.0089 90 89.9968 0.0Q32 15 14.9940 0.0060 41 40.9896 0.0104 66 65.9913 0.0087 91 90 9971 0.0029 16 15.9937 0.0063 42 41.9896 0.0104 67 66.9914 0.0086 92 91.9974 0.0026 17 16.99J4 0.0066 43 42.9896 0.0104 68 67.9916 0.0084 93 92.9977 0.0023 18 17.9931 0.0069 44 43.9895 0.0105 69 68.9918 0.0082 94 93.9981 0.0019 19 18.9929 0.0071 45 44.9895 0.0105 70 69.9920 0.0080 95 94.9984 0.0016 20 19.9926 0.0074 46 45.9895 0.0105 71 70.9922 0.0078 96 95.9987 0.0013 21 20.9924 0.0076 47 46.9895 0.0105 72 71.9923 0.0077 97
%.9990 0.0010 22 21.9921 0.0079 48 47.9986 0.0104 73 72.9925 0.0075 98 97.9993 0.0007 23 22.9919 0.0081 49 48.9896 0.0104 74 73.9928 0.0072 99 98.9997 0.0003 24 23.9917 0.0083 50 49.98 %
0.0104 75 74.99J0 0.0070 100 100.0000 0
25 24.9915 0.0015 b'
The Jeeemel et the Acessencal Society of Amence 1445
u I
DEL G ROSSO AND MADER f]
This equation de to the combined data pMicts a precision (standard devtstion dve times larger
'Q sound. speed magmum of 1555.147 m/sec at a te tpera-greater scatter (twenty times larger) where and ture of 74.172*C on the T scale. Sound speeo., cal-measurements over a smaller temperature culated with th*se coerficients are given in Table IV for tenth d*F Celsius intervals. A rounding off of (6*C5 T$81*C) showed "no signi6 cant discontinu or other anomalous behavior." These latter authort-these coerficients is employed at NAVUSEARAND-CEN for veloctmeter calibrations.'
found an eighth-order polynomial was required to 6:
their data, and they ignored a deviation three tima.
greater than their scatter.
IV. DISCUSSION OF RESULTS In light of the above, this present data is presemer[.
I **
The standard deviation of the equation fit to the values i s und speed m.Pse and ho#uW ac data is 0.003 m/sec or 2 ppm. As stated, the measure-pure water.
ments are most probabiy accurate to 0.015 m/sec.
A temperature scale c nversi n table is presented id Another measure of the precision of the data (apart Table VI to assist those still operating on the T.s scale.
I from accuracy) in the form of reproducibility over replications can be obtained from Table V, which lists the average mgression deviation and scatter thereof, pd i,O[I 0'"*no and C. E Hsdu, J. Acouse. Soc. Amin, c.
^'
for nominal experimental temperatures. It is tempting 8 V. A. Del Grosso, J. Acoust. Soc. Amer. 47. 947-049 (1970),
to postulate the existence of anomalies not only about
.' V. A. Del Grosso, J. Acoust. Soc. Amer. 48, 770-771 (1970).
4*C but also at 40. and 90'C, but such an assertion is V. A. Del Groneo, Acusuca 24,299-311 (1971).
- K. V. Mackenzie, pnvate comunication (January 1971).
strongly resisted since the deviations are of the order of
- K. V. Mackensae, pnvate communicauos (February 1971),
the scatter and standard deviation. Comparison of the NMen Acous Soc A 333 present results may be made to other work' of lesser Chem. Phys. 51, 25 0 -2543 (1969).
,~
V CL) 1 IM6 velame 52 Number $ (Port 2) 1772 i
Bubble Growth by Diffusion in an 11-kHz Sound Field ANTaoNY I. Ett.r.m Namel Pourredmau Scheet, Momery, Califer sa g3peo (Received 20 Apn! 1972)
Bubble growth by recti 6ed difusion of gas was measured for angle bubbles in an 11 kHz underwater sound 6 eld. Observed results are compared to calculated results for assumed isothermal or adiabatic pulsations of the bubbies. The calculated threshold for growth is raa='aat with observauons, but the calculated tunes of growth escoed the observed umas by factors of about 10-100.
Sempet CussmCADON: 13.8.
