Flow of brine in pipes,

HILL I N 0 I SUNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

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Vol. XXVI September 11, 1928 No. 2[Entered as second-class matter December' 11, 1912, at the post office at Urbana, Illinois, under

the Act of August 24, 1012. Acceptance for mailing at the special rate of postage providedfor in section 1103, Act of October 38 1917, authorized July 31, 1918.]

FLOW OF BRINE IN PIPES

BT

RICHARD E. GOULDAND

MARION I. LEVY

BULLETIN NO. 182 -

ENGINEERING EXPERIMENT STATIONPULOURHS BY THIN UNIVERSITY 0o ILtINIB, U**tAW

PaRIE: FIrFTan CEN T

T HE Engineering Experiment Station was established by act ofthe Board of Trustees of the Tiniversity of Illinois on Decem-ber 8, 1903. It is the purpose of the Station to conduct

investigations and make studies of importance to the engineering,manufacturing, railway, mining, and other industrial interests of theState.

The management of the Engineering Experiment Station is vestedin an Executive Staff composed of the Director and his Assistant, theHeads of the several Departments in the College of Engineering, andthe Professor of Industrial Chemistry. This Staff is responsible forthe establishment of general policies governing the work of the Station,including the approval of material for publication. All members ofthe teaching staff of the College are encouraged to engage in scientificresearch, either directly or in cof6peration with the Research Corpscomposed of full-time research assistants, research graduate assistants,and special investigators.

To render the results of its scientific investigations available tothe public, the Engineering Experiment Station publishes and dis-tributes a series of bulletins. Occasionally it publishes circulars oftimely interest, presenting information of importance, compiled fromvarious sources which may not readily be accessible/to the clientele ofthe Station.

The volume and number at the top of the front cover page aremerely arbitrary numbers and refer to the general publications of theUniversity. Either above the title•pr below the seal is given the num-ber of the Engineering Experiment Station bulletin or circular whichshould be used in referring to these publications.

For copies of bulletins or circulars or for other information address

THmE ENGNEERING EXPEtIMtNT STATION,

UNIVEnSITe OR ILL;NOiS,

UR. ANA, ILLINOI

UNIVERSITY OF ILLINOIS

ENGINEERING EXPERIMENT STATION

BULLETIN No. 182 SEPTEMBER, 1928


BY

RICHARD E. GOULD

RESEARCH ASSISTANT IN MECHANICAL ENGINEERING

AND

MARION I. LEVY

GRADUATE STUDENT IN MECHANICAL ENGINEERING

ENGINEERING EXPERIMENT STATIONPUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA

