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The effect of wall roughness on heat transfer in pipes Smith, James Wilmer 1955

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THE EFFECT OF WALL ROUGHNESS ON HEAT TRANSFER IN PIPES by JAMES WILMER SMITH A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING We accept th i s thesis as conforming to the standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE Members of the Department of CHEMICAL ENGINEERING THE UNIVERSITY OF BRITISH COLUMBIA September, 1955 ABSTRACT Heat transfer and f r i c t i o n data were obtained f o r a i r flow through seven commercial pipes with equivalent sand roughness r a t i o s varying from 0.020 to 0.000lj.l i n the Reynolds number range 10,000 - 80,000. Heat transfer f o r a given power l o s s decreased with increasing roughness r a t i o except at very high power losses, where t h i s trend was to some extent reversed. The r e s u l t s f o r the Karbate pipe were somewhat out of l i n e with those f o r standard pipes. This i s attributed to a difference i n the nature of the Karbate roughness. In the p l o t s of f r i c t i o n factor and versus Reynolds number, the experimental data show that J H continues to decrease with Reynolds number when f r i c t i o n factor has become constant f o r a rough pipe. This £act contradicts not only Reynolds' simple turbulence analogy and Colburn's modifi-cation thereof, which are i n other respects inapplicable, but i s also at odds with the more rigorous analogy of Taylor and Prandtl and the similar, semi-empirical equation of P i n k e l . I t i s , however, i n agreement with the Karman analogy, which also gives a good absolute p r e d i c t i o n of the heat transfer data. ACKNOWLEDGMENTS I wish to acknowledge the assistance of Mr. B. C. Almaula, who i n i t i a t e d construction of the apparatus, and of Dr. Norman Epstein, under whose guidance the work was performed. I am also indebted to the National Research Council f o r a Bursary and f o r supplementary f i n a n c i a l grants during the summers of 1951+- and 1955• TABLE OP CONTENTS ACKNOWLEDGMENTS ABSTRACT INTRODUCTION CRITICAL REVIEW OP PREVIOUS PERTINENT WORK Appendix l a - C a l i b r a t i o n Curves.-for O r i f i c e Plates Appendix l b - C a l i b r a t i o n of Pressure Gauge i 1. Correlation of Isothermal Data i n Rough Pipes 2. Correlation of Non-isothermal F r i c t i o n Data 3. Correlation of Heat Transfer Data I).. Previous Investigations of the Ef f e c t of Surface Roughness on Heat Transfer Ij. 5 . Theoretical Heat Transfer - Momentum Transfer Analogies 6 6. Empirical Heat Transfer - Momentum Transfer Equations 8 7. Conclusions Based on the Literature Survey 9 DESCRIPTION OP APPARATUS AND EXPERIMENTAL METHOD 10 1. The Apparatus 10 A. The A i r System 10 B. The Steam System 13 2. Experimental Method l L 3. Treatment of Data l o A. Calculation of Flow Rate 16 B. Calculation of Isothermal Data 16 C. Calculation of Heating Data 17 RESULTS AND CONCLUSIONS 19 Table I - Comparison of j H Calculated from Reynoldsi Analogy and from Experi-mental Curves 31a SUMMARY 3k NOMENCLATURE 35 BIBLIOGRAPHY AND REFERENCES 38 APPENDIX k-2 to Appendix 2 Appendix 3 Appendix J+a Appendix i+b Appendix i+c Appendix i^ -d Appendix 5 - Approximate Tolerances f o r O r i f i c e Meter - Results of Heat Balance Runs - Physical Dimensions of Pipes - Results of Isothermal Runs - Calculated Values of Relative Roughness and Deviations - Results of Heating Runs - Heat Transfer and F r i c t i o n E f f i c i e n c y Data Appendix 6 - Experimental Non-isothermal Data LIST OF FIGURES Figure 1. Figure 2. Figure 3. Figure I+. Figure 5» Figure 6. Figure 7. Figure 8. Figure 9* Figure 10. Figure 11. Schematic Diagram of Apparatus 11 1/8 i n . Galvanized Pipe -Heat Transfer and F r i c t i o n Data 20 1/lj. i n . Galvanized Pipe -Heat Transfer and F r i c t i o n Data 21 1/2 i n . Karbate Pipe-Heat Transfer and F r i c t i o n Data 22 3/8 i n . Galvanized Pipe-Heat Transfer and F r i c t i o n Data 23 l A i n . Standard Steel Pipe-Heat Transfer and F r i c t i o n Data 2I4. 