This paper reports measurements of bubble growth results are presented in Fig.1. The symbol X indicata ay recti 6ed diffusion in an 11-kHz underwater sound the values of peak sound pressure amplitude and bubb seld. Bubble radii ranged from about 50g to greater radius for bubble that grew smaller and, hence, were than 200g, and peak acoustic pressures ranged up to below threnhold. The symbol O indicates bubbles that About 0.3 bar. The results are compared to predictions grew larger; they were above the threshold. The solid
- itheory, curves are calculated thraholds for isothermal and Threshold conditions for growth, and the subsequent adiabatic pulsations of the bubble, These curves were rates of growth, were previously reported for a sound calculated from Eq. 8, which is derived later. The irequency of 26.6 kHz.* The present results extend the adiabatic threshold curve is consistent with the observa-orevious study to a lower frequency and were obtained tions, and, with a few exceptions, this curve separates ay a procedure similar to that described in Ref.1.
the conditions for growing and dissolving bubbles.
The experunents were conducted with air bubbles in In a review of the thermal properties of pulsating gas sir saturated water in a vertical 6-in.-diam Pyrex pipe, bubbles, Devm' de6nes a parameter a that indicates the
- lriven by a transducer at the bottom. The water column Proximity of the bubble motion to isothermal or adia-wu 43 cm high and resonated at 11.08 kHz. The water batic behavior Values of y/a range from 1, for an surface at the top and the glass walls were approximate isothermal process, to 1.4, for an adiabatic process in oressure-release surfaces. Individual air bubbles were which the ratio of spect6c heats y is 1.4. For the experi-acoustically trapped near a pressure antinode located mental conditions, computed values of v/a range from 2ne quarter wavelength, about 4.6 cm, below the sur.
1.07, for a bubble radius of 50 u, to 1.27, for a bubble face. Bubble size was monitored by means of rise-time radius of 150 u. Thus, Devin's parameter indicates that measurements at regular time intervals. The scoustic the expenmental bubbla fall between isothermal and pressure was monitored with a calibrated hydrophone. adiabatic behavior, with smaller bubble closer to After each set of measurements, the pressure amplj. isothermal conditions and larger bubbla closer to tule at the bubble was calculated through knowledge adiabatic.
of the bubble and hydrophone locations and the geome.
In a second series of experunents, the acoustic pre-try of the sound Seld. The bubble radius R was com. sure amplitude was held constant at 0.25 bar. The puted from the rise velocity a by iterating the following growth of a single bubble located near the pressure approximate equation from Langmuir and Blodgett": antinode was monitored by means of frequent rise time mensurements. Seventeen different bubbles were ob-R'= (9p/2g)=[1+0.197(2Rs/r)' **],
(1) served, and the data were used to compute the average time required for a bubble to grow from selected values where, is the kinematic viscosity of water at the ap-of initial and naal radius. The observed average time propriate temperature, and g is the gravitational of growth are presented in Table I and cornpared to acceleration.
calculated times of growth during isothermal and adis-During one seria of expenmental runs, the sound batic pulsations. The observed tima are considerably pressure was continually adjusted to bring it close to shorter than the calculated times. Bubble radii were ob-l the thrahold for growth of the bubble present. The served to increase from 120 to 180g, for example, in The Jeweel of the aceseheel Socisey et Amence 1447
_ _. - - _ _. _ _. _ _ =. _. _ _ - _ _. _ _ _ _.. _ _. _ _ _ _. _ _
_.m Received : December 1968 C
t o.o w
l Echo Phase-Comparison Technique and Measurement of Sound Velocity in Water R. C. Wtu.tAMSON
. VASA Elecwnia Rueerch Cenur, C.ambeske, Maunchaueouinup A tecnniove is desenbed in which the ultrasonic time delay between succennive ecnoes in an echo train i determined by phase coa.panson of the echoes with a coherent continuous signal. Correcuens for phase s of an echo upon redecuan frasi the face of a treasducar and for aifracuon edacts are discussed.The veioory of sound at 1 MHz in distilled water (com 23' to 75'C has been mensuend with this technique. Measuremen of time delay are accurate to 20 ppm while the over all accuracy is 127 ppm or *0.20 rn/sec. Excellent agreement with values in the literature is found.