I

CONTENTS

I. INTRODUCTION

1. Preliminary Statement2. Objects of Investigation

3. Acknowledgments .

II. FLOW OF FLUIDS IN PIPES

4. Types of Flow .

5. Friction Factor

6. Reynolds' Number .

7. Viscous Flow .

PAGE

77

. 77

77

. 88

. 10

III. DESCRIPTION OF APPARATUS . . . . . 10

8. Experimental Pipe Line . . . . . . 10

9. Pressure Measurement . . . . . . . 11

10. Temperature Measurement . . . . . . 11

11. Velocity Measurement . . . . . . . 11

12. Auxiliary Apparatus . . . . . . 11

13. Insulation . . . . . . . . 12

14. Brine Solution . . . . . . . . 12

IV. METHODS OF CONDUCTING TESTS . . . . . 12

15. Selection of Test Conditions . . . . . 12

16. Control of Test Conditions . . . . . . 12

17. Purging the Manometer Connections . . . . 13

18. Recorded Readings . . . . . . . . 13

V. CALCULATIONS . . . . . . . . . 13

19. Effective Length . . . . . . . . 13

20. Friction Factor . . . . . . . . 13

21. Reynolds' Number . . . . . . . . 13

VI. RESULTS OF TESTS

22. Turbulent Flow

23. Critical Region

24. Viscous Flow

. 13

. 13

. 17

. 17

4 CONTENTS (CONTINUED)

VII. COMPARISON OF RESULTS . . . . . . . 17

25. Comparison with Brass Pipe . . 1726. Comparison with Steel and Iron Pipe . 17

VIII. CONCLUSIONS . . . . . . . . . . 19

27. Summary of Conclusions . . 19

APPENDIX: VISCOSITY OF COMMERCIAL CALCIUM CHLORIDE

SOLUTIONS . . . . . . . . . 20

1. Introductory Statement . . 202. Description of Viscometer . . 203. Calibration of Viscometer . . . . 20

4. Method of Conducting Experiments . . 215. Results of Experiments . . . . . 22

6. Conclusions . . . . . 24

LIST OF FIGURES

NO. PAGE

1. Schematic Plan of Pipe Friction Plant . . . . . . . . 11

2. Variation of Friction Factor with Reynolds' Number for Brine Flowing in

Wrought-iron Pipe . . . . . . . . . . . . 16

3. Variation of Friction Factor with Reynolds' Number for Various Fluids in

Pipes of Several Materials . . . . . . . . . . 18

4. Details of Viscometer . . . . . . . . . . . . 22

5. Relation between Reciprocal of Kinematic Viscosity of Calcium Chloride

Brine and Temperature for Different Specific Gravities . . 23

6. Comparison of the Reciprocal of the Kinematic Viscosity of Commercial Brine

and Pure Brine . . . . . . . . . .. . 24

LIST OF TABLES

1. Principal Results of Tests on Flow of Brine in Pipes . . . . . 14


I. INTRODUCTION

1. Preliminary Statement.-In all applications of refrigerationinvolving the circulation of brine, a knowledge of the magnitude offrictional losses is essential to the economical selection of pipe sizes.The optimum size of pipe is that one which strikes an economic bal-ance between cost of material, cost of installation, and cost of powerrequired to overcome frictional resistance. The calculation of fric-tional resistance involves the use of a friction factor, the value ofwhich must be determined for any given set of conditions. A definiterelation exists between the friction factor and a ratio known asReynolds' number. This ratio is a function of the dimensions ofthe pipe, the average velocity of the fluid, and the density andviscosity of the fluid.

2. Objects of Investigation.-The principal object of thisinvestigation was to determine the relation between the frictionfactor and Reynolds' number when commercial calcium chloridebrine is circulated in standard wrought-iron pipe under the condi-tions encountered in refrigeration practice.

A secondary object was to determine the viscosity of commer-cial calcium chloride brine.

3. Acknowledgments.-These tests have been a part of the workof the Engineering Experiment Station of the University of Illinois,of which DEAN M. S. KETCHUM is the director, and of the Depart-ment of Mechanical Engineering, of which PROF. A. C. WILLARDis the head. The authors are indebted to PROF. A. P. Kratz forhis suggestions with respect to the experimental work and his assist-ance in preparing the manuscript. They are also grateful to PROF.H. J. MACINTIRE for his advice in that part of the work undertakenas a project in the Graduate School.

II. FLOW OF FLUIDS IN PIPES

4. Types of Flow.-The experiments of Osborne Reynolds*showed that there are two types of fluid motion in pipes. At low

*Osborne Reynolds, Proc. Roy. Inst. of Great Britian, Vol. 14, 1893.

ILLINOIS ENGINEERING EXPERIMENT STATION

velocities .the fluid particles move in parallel lines with no eddiesin a condition that is known as stream line or viscous flow. Underthis condition the frictional resistance, or loss of head, varies directlywith the velocity. At higher velocities the flow becomes unordered.This condition is known as the turbulent condition, and the lossof head varies approximately as the square of the velocity. Thelowest velocity at which the transition from viscous to turbulentflow occurs is known as the lower critical velocity. Reynolds showedthat the critical velocity varies inversely as the diameter of the pipewhen pipes of the same relative roughness are considered. Thevelocities of flow ordinarily encountered in pipe lines in engineeringpractice are in the turbulent flow range.