3/8 i n . Standard Steel Pipe-Heat Transfer and F r i c t i o n Data 25 i n . Copper Pipe-Heat Transfer and F r i c t i o n Data 26 7 Commercial Pipes Heat Transfer and F r i c t i o n Data 27 Heat Transfer - F r i c t i o n E f f i c i e n c y 29 Test of von Karman's Analogy 32 1 INTRODUCTION Although extensive l i t e r a t u r e on the e f f e c t of sur-face roughness on f l u i d f r i c t i o n i s available (7, 30, 39, ii.2), few investigations of the e f f e c t of roughness on heat .transfer have been made. The work which has been done has been almost e n t i r e l y on a r t i f i c i a l l y roughened pipes (8, 1+-0), the excep-t i o n being a study of the performance of a s i l i c o n carbide tube by Sams and Desmon (ill.). This i n v e s t i g a t i o n was I n i t i a t e d to study the e f f e c t of normal wall roughness i n commercial pipes on heat transfer rates; to determine whether rough pipes are more or l e s s e f f i c i e n t heat transmitters than smooth pipes f o r a given power expenditure; and to t e s t some of the t h e o r e t i c a l equa-tions which have been developed (I4., 19* 35* 37* M*) f o r pr e d i c t i n g the r e l a t i o n between f l u i d f r i c t i o n and heat transfer. Seven commercial pipes (1/8, l/Lf., 3/8 In. standard galvanized; 1/lj., 3/8 i n . standard s t e e l ; l/Lf. i n . standard copper; and 1/2 i n . "Karbate" graphite) were investigated. The data on each pipe were correlated using the f i l m temper-ature concept, which had previously been found to correlate both f l u i d f r i c t i o n and heat transfer data most consistently by Humble, Lowdermilk and Desmon (15) • The maximum Reynolds number attainable (80,000) was l i m i t e d by an inadequate supply of high pressure a i r . 2 CRITICAL REVIEW OF PREVIOUS PERTINENT WORK 1, Correlation of Isothermal F r i c t i o n Data i n Rough Pipes Numerous correlations are available f o r c a l c u l a t i n g f r i c t i o n f a c t o r s In rough pipes, a term which may be applied to most commercial pipe other than drawn tubing. An early equation of Drew and Genereaux (11) = 3.2 log(Re-Vf) • 1.2 (1) represents the average of widely scattered data f o r turbulent flow i n rough pipe. This equation neglects the e f f e c t of varying wall roughness r a t i o s which Is taken i n t o account i n the t h e o r e t i c a l equation f o r turbulent flow derived by von K arm an (19a)» -L- - 4 .06 log(D w/e) • 2.02 (2) and the equivalent empirical equation of Nikuradse (32)J -JL- - 1|. log(D w/e) • 2.28 (3) V f w Colebrook (7) used Nikuradse's data to derive an equation applying i n the t r a n s i t i o n region between laminar and turbulent flow, = k log(D w/e) • 2.28 - k l o g / l • k M ^ l e ) V? \ Re-Vv (k) which reduces to Equation 3 at large Reynolds numbers. Moody (30) and Rouse (39) have presented i d e n t i c a l f r i c t i o n f a c t o r p l o t s based on Equations 3 and ij.. Moody includes a chart from which, f o r any given commercial pipe, e/D w may be obtained, and the corresponding f r i c t i o n factor f may be obtained at any Reynolds number from the f r i c t i o n f actor p l o t . 2• Correlation of Non-isothermal F r i c t i o n Data Methods of c o r r e l a t i n g non-Isothermal f r i c t i o n data have been investigated by McAdams (29)» Epstein and P h i l l i p s (lljl), Sams (I4.O), and Humble, Lowdermilk and Desmon (15). These workers conclude that i f the f i l m temperature (average of bulk f l u i d and wall temperatures) i s used f o r evaluating the f l u i d properties, good c o r r e l a t i o n may be obtained with non-isothermal f r i c t i o n data. Thus, the f i l m Fanning f r i c t i o n f a c t o r may be calculated from the equation and the f i l m Reynolds number from the equation Re f = D wV be f/fc f (6) Humble, Lowdermilk and Desmon (15) and Sams (lf.0) found that heating data calculated i n this manner l i e on the curve represented by isothermal data, except at Re^ l e s s than 20,000, where the method appears to