L ItrT10 DUCTION with sundar measurements by McSkimmin12 and other Ultrasonic pulse techniques for the measurement of authors who used diferent techmques.
sound velocity in solids and fluids have become well e
developed in recent years. For ultimate accuracy and g,
sensitivity, these techniques must measure time delays A. Standard P' -- %perison Technique with a resolution much smaller than one cycle of the carrier frequency. Dis usually.mv,gves some type of Before decribing the manner in which the phase.
phase comparison. Ultrasome delays are determmed by g,
g M M. its W fu WW a W M@ d & 4 comparmg the phase of an echo in an echo train with
,;q, m is b bM % d that of another echo'-8 or with a coherent contmuous wave at the carrier frequency.,,It is the purpose g the circuitry is shown m. F.ig.1. De output of a n.gnal this paper to present an application of a sendard generator is fed through a gated amplifier to provide phase. comparison technique of the latter type (phase. a burst, which excites the transmitting transducer. De sensitive detection or homodyne technique) to measure
- signal generated in the receiving transducer (or in the ment of the absolute velocity of sound. De necesarY dual purpose transmitting transducer) by the train of corrections for difraction and for phase shift of a pulse echoes bouncing back.and forth between the trans-on redection are menu. Data on sound velocity ducers is amplified and mixed in the phase detector (mixer) with a continuous reference signal from the in distilled water are given and compared in detail signal generator.
By means of a variable delay line, the phase of the
- E. h. Mc5kimmin J..w-r Soc Amer. 33, 12-16 #1961).
'O'"C' 5ignal can be placed in quadrature with the i H.
. P=pam J. Acnsst. Soc. Aaser. 42.1045-1051 f t967).
received su.
i H. J. Meskimana J. Acouse. Soc. Amer. 29.1Iss-t192 (1956L pial of a chosen echo thus givmg a null Williams and J. Lamb, J. Acoust. Soc. Amer. 30, Jos-J13 output from the phase detector during the receipt of that echo. As the ultrasonic delay changes, the setting
- R.'P. Esoineia and P. C. Watermaa. J. Appl Phys. 29.
of the delay line can be changed to maintam the null 718-721 (1958).
8 W. Schaass and C. Kalwest. Acusuca 10. 385-393 (1960).
condition. Changes of delay.line settings are thus equal t R. W. Leonare and H. despua. J. Acousc. Soc. Amer, so.
to changes m. ulay of the ultrasonic signal.,,,,,. Uter.
1467-1472 (1966L natelv, the frequency of the signal generator can be il.I
.' fhy varie i to maintain a null condition.' Because these are 1 2
- e W. M. Whitaev and C. E. Chase. Phys. Rev. 158. 200-214 null techniques. : hey can be made extremeir lens tive 1%7).
,' 3968).
't R. C. Williamson sad C. E. Chase. Phys. Rev. 176. 235-294 l
3 H. J. Mc5kimmin. J. Acoust. Joe. Amer. 37. J23-i23 1965).
M $9efitG4 of file AcGetr6Cel 40ClerY dlF ANIeftCe IMI
- _ _ - - ~. - -. -. - - - - -
_.. _ - ~..
R C
W I L 1.1 A \\l S O N t.
}
-G raicota I b e)-
stataaron i l
utraasoNIC tratoN ym gq it l
}o sicmat cargo f
I naut d Fic.1. Schematic dia, au,ygg,
"""""l
'"'UF 'E '
4 raansurrao I
gram of ultrasonic phase.
accrivwo
- P'"*"
ran=soucra raa=soucta na.L.
anast ocL,,
DETEc70a
,,,,,,y l
unc o
to small phase shifts. Sensitivities of 10-8 sign I periods are routinely obtainable and, with an ultrasonic path the signal generator (Fig.1) is applied to the t J
containing 108 wsyelengths, this results in an over-all mitting transducer, a series of echoes will be detecte by the receiving transducer. The frequency of the sensitivity @ ions where high attenuation exists phase signal generator and the phase of the reference can be In situat companson techniques have another distinct advantage-adjusted until the reference signal is s over other velocity. measurement schemes. The circuit quadrature with the received signal during all of the echoes. This condition is shown in Fig. 2. When the shown in Fig.1 is essentially that of a phase-sensitive reference and received signals are mi coherent detector. By using a boxcar integrator at the detector, a null output will result for every ec phase detector output gated on a particular echo for this " null condition" we can say (usually the first when high attenuation exists), it is possible to measure ultrasonic delay and attenuation a
even when the signal is buried in receiver noise.