5. Friction Factor.-The Darcy* formula for the loss of head inthe turbulent flow range is

1 v2 41 v2

h =f m - f (1)m 2g d 2g

in which

h = loss of head due to friction in feet of fluid flowingf = friction factor1 = effective length of pipes, in feetv = average fluid velocity, in feet per second

dm = hydraulic radius, in feet (m = d when fluid fills a circular

pipe)d = inside diameter of pipe, in feetg = acceleration of gravity, in feet per second per second.

It is sometimes convenient to express the head loss due to fric-tion in terms of lb. per sq. in. instead of feet of fluid. In this caseequation (1) becomes

Isv2

Pl - P2 = 0.8 7 f dg (2)

in whichP1 - P2 = pressure loss due to friction, in lb. per sq. in.

s = specific gravity of fluid flowing.

6. Reynolds' Number.-Experiments have shown that the valueof the friction factor f, as determined by equation (1), dependsupon the roughness of the inner surface of the pipe, and that itvaries with the diameter of the pipe, the velocity of flow, and the

*Certain modifications of this formula are also credited to Chezy, Weisbach, Unwin, and Fanning.


density and viscosity of the fluid. The application of Rayleigh's*principle of dynamical similarity to the problem of flow of fluids inpipes has led to a general theory of fluid flow in which the frictionfactor f is found to be a function of a dimensionless ratio known asReynolds' number, or

R = dvp (3)

in which

d = inside diameter of pipe, in feetv = average fluid velocity, in feet per secondA = absolute viscosity, in lb. per ft. per secondtp = density, in lb. per cubic foot.

The ratio of the absolute viscosity to density, -, may be represented

bythe single symbol v. Reynolds proposed the name kinematicviscosity for this ratio. Equation (3) may then be written

dvR - A (4)

in which

v = kinematic viscosity, in square feet per second.

By utilizing the relationship between the friction factor f andReynolds' number R in connection with equation (1) the resultsof experiments with any fluid may be used to determine the loss ofhead which will be encountered by any other fluid flowing in pipelines having the same relative roughness. This relationship fordrawn brass pipe based on the experiments of Stanton and Pannelltwith air and water, and Saph and Schoder§ with water is shown inFig. 3. Since equation (2) was derived directly from equation (1),the same numerical value for the friction factor f may be used inboth equations provided no change is made in the units specified.Therefore, Fig. 3 is applicable to both equations (1) and (2).

*Lord Rayleigh, Phil. Mag., Vol. 34, 1892.Lord Rayleigh, Phil. Mag., Vol. 8, 1904.

tThe absolute viscosity of a substance is measured by the tangential force on unit area of eitherof two horizontal planes of indefinite extent at unit distance apart, one of which is fixed while the othermoves with unit velocity; the space between being filled with viscous substance.

$Stanton and Pannell, Phil. Trans. Roy. Soc., Vol. 214, 1914.§Saph and Schoder, Proc. Amer. Soc. Civil Eng., Vol. 51, 1903.


7. Viscous Flow.-Poiseuilles' Law for the loss of head in theviscous flow range is

321vvh = - (5)gd

2

in which the notation is the same as that in equations (1) and (4).This law applies to any pipe line, regardless of the roughness of thewalls, when the flow is at constant temperature in the viscous range.It may be expressed in terms of Reynolds' number and the frictionfactor as determined by equation (1) from the following considera-tions:

At the critical velocity it is reasonable to assume that the pres-sure loss h for a given length of pipe would be the same for bothviscous and turbulent flow since this is a transition point.Therefore, from equations (1) and (5)

32vl 41v 2

-- =f (6)

Solving for f16v

f-dv (7)

Combining equations (4) and (7) the expression becomes

16f - R (8)

By employing equation (8) a single line has been drawn in Fig.3 representing the values of f to be used in equation (1) when theflow is in the viscous range. This line is applicable to any fluidflowing in any pipe regardless of the nature of the inner surface.