overcompensate f o r r a d i a l temperature gradients. k 3. Correlation of Heat Transfer Data Standardized methods of c o r r e l a t i n g heat transfer dataare given i n many excellent works, including those of McAdams (29), Kern (21), and Jakob (17). The j„ f a c t o r i s ii frequently used f o r c o r r e l a t i n g heat transfer data because of the simple, approximate r e l a t i o n between the j H and f versus Re curves noted by Colburn (6) f o r smooth tubing. Humble, Lowdermilk and Desmon (1^) and Sams (l|JL) found that the best c o r r e l a t i o n between J H and Reynolds number resulted i f , as i n the c a l c u l a t i o n of the non-iso-thermal f i l m f r i c t i o n f a c t o r , the f l u i d properties were evalu-ated at the f i l m temperature Tf. Thus, Re f may be calculated from Equation 6 and j h from the equation: • v f e M f - s t ^ / 3 Previous Investigations of the E f f e c t of Surface Roughness  on Heat Transfer The early work of Cope (8) on the e f f e c t of a r t i f -i c i a l , m i l l e d roughness on heat transfer rates indicated that the increase i n the heat transfer rate i s not nearly as great as the increase i n f r i c t i o n , at l e a s t i n the turbulent region. He concluded that the smooth pipe i s a more e f f i c i e n t trans-mitter of heat than the a r t i f i c i a l l y roughened pipe on the basis of heat transferred f o r equal power l o s s . Colburn ( 6 ) , using the data of King (22) and of 5 Nagaoka and Watanabe (31)» who studied the e f f e c t of i n t e r n a l m e t a l l i c turbulence promoters, appears to contradict the conclusion of Cope that rough pipes are less e f f i c i e n t than smooth tubes. However, t h i s contradiction i s probably more apparent than r e a l , since the turbulence promoters may be acting as extended surfaces. A similar conclusion reached by Drexel and McAdaras (12) f o r wavy surfaces may be duetto the nature of the surface studied. Leva and^Grummer (2i|.a) studied the e f f e c t of part-i c l e c h a r a c t e r i s t i c s , including surface roughness, on heat transfer i n packed tubes, and found that even though f f o r very rough p a r t i c l e s was more than twice that f o r smooth p a r t i c l e s (2i|b), the corresponding increase i n the heat trans-fe r rate was only 10$. Arni and Meyers (2) investigated the e f f e c t of i n t e r n a l roughness on heat transfer and pressure drop i n i n t e g r a l finned tubes, but f e l t that the 10$ increase i n f over the t h e o r e t i c a l smooth curve did not merit an estimation of the increase i n the heat transfer c o e f f i c i e n t . Sugawara and Sato (1|7), studying the e f f e c t of grooves and projections on the surface of a f l a t p l a t e on heat transfer rates, found that t h i s type of roughness had an appreciable e f f e c t but d i d not calculate f r i c t i o n f a c t o r s . They also found that at high Re heat transfer c o e f f i c i e n t s became e s s e n t i a l l y independent of Re. 5« Theoretical Heat Transfer - Momentum Transfer Analogies Several attempts have been made to deduce the form of the function <|) i n the expression St = $(Re, Pr) (8) which may be obtained by dimensional analysis. These attempts have been made a n a l y t i c a l l y f o r turbulent flow by comparing the exchange of momentum and heat. Reynolds (38) dealt with a purely turbulent system i n which exact s i m i l a r i t y between . the temperature and v e l o c i t y of f l u i d s was postulated ( I . e., Pr r 1 ) . The equation representing t h i s system i s simply: J H s § ( P r ) 2 / 3 (9) Colburn introduced a modification of t h i s analogy which was found to f i t the data f o r smooth tubes better and on which the d e f i n i t i o n of j i s based: H J H = § = St ( P r ) 2 / 3 (10) Prandtl (35) and G. I. Taylor (I4.8) extended the analogy to other values of the Prandtl modulus by introducing the concept of a laminar sublayer and a turbulent core. Their derivation can be expressed as: , . t ( P r ) 2 / 3 Von Karman (19b) defined a buffer