T= nr=.
(1)
With all the advantages of the phase-companson
/
technique enumerated above, the standard application of the technique has been of limited usefulness because where T is the time delay between echoes; n, an it is capable of measuring only changes in ultrasonic integer; and r=l/f, the pen,od of carrier frequency.
delay caused by in sits changes in experimental pa.
The values of f that satisfy Eq. I are referred to as o
rameters, e.g. temperature or pressure. With the tech.
nuu frequncies.,,
nique described above, it is not possible to measure By obtaining this null condition for a series of the total ultrasonic delav across a tixed path and values of n, it is possible to determine the value for therebv determine the absolute sound velocity.
n for any given null frequency and thus to determine The' technique described in this paper is a means of T." From the value of T and the path length between using the standard circuit shown in Fig. I to measure the transducer faces d, the ultrasonic velocity u can be the velocity of sound to high accuracy. As is shown, determined:
the technique is competitive with any existing means for the a curate measurements of absolute sound ve.
v-2d/T'= 2df/n, locity and is simultaneously able to exploit the unique T'mrmtc ou = T.
(2) capAilities of phase sensitive detection for measure-ment of small velocity changes and highly attenuated The mall corrections, which are applied to the mes-signals.
sured delay T in order to obtain the ultrasonic delay T', are discussed later.
B. Echo Phase Companson Techniqu' Let us examine, more :;enerally, the form of the phase detector output for arbitrary frequencies. The Consider the arrangement of transducers and speci. output E of a balanced mixer (phase ejetector) is pro-men shown in Fig. 2. When a short burst ;;ated from a R. C. Williamson. " Measurement of the Velaatv and Attenu-i'In sauauons where it is not nouable to make manaurement5 d
stion of I'Itrasonic Pulses in the Presence ot Neese," Rev. So.
over a susficently wide rance of freovences in deternune =, 4 Instrum. 44.670-674 (1909).
tess accurate value for the sound vetoote may be obtaaned trom a = 2das,as.
1252 v.6.=
45 N==6er 5 1969
s o t' N D V E t. 0 C I T Y IN WATER
-TRANsouctas -
./
t s9ECientN siGNat in e -.-
(/
f.
---* sicNat our
~ ~./j w
Frc. 2. Schernatic dia-EC"O '
grarn iUustrating the phase relationships of Echo 2 the received and refer.
l l
ESo3 ence sagnals for a null
- EcElvt0 l
l l
l (CNo it 56 Gnat.
i i
condiuon.
{,
{'
w i
a l
i
-rm i
j l
l l
arreneNet i slGNAL l r-portional to the amplitude of the received signal and for ultrasonic transmission through water at f= 1 MHz a sinusoidal function of the phase difference e between for various values of f and e. The damped sinusoidal the references and the received signals. For the kth form of the output predicted by Eq. 8 is evident.
received echo with amplitude A.,
The accuracy with which null frequencies can be determined depends on the precision with which the E= =.4 a s,mo..
(3) phase of echoes far out in the echo train can be re-The time delay and amplitude of the kth echo are solved. This in turn depends on the attenuation con-8 * *"
stant a, the noise level m the system, how well the
,a phase within each echo is desned, the capabilities of T. = (k-f)T= (k- {)/f.,
(4) the phase detector, and the number of wavelengths in
\\.
a.= a.e-2m6-u
,o #'N5), the ultrasonic path. As a result, the precision varies
's(d
'a,n,.,, m g considerably from one experiment to another. How-where a is the attenuation consta d'k the echo ever, a general idea of the considerations involved can number. Therefore,
/,
be obtained from the following example, which ap-v proximately corresponds to the measurements in dis.
E.= A.e-2d*-D sin (2II(k-})f/f.++).
(6) tilled water that are discussed later.