III. DESCRIPTION OF APPARATUS

8. Experimental Pipe Line.-The pipe used for these tests wasstandard weight, new wrought-iron pipe having a nominal insidediameter of 11Y inches, and an actual average inside diameter of1.38 inches. The section through which the friction pressure dropwas measured consisted of two parallel lengths of 51 feet each,connected by a 1Y2-foot radius return bend of the same pipe, givinga total length of 106.71 feet. This test section, including the en-trance and exit lengths of pipe, was made up of 20-foot lengths,the ends of which were sawed square. After the burrs were removed


Fla. 1. SCHEMATIC PLAN OF PIPE FRICTION PLANT

the lengths were carefully aligned and the joints butt welded. Theinner surface of the pipe at these joints was examined after the testswere completed, and it was found to be free from any exceptionalroughness. The continuous pipe was suspended in a horizonal planeas shown in Fig. 1.

9. Pressure Measurement.-All pressure losses were measuredin feet of fluid flowing by means of inverted U-tubes. These U-tubeswere connected to the piezometer rings shown in Fig. 1, and wereso arranged that any air which collected could be easily expelled.The piezometer ring at the entrance to the test section was precededby a straight run of 15 feet.

10. Temperature Measurement.-The temperatures of the brineentering into and discharging from the test section were obtained bymeans of two calibrated thermocouples. Each thermocouple wasmade of No. 22 B. and S. gage copper-constantan wire immersed inoil in a 1

4-inch glass tube which was inserted a distance of 4 inchesdirectly in the flowing brine at positions shown in Fig. 1.

11. Velocity Measurement.-The rate of flow of brine was de-termined by observing the time required to discharge a given weightof brine.

12. Auxiliary Apparatus.-The brine was drawn by a motor-driven centrifugal pump from a reservoir having an approximatecapacity of 230 cubic feet, and was discharged through forty feetof pipe before the test section was reached. The piping on the dis-


charge side of the test section was offset upwards to cause the ex-perimental pipe to run full of brine under all conditions. The brinewas discharged into a tank mounted on a platform scale. This tankdischarged back into the reservoir. Suitable by-passes were arrangedso that the brine could be sent through either a steam heater ora mechanically refrigerated brine cooler before entering the testsection.

13. Insulation.-All piping was lagged with a layer of 112 inchesof hair felt, which was covered with building paper and muslin.

14. Brine Solution.-All brine solutions used were made bydissolving commercial calcium chloride in deep-well water. Con-centrations were determined by means of a Westphal balance. Atypical analysis on the dry basis of the calcium chloride used is asfollows:

C aCl12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 .09N aC l..................... .......... 1.68C aSO 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 .08C a(OH )2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.09Insol. in H 20 ........................ 0.06

100.00

IV. METHODS OF CONDUCTING TESTS

15. Selection of Test Conditions.-For the purpose of this in-vestigation the concentration, temperature, and velocity of the brinewere regarded as independent variables, and were varied as far aspossible within commercial ranges. The pressure loss was a func-tion of these three independent variables, while the viscosity wasdependent on the brine concentration and temperature only.

A test series consisted of a number of groups of tests withpractically the same brine concentration for each group. Eachgroup of tests was run with the brine at approximately the sametemperature, and contained a number of tests each at a constantvelocity and temperature.

16. Control of Test Conditions.-The specific gravity of the solu-tion remained practically constant, in each series of tests, exceptfor the slight variation due to changes of temperature. At the be-ginning of each group of tests the brine was brought to the desiredtemperature by means of the heater or cooler, and maintained ap-


proximately at this temperature. With the pump running at con-stant speed it was necessary to throttle the discharge to obtain achange of velocity for various tests in the group.

17. Purging the Manometer Connections.-Before any readingsfor a group of tests were taken, and occasionally before individualtest readings were taken, the connections from the piezometer ringsto the manometer were thoroughly purged of any entrapped airwhich would have affected pressure loss readings.

18. Recorded Readings.-A period of several minutes was alwaysallowed before each test for conditions of flow to become constant.The time required for each test was approximately five minutes,during which time simultaneous observations of the pressure loss,temperature, velocity, and specific gravity were made.

V. CALCULATIONS

19. Effective Length.-Preliminary work indicated that the pres-sure loss around the return portion, which included two feet ofstraight pipe and 4.71 feet of curved pipe, was 7.5 per cent of thepressure loss through the entire test section of 106.71 lineal feet.The equivalent length of the return portion accordingly was

106.71 x 0.075 = 8.00 feet of straight pipe.

Therefore, the effective length of the test section was

106.71 - (2 + 4.71) + 8.00 = 108.00 feet.

20. Friction Factor.-The friction factors shown in Table I,column 7, were calculated from equation (1) using correspondingvalues of head loss h from column 6, and velocity v from column 5.

21. Reynolds' Number.-The values of Reynolds' number shownin Table I, column 8, were calculated from equation (4). This equa-tion was modified to use the reciprocal of v instead of v directly, andthe values of these reciprocals are given in column 4. These valueswere obtained by experiment as described in the Appendix.

VI. RESULTS OF TESTS

22. Turbulent Flow.-The result of plotting the friction factorsas ordinates against the corresponding Reynolds' numbers as ab-scissas on logarithmic cross-section paper is shown in Fig. 2. The


TABLE 1

PRINCIPAL RESULTS OF TESTS ON FLOW OF BRINE IN PIPES

TestNo.

1

23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657

SpecificGravity

2

1.0221.0221.0221.0221.0221.0221.0241.0241.0241.0241.0241.0241.0231.0231.0231.0231.0221.0221.0221.0221.0221.0221.0221.0221.0221.0221.0221.0221.0221.0221.0221.0701.0701.0701.0701.0701.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.0691.069

AverageTemp.deg. F.

3

39.939.738.840.040.040.136.136.336.536.836.937.137.837.337.838.344.244.344.544.744.844.944.844.456.757.057.257.557.557.558.132.732.932.933.033.237.937.937.637.537.537.544.746.244.444.744.844.844.544.544.744.844.849.250.450.449.3

Reciprocal ofKinematicViscositysec. persq. ft.1 -v

4

57 50057 40056 50057 60057 60057 70053 60053 80053 90054 20054 30054 40055 40054 80055 40055 70062 00062 10062 20062 40062 50062 70062 50062 10075 40075 80075 90076 10076 10076 10076 90045 50045 90045 90046 00046 10050 50050 50050 20050 20050 20050 20056 60058 00056 60056 60056 70056 70056 60056 60056 60056 70056 70060 80061 90061 90060 800

AverageVelocityft. per

sec.v

5

3.8234.5855.6885.0842.1971.4555.7525.3504.9534.3083.3912.5571.5845.7203.9921.8965.9275.0334.3243.5742.6801.5253.6525.0205.8765.0584.1753.1892.4911.8141.1833.2074.2695.3125.7454.1922.2013.2844.2465.2935.7263.9220.5050.7221.3022.0472.8033.7294.6675.4015.6783.5971.8040.4961.0251.9132.935

HeadLossft. ofbrine

h

6

6.058.43

12.269.942.221.08

13.2711.749.847.744.993.101.32

12.646.731.78

13.299.837.365.253.201.175.539.84

12.699.606.844.232.801.600.734.627.83

11.5913.547.402.334.717.39

11.1012.836.390.180.330.902.003.495.778.75

11.3112.375.461.590.180.591.763.69

FrictionFractor

f

7

0.007110.006860.006490.006790.007860.008750.006880.007030.006890.007140.007440.008110.009070.006620.007250.008450.006480.006660.006760.007060.007640.008570.007130.006690.006310.006430.006700.007110.007740.008360.009000.007690.007380.007050.007010.007210.008250.007480.007000.006800.006710.007110.012100.010860.009130.008160.007630.007120.006880.006640.006570.007200.008410.012540.009540.008270.00732