The difference.m electrical delay between the reference Consider the situation in which the phase diHerence and signal paths (Fig.1), meluding delay m the delay between the lith echo in an echo train and the refer-line, ts absorbed in the phase angle 4 ence signal can be resolved to within 10-2 signal periods When d is adj,usted to O' or 180* (with the variable
- v. Further echoes are discarded since the resolution of delay-line), E. is zero for all echoes (all k's), when* their phase rapidly deteriorates owing to increased ever f= nf and n an integer. This is the null condition. attenuation. If the round trip delay between successive echoes is 102 r, the delay between the drst and lith In practice, the delay line must be adjusted slightly echois 108 to obtain nulls at different values of n because phase
- r. Therefore, the over.all time (or frequency) shifts that occur in the electronics and m the acoustical resolution is 10-2 r out of 108 r or 10 ppm.
coupling change with frequency.
Although the time delav between anv two selected When f is not an integer multiple of f., we can write echoes in an echo train can be measure'd as described above, the null frequencies are actually determined by f= (n+x)f., ' zi < }
(7) viewing an over-all scope display described bv Eq. 8, and not by careful attention to any given pair or echoes.
It is, therefore, instructive to view, in an alternate E.= A.e-2*-94 sin (2rI(A -t) -re).
(8) way, the precision with which the null frequencies can In this case, the phase-detector output is a damped be determined. The smallest value of x that can be sinucoidal function of the echo number k with period resolved. ix, is reached when x, the frequency of the equal to 1/x. Figure 3 shows the phase-detector output damped oscillation, becomes small compared to the
- ,;j is For the satuation in which only one transducer is used as lioth frequencv or time delar is ax/n (see Eq. 7). N*ote that at the crossover point where dx= 2ad, the resolution h
uons
= 2abn=oA= fi/Q, where aA is the attenuation per The joumet et the Acoustscal $eciety of Amence 1253
i R.
C.
WI L LI A M S O N (a)
(h)
- ca
}
I e,,
$WW~
)
een-~k.*
y':~~w
.,,tf =*=ere**ere -r 3--.sa I
r I
t,'
=*
l i
1 1
l
{
Fic. 1 ta) tlnrec:ded ecno train transtrutted throug5 water: ibi ocase detector output for, = 70.100 c.,
I
..j,.....~~~....y;;n w fol, ;fg 9,?,
h.
f,,'
0 j
j for y = 70.000 j.- 180*: ie) same tor f = 70.000 f. - - 00*.
Total i
0,t8 sweep lench is 2 mnec in all cases.
f (d) i, (e) i wavelength in the sample and Q, the mechanical quality of the sample. In our example, 2ad= 10-t or 180*, whenever (a) l2lKl2.l; (b) l2iDjZ l; or and (c) 2 a real number.
therefore, resolution is limited to values of x of the order of 10-3 The value of n in Eq. ~ is about 100 The technique for minimizing y for measurements in (number of signal periods in one round trip delay) and solids has be n discussed by several authors.'-* For the over-all frequency resolution is therefore 10 ppm. solids, the characteristic impedance of the transduce as obtained previously.
material Zr is of ten close to Zs, In this case, the object i
is to approach Condition a by operating the trans-l ducers at C. Corrections for Phase Shift upon Reflection resonance since in the ideal case where efects of bonds and electrical loading are neglected, The time-delay T between successive echoes in an echo train diHers from the ultrasonic delay T'-2d/u, Z=i2r tanH///,,
(11) whenever a nonzero phase shift, y, occurs upon redec.
tion at a transducer-sample interface. For a two.
and 2 goes to zero when the signal frequency / is transducer arrangement (two identical redections in equal to the resonant frequency f-each round trip)
For measurements in duids, Condition c can be ob-tained by the use of buder rods." This technique has T*- T= 2(y/2H)(!//),
the disadvantage of limiting the tength of the echo train, which may be examined before unwanted echoes or interfere.
i
/T'-n = 2(7/2H).