Reynolds'Number

R

8

25 28030 27036 96033 68014 5509 660

35 46033 10030 70026 85021 18016 00010 09036 05025 43012 15042 26035 94030 93025 65019 26011 00026 25035 85050 95044 09036 44027 91021 80015 88010 46016 78022 53028 04030 39022 22012 78019 07024 51030 56033 06022 640

3 2904 8208 480

13 32018 28024 32030 38035 16036 96023 45011 7603 4707 300

13 62020 520


TABLE 1 (Concluded)

PRINCIPAL RESULTS OF TESTS ON FLOW OF BRINE IN PIPES

TestNo.

1

585960616263646566676869707172737475767778798081828384858687888990919293949596979899

100101102103104105106107108109110111112113114

SpecificGravity

2

1.0691.0691.0691.0691.0691.0691.1341.1341.1341.1341.1341.1341.1341.1341.1341.1341.1341.1341.1331.1331.1331.1331.1331.1331.1331.1331.1331.1331.1331.1331.1331.2061.2061.2061.2061.2061.2061.2061.2061.2021.2021.2021.2021.2021.2021.2021.1971.1971.1971.1971.1971.1971.1961.1961.1961.1961.196

AverageTemp.deg. F.

3

49.349.149.549.549.549.817.218.620.520.520.729.529.030.630.430.130.931.642.043.240.040.542.042.042.051.553.052.551.752.051.5

-1.52.03.04.04.55.05.36.5

16.016.516.717.018.019.017.534.835.434.734.935.535.346.146.746.547.547.0

Reciprocal ofKinematicViscositysee. persq. ft.1+ -

4

60 80060 60061 00061 00061 00066 30028 60029 50030 90030 90031 00037 00036 60037 70037 50037 30038 00038 40045 50046 40044 10044 50045 50045 50045 50052 20053 40052 90052 30053 60052 20014 90016 30016 60017 00017 20017 40017 60018 10022 30022 50022 60022 70023 20023 70022 90031 50031 70031 30031 60031 80031 80037 40037 80037 60038 10037 900

AverageVelocityft. per

sec.v

5

4.2225.4375.8344.5472.4780.7721.0751.5092.7153.8565.0555.5894.4303.4722.2381.4380.6820.2950.5571.1472.0222.5813.5335.1355.5210.7431.7092.8403.7765.1355.6800.3880.8051.4082.7303.6864.6933.5580.4315.1613.8883.1301.8290.9590.2833.9165.3723.9973.1591.0254.2690.6044.8653.8981.6100.7840.400

HeadLossft. ofbrineh

6

7.1711.5212.928.172.770.360.751.353.726.96

11.3313.298.855.612.581.180.320.070.210.762.063.225.57

10.9412.640.351.473.616.03

10.5112.760.210.441.294.327.25

11.106.750.20

12.697.585.152.010.540.107.52

12.427.194.800.678.200.229.916.651.430.410.10

FrictionFractor

f

7

0.006910.006670.006520.006770.006720.010350.011080.010150.008620.008010.007590.007300.007740.008010.008810.009770.011800.013800.011610.009900.008640.008290.007650.007100.007100.010860.008630.007670.007230.006820.006770.023840.011640.011110.009940.009140.008640.009110.018430.008180.008610.009010.010290.010070.021400.008370.007390.007700.008230.010840.007720.010330.007170.007500.009460.011430.01071

Reynolds'Number

R

8

29 52037 89040 93031 90017 3805 8903 5405 1209 650

13 70018 02023 78018 65015 0509 6506 1702 9801 3002 9206 120

10 26013 21018 49026 87028 890

4 46010 50017 28022 71031 65034 100

6601 5002 6905 3407 2909 3807 190

90013 24010 060

8 1404 7802 560

77010 31019 46014 57011 370

3 73015 610

2 21020 92016 9506 9603 4401 740

I I I II



portion of the curve having abscissas greater than 2500 applies tothe condition of turbulent flow. All experimental points in thisregion fall within a narrow band, and may be represented by asingle, well-defined line for all conditions of specific gravity, temper-ature, and viscosity.