(9)
A simple alternate to the use of buder rods is de-i Therefore, in order to obtain T' from the measured T, scribed here. Since Zs for most duid-transducer com-it is necessary to calculate y accurately or to arrange binations is smaller than Zr, the attainment of Co dition b is the experimental apparatus to rnake y as close to 0*
suggested. Consider an open-circuited, or 180* as possible. In practice, the latter course is lossless transducer with resonant freq :-7cy f, immersed usually chosen.
in a fluid medium cf impedance 23 this case, the The redection coef5cient r at a transducer-sample input impedance 2 for a planar acoustic save mci interface is given by on the transducer is r= ! ri e"= (2-2.)/(2+2.) (for pressures), (10) 2-z7 (12) where 2 is the acoustic input impedance to the trans.
ducer assembly (including edects of electrical loading, Under the assumptions 2sWZr ar.d av/'gl. uhere bonding materials and backings, when present) and
- 2. is the acoustic irnpedance of the specimen (usually f' = f,/2 and 2/= f-f', y in Eq.10 is vven on assumed to be pure real). According to Eq.10, y=0*
y/ 2H = -(l)(af/f'!(Z w Zri.
'13) 1254 vel.
45
%.ber 5 1969
S O tl N D VELOCITY IN WATER At M=0, y=0* and the transducer is operating as a distilled water specimen. The temperature of the bath
(
quarter. wave termination with inrinite input impe. was read on a -1* to 101*C (0.t'C division) mercury
}
dance. This is the technique that was used in the mea.
in glass thermometer supplied with the National Bureau s
surements of sound velocity in distilled water, which of Standards certiscation. When fully immersed, the l
l are described in this paper.
indicated thermometer corrections usually amounted to less than 0.03*C. At the higher temperatures.
l II. SOUND VILOCITY IN DISTILLED WATER emergent stem corrections of as rnuch as 0.2*C were A. Introduction
- '9"id' Distilled water provides a good specimen for testing C. Method and comparison of different sound velocity measure.
At a few temperatures, null conditions were obtained ment techniques. Water is stable, readily available, for a series of frequencies above and below 1 MHz.
has fairly constant acoustic properties and is relatively By making such measurements over a surfteiently wide unaffected by impurities, particularly dissolved air.u range of frequencies, it was possible to determine un.
Many measurements of sound velocity in water have ambiguously the proper value of is for each null fre-been made and good data exist in the literature with quency (Eq. 2). At each temperature, the delay T which to make comparisons. However, as Greenspan was calculated for each of the null frequencies (Eq.1).
a and McSkimmin" have pointed out, considerable dis. The values of T obtained in this way difered by a agreement exists between quoted values of absolute small amount due to the frequency. dependent phase velocitv. McSkimmin has made a study of the absolute shift y predicted by Eq. 9. The value of T at 1 MHz, sound ' elocity with a techriir <. of high absolute accu. half the resonant frequency, was assumed to be equ i
v racy and his values therefor provide a good standard to the ultrasonic delay T'since Eq.13 implies y=0 of comparison. As is shown later, our values for sound at this frequency. Representative data at a tempera.
velocity agree quite well with those of McSkimmin.
ture of 25*C are presented in Table I.
The third column of Table I represents the phase B. Experimental Apparacus shift upon redection as obtained from Eq. 9, where T' The electronic circuit used is basically the same as is the ultrasonic delay computed for /=1 MHz by interpolation between the values of T computed at the p).
that shown in Fig.1. For case in setting and measuring null frequencies. The quantity y/2II should vary frequency, a frequency synthesizer was used as the
(
signal generator. The phase detector was a modified cordmg to Eq.13. However, the data in Column 3 have a slope versus frequency approximately twice as AC-DC converter. 8 A diode switch followed by a large as the predicted value. This result is probablv power amplifier served as the gated amplifier. The due to electrical and mechanical loading efects on th'e remainder of the circuit was composed of standard commercial components-transducer, which are not accounted for in Eq. 9.
More important, such efects may cause the frequency The ultrasonic transducers were two 1.,m. diam x-cut, at which y=0 to shift away from 1 MHz, if we make quartz crystals, resonant at 2 MHz. These crystals the assumption that the frequency at which y=0 is were fully plated on both sides and spring loaded within *27o of 1 MHz, we can tise the slope of the against opposite ends of an accurstely machined brass spacer. The length of the spacer at room temperature data in Column 3 to estimate the possible error intro-(=25'C) was measured with a micrometer. Several measurements were made around the circumference of TASt.a I. Null frequences and phase. shift upon reflection in water at 25.00*C.
the spacer, and were averaged to compute the path length d= 5.1517 0.00N cm. The spacer was con.