23. Critical Region.-On plotting the experimental data cor-responding to values of Reynolds' number of approximately 2500,a decided decrease in the values of the friction factor may be noted,indicating that a discontinuity occurs in the actual flow curve.This region is known as the critical region, in which the flow tendsto change from turbulent to viscous.

24. Viscous Flow.-The portion of the curve including abscissasof from 500 to approximately 2500 represents the condition of vis-cous flow, and the curve shown is the theoretical relation existingfor any fluid flowing at constant temperature in any pipe. It may benoted that the experimental points in Fig. 2 representing conditionsof viscous flow fall practically on the curve representing the theoret-ical relation expressed by equation (8).

VII. COMPARISON OF RESULTS

25. Comparison with Brass Pipe.-The substantiation of theexperiments of Stanton and Pannell on the flow of water and air inhard-drawn brass pipe by the work of Saph and Schoder on theflow of water in similar pipe has given a definite relation betweenthe friction factor and Reynolds' number for this kind of pipe. Thisrelation is shown in Fig. 3. For the sake of comparison the curve ofFig. 2 has been reproduced in Fig. 3 omitting, however, the ex-perimental points. For the same value of abscissa, the brass pipein all cases of turbulent flow shows a smaller value of the frictionfactor than does the wrought-iron pipe. This is consistent with therelatively smooth inner surface of brass pipe. Almost exact agree-ment exists in respect to the value of Reynolds' number at whichturbulent flow changes to stream line flow.

26. Comparison with Steel and Iron Pipe.-From a compilationof the results of various investigations on the friction of fluids otherthan brine flowing in steel, wrought-iron, and cast-iron pipe Mc-Adams* has proposed a single curve to represent flow in pipes of this

*W. H. McAdams, "Flow of Fluids," Mass. Inst. Tech. Serial No. 121.



nature. This curve is reproduced in Fig. 3. In commenting on this

curve, and on the curve for brass pipe, McAdams states, "It would

be interesting to obtain test data for the friction of brine solutionsin pipes of commercial refrigerating equipment of the closed typein order to determine which curve applies." It may be noted from

Fig. 3 that the proposed curve of McAdams is in fairly close agree-

ment with the results of this investigation. The values of the fric-

tion factor from the experimental results are slightly lower than

those obtained from the proposed curve, particularly for smallervalues of Reynolds' number. The proposed curve is a composite of

the results of a number of investigators, and probably included some

data from experiments made on pipe having rougher surfaces thanthe surface of the commercial wrought-iron pipe used in this inves-tigation.

VIII. CONCLUSIONS

27. Summary of Conclusions.-As a result of this investigationthe following conclusions may be drawn:

(1) The general theory of flow which involves the expres-sion of the friction factor as a function of Reynolds' number is

applicable to commercial calcium chloride solutions flowing inpipes.

(2) The curve established for the flow of brine in commer-cial wrought-iron pipe is slightly lower than, but in close agree-ment with, the mean curve established by other investigators forthe flow of air, steam, water, and oil in clean steel and cast-iron pipes.


APPENDIX

VISCOSITY OF COMMERCIAL CALCIUM CHLORIDE SOLUTIONS

1. Introductory Statement.-In order to evaluate Reynolds'number which was used in the analysis of the friction of brine, aknowledge of the viscosity of the fluid over a wide range of condi-tions was necessary. Although the results of several investigationsof the viscosity of calcium chloride solutions were available, all ofthe published data referred to solutions of chemically pure salt indistilled water and, therefore, were not considered applicable to thecommercial brine used in this investigation. A study of the solu-tions actually used was therefore considered advisable.