Nurnber of structed such that the region surrounding the ultra.
frequency waveiengths iT-e f Ref. as sonic path contained no solid material except for two N 2' P" '** "" 5" P T *' * *F*l
brass posts, which supported the opposing 0.90105 o2 1.9 narrow transducer holders with respect to each other. By d
Ij placing these supporting posts about I cm beyond the 0.94453 65 1.2 outside edges of the transducers. the ultrasonic path jg y
y l
was essentially free of obstructions and the sound 0.93798 68 0.3 propagation was free seld.
1.00246 69
-0. I l
The transducer assembly was ilirectly immersed in M
-d a temperature-controlled water bath tilled with the t.04589 72
- l.1 1.06037 73
- I.3
( Q)s a M. Greenspan and C. E. Tsetuerg. J. Ace,ust. Soc. Arner.
[0
- 23. 301 f1956L
\\
" M. Greenspan. J. Acouse. Soc. Arner. 31. $47(A) Il959).
- Paatic Measurements rneact 1006.
.weim, i
i The Jeemel of the Acoustical Secsety of Amence 1255 t
R.
C.
WI L LI A M SO N Tauts !!. t!ncertainues.
Tute !!!. Veiacity of snund in ihsnueu water as a iunction of temperature.
Quantity Uncertainty Uncertaanty
=
in velocity Temperature Velocitv
.1 i Ref. as
'Q t*C) im seer
.m see Temperature 20.03*C (23*C) 2 0.0053 22.97 1491.07 0 03
- 0.04*C (50*C) 2 0.0032 2198 1493.37 0.01 20.0$*C (75'C) 2 0.0000 2100 1496.63 0.00 Path length
- 0.0004 cm 2 0.0080 26.01 1499.29 0.06 Thermal espansion 0.0000 cm (25'C) 2 0.0000 26.97 1501.70 0 03 20.0001 cm (30*C) 2 0.0025 28.00 15M.31 0.02 0.0002 cm (75*C)
- 0.0059 29.00 1306.71
- 0.01
(
Frequency 2 20 Hz at 1 M Hz 2 0.0020 30.00 1500.10
- 0.07 Phase sluf t 20.004 cycles 2 0.0057 35.00 1519.85 0.03 upon reflection Didraction 40.00 1328.92 0.09 I
- 0.0050 4100 1536.42 0.05 Over-all
- 0.20 misee tall n 2 0.0127 30.00 1342.36
-0.0 t 33.00 t 347.41 0.03 60.00 1331.13 0.17 6104 1331 61 0.19 duced by a nonzero 'r at 1 MHz. The resultmg un-70.00 1334.90 0.09 73.00 1333.22 0.13 l
certainty is i0.004 cycles.
74.00 1355.30 0.21 Once a for each null frequency has been determined 7100 13313a 0.22 at a given temperature, it is not necessary to repeat the whole procedure at nearby temperatures if the change
' C**"n n.nn aw. a smui.
in sound velocity is sufEciently small. Over most of the temperature range, measurements were made only for a It should be noted that the frequency of 1 MHz small range of frequencies close to 1 MHz and the value used in these measurements is much lower than the of the ultrasonic delay and sound velocity at 1 MHz were interpolated from these measurements.
frequencies normally used in ultrasonic pulse measure-The fmal value for the sound velocity was obtained ments. If, for example, a frequency of 30 MHz were by applying a correction for the thermal expansion of used, the number of wavelengths in a round trip
(= in Eq. 7) would be 30 times as large and the corre-brass (17 ppm /*C) and for effects of diffractica. The sponding accuracy would be 30 times greater. In addi
/
magnitude of the diffraction correction for each echo tion, ditTraction effects would be much smaller. How.
I was computed from the equations and empirical study ever, the increased accuracy obtainable by going to by McSkimmm." Beycad the third echo, this correc-higher frequencies is limited by the correspondingl tion was relatively constant at -(1.8 0.5)X 10" for higher attenuation, which limits the number of usable all visible echoes. Therefore, when determining the frequencies for the best null conditions, the first two echoes. More fundamentally, it is dif5 cult with any technique at any frequency to obtain a velocity resolu-or three echoes were ignored and a constant correction tion much less than the inverse of the mechanical was applied for all the remaming echoes.
quality of the sample.
D. Uncertainties E. Results The major sources of possible error in this experiment Table III shows the data obtained in this experiment are listed in Table II. As can be seen from the Table, over the temperature range from 23' to 73*C. These the largest source of error is uncertainty in the path data are compared with the values obtained by inter-length and in the correction br thermal expansion. potation from the data of McSkimmin," whose values The values listed for thermal expansion and diffraction are lower than those listed by.L Excellent agreem in Table II are the uncertainties in the magnitude of obtained up to 33*C. Above this temperature, the a the correction to the measured sound velocity and are ment is not as good, but a remains within the combined not equal to the magnitude of the co:Tections them-uncertainties of our measurements (McSkimmin :
u selves. The fact that the uncerta nty in frequency is
- 0.10 misec, this work: *0.20 m/sec). These measure-among the smallest in Table II indicates that the echo ments confirm the accuracy of McSkimmin's results phase-companson technique has capabilities for mes-and indicate the accuracy and usefulness of'the echo suring time delays that have not been fully exploited phase. comparison technique.
in these measurements. The over.all uncertainty of Recently, very accurate measurements of' sound ve-
- 0.0137o or (1.20 misec is computed by treating all locity in water have been made by Camvale et 4. at values in Table II as random errors.
the Naval Oceanographic Office." Our data overisp
- H.
(1960). J. McSkimmin. J. Acoust. Soc. Amer. 32. 1401-1404
" A. Carnvale. P. Bowen, M. Basileo, and J. Spranke. J.
(
Acoust. Soc. Amer. 44. 1096-1102 i1968).
1256 vei==e 45 Number 3 1969
.. - - - ~. -...
-. - -, _. - ~. ~ _ -.-. -...=.... -.
SOU N D VELOCITY IN WATER theirs at four points. 25', 30*, 33' and 40*C. The measurements except those of Greenspan and Tschier,"
f differences in the sound velocities that we measure are and Wilson," whose values for velocite lie consisten'th-i
(
(this work-NAVOCEANOi: -0.04, +0.04, +0.10.
higher than ours.
and +0.10 m Jsec,respectively. Again, agreement within the stated accuracy is obtained.
ACENOWLEDGMENTS A comprehensive comparison with other data in the The author is grateful for the hospitality of the literature can be made by referring to Refs.12 and 21.
Center for Materials Science and Engineering, MIT.
Our data agree quite well with all of the most accurate where this research was performed while the author w&S a research affiliate.
88 R. A. McConnell and W. F. Mruk, J. Acoust. Soc. Amer.
31 75 7 [95 2
'^
^ '
27, 672-676 (1955),
a w, p, wilson, J. Acoust. Soc. Amer. 31, 1067-1072 (1959).
9 9
)
i%/
w N /*""*1 of '8= Acesseic.i su,,,
4,,,,,,,,
m
~ _ _ _ _ _. _. _. _ _. _. _ _ _. _. _ _ __
Responses to NRC Questions: September 29.1998 Question 29:
How is the LEFM used currently to provide coridction factors to the venturis? Is the correction determined on the basis of the absolute accuracy or the repeatability of the LEFM?
Answer:
The LEFM is used at Comanche Peak to directly calibrate the nuclear instrumentation.
The correction factor is used only to keep the venturi calibration contemporary for use in t
the event that the LEFM is unavailable.
A correction factor is calculated in accordance with a plant procedure which has its methodology based on approved calculation. A minimum of 50 separate two hour data sets of FW mass flow rate from the LEFM and venturis are recorded in a spreadsheet.
The percent difference of each data set, the average percent difference of all data sets, and the standard deviation of all data sets is calculated. The correction factor is calculated from the average percent difference plus the two standard deviation margin.
The spreadsheet calculation is independently reviewed, documented by a TE, and given to the System Engineering Computer Group to implement in the appropriate plant computer software under an approved change process.
The Plant Computer multiplies the feedwater flow rate as determined by the venturis by the correction factor. This correction is displayed on the plant computer as " NET LEFM
'(
t CORRECTED POWER" and is available for use when the LEFM is out of service. The LEFM is used directly when it is in service. The 2 standard deviation margin used in the correction factor calculation prevents this corrected MWth from being equal to the MWth calorimetric power determined directly from the LEFM.
The correction is based on the absolute accuracy of the LEFM but a high degree of repeatability is also required.
Attachments:
None.
O I
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