2. Description of Viscometer.-A specially constructed pyrexviscometer was used for this work, and is shown in Fig. 4. Theliquid was maintained at constant temperature, and gravity flowthrough the capillary tube was allowed to take place under a variablehead. The main portion of the viscometer was water jacketed and,with the exception of two narrow bands adjacent to the etched ref-erence lines, it was entirely lagged with 1,-inch of hair felt.

The samples of brine solutions on which viscosity determina-tions were made were taken from the reservoir during friction ex-periments.

3. Calibration of Viscometer.-Before the viscometer could beused it was necessary to calibrate it over the range of viscositiesencountered in the friction tests. Two standard solutions for whichthe kinematic viscosities were known over a wide range of tempera-tures were selected. The first of these solutions was distilled water,for which the viscosity values have been obtained by Bingham andWhite.* The second was a 20 per cent solution of pure cane sugarand distilled water, having a specific gravity of 1.081,t for whichthe viscosity values are given by Hosking.1 Samples of these stand-ard fluids were allowed to flow through the viscometer at varioustemperatures between 32 and 75 deg. F. The samples were main-tained at a constant temperature while flowing through the vis-cometer by keeping the temperature of the jacket water within 0.5deg. F. of the temperature of the sample. The time of efflux be-tween the two reference lines as noted by means of a stop watch

*Landolt and B6rnstein Physical Chemistry Tables.tVan Nostrand's Chemistry Annual.:Landolt and Barnstein Physical Chemistry Tables.


Cao//ary

FIG. 4. DETAILS OF VISCOMETER

was plotted against the kinematic viscosity, and it was found that

the accuracy was such that the ends of the two standard fluid cali-

bration curves superimposed and gave one continuous curve over

the desired range.

4. Method of Conducting Experiments.-The brine samples were

each run through the viscometer three times for every given tem-

perature. The average of the three time readings obtained for, each

condition was regarded as the time of efflux.

5. Results of Experiments.-From the calibration curve and the

average time of efflux, the kinematic viscosities for the various con-

ditions of temperature and specific gravity were obtained. The re-

ciprocal of the viscosity was found to be nearly a linear function of

the temperature and, accordingly, in order to obtain greater accu-

racy in extrapolation the results have been plotted as reciprocals of

kinematic viscosity, as shown in Fig. 5. The portions of the curves

1~//7/sh/'7a'

h.Pe


FIG. 5. RELATION BETWEEN RECIPROCAL OF KINEMATIC VISCOSITY OF CALCIUMCHLORIDE BRINE AND TEMPERATURE FOR DIFFERENT SPECIFIC GRAVITIES

which have been extrapolated toward the freezing points have beenshown as dotted lines.

The results of Walker* and Simeont on chemically pure solu-tions are in agreement with each other, and are plotted in Fig. 6.

*W. J. Walker, Phil. Mag., Vol. 27, 1914.tF. Simeon, Phil. Mag., Vol. 27, 1914.


T~,vera/~w-e /A' d~ F

FIG. 6. COMPARISON OF THE RECIPROCAL OF THE KINEMATIC VISCOSITY OFCOMMERCIAL BRINE AND PURE BRINE

For the sake of comparison the curves in Fig. 5 have been transferredto Fig. 6. From Fig. 6 it may be noted that the commercial solu-tions deviate from the pure solutions. If the values of the viscosityof pure solutions had been used instead of that of commercial solu-tions in computing Reynolds' numbers, a maximum error of plusor minus 10 per cent could have occurred.

24 ILLINOIS ENGINEERING EXPERIMENT STATION

6. Conclusions.-As a result of these experiments the followingconclusions may be drawn:

(1) The viscosity of commercial brine solutions may de-viate by as much as 10 per cent from the viscosity of solutionsof chemically pure salt in distilled water at the same tempera-ture and concentration.

(2) It is advisable to determine the viscosity of the actualsolution in use in establishing the values of Reynolds' numbers.

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