layer of p a r t i c u l a r chara-c t e r i s t i c s between the laminar l a y e r and the turbulent 7 core. His equation may be written: y f ( p p ) 2 / 3  J H = 5[Pr f i n d 4 5PD + 0 .5 l a g / f ] ( 1 2 ) Boelter, M a r t i n e l l i and Jonassen extended the Karman analogy to include the cases where the physical properties of the f l u i d vary across the diameter of the tube. They obtained the expression: 2/3 £ ( F r ) * / J A T W Z f f m e a n  J H S $[Pr • l n ( l + 5Pr) + 0 .5 l a ^ / ^ U 3 ) M a r t i n e l l i 1 s (27) further modification of von Karman»s analogy includes the e f f e c t of the eddy d i f f u s i v i t i e s of heat and momentum (assumed equal). The f i n a l equation i s : j - 71 ( P r ) 2 / 3 ^max/AT mean H = 5[Pr * l n ( l + 5Pr) + 0.$D.R. l n | § / | ] where D.R. Is a function of the eddy and molecular d i f f u s -i v i t i e s of heat. M a r t i n e l l i tested h i s analogy with the data of Cope (8)and obtained a reasonably good c o r r e l a t i o n . He used t h i s f a c t to i n f e r that a laminar sublayer also exists In rough pipe. Other investigators, such as M a t t i o l i (28) and Reichardt (37), have presented more involved r e l a -tionships between heat and momentum transfer. An objection to these analogies has been made by Cavers et a l (5)* who note that i n a l l the analogies the r a t i o of eddy conductivity to eddy d i f f u s i v i t y i s unity, whereas experimental measurements indicate that t h i s i s not so f o r Pr near 1, except possibly at high Re. 8 6. Empirical Heat Transfer - Momentum Transfer Equations Pratt (36) has proposed that turbulence promoters and packings should be characterized by a factor B r e l a t i n g t h e i r performance from the point of view of heat or mass transfer to that i n a smooth tube. He points out that sur-face roughness may po s s i b l y act as a turbulence promoter and therefore may also be c l a s s i f i e d by the f a c t o r B. However, thi s method has a maximum error of 2%<f0, which i s probably as great as the heat transfer variations caused by variatio n s i n wall roughness, PInkel (3I+,) extended the concepts developed by Dei s s l e r (10) to include rough pipes. His f i n a l equation can be rearranged to f f ( P r ) * / 3 where O.9I and 1370 were determined from experimental data and y Q i s a measure of the e f f e c t i v e height of the influence of the roughness. Equation 15 i s quite s i m i l a r In form to the analogy of Prandtl and Taylor (Equation 11). Pinkel used Equation 15 to obtain excellent c o r r e l a t i o n of data with widely varying f i l m temperatures and degrees of a r t i -f i c i a l roughness. 9 7. Conclusions Based on the Literature Survey The general conclusions which may be drawn from the l i t e r a t u r e survey on the e f f e c t of a r t i f i c i a l roughness on heat transfer i s that roughness does not have nearly the same e f f e c t on heat transfer that i t has oh f l u i d f r i c t i o n , and that d i f f e r e n t types of roughness or turbulence promoters may have appreciably d i f f e r e n t e f f e c t s f o r the same power loss per u n i t area of heat transfer surface. The lack of data on heat transfer i n commercial pipes; the p o s s i b i l i t y that commercial rough pipes may be more e f f i c i e n t heat transmitters per u n i t area heat transfer than smooth tubing; and the d e s i r a b i l i t y of testing the heat - momentum transfer analogies were reasons f o r i n i t i -ating t h i s p r o j e c t . 10 DESCRIPTION OP APPARATUS AND EXPERIMENTAL METHOD 1. The Apparatus The apparatus consists of a double pipe heat ex-changer (Pig. 1 ) . A i r passes through the Inner experimental pipe where i t i s heated by steam contained i n the outer pipe (steam jacket). The equipment may be divided into two systems, the a i r system and the steam system, each of which w i l l be described i n d e t a i l . A. The A i r System A i r was supplied at 20 p s i g . by the b u i l d i n g Nash compressor (ijOO cfm.), or at 80 p s i g . by a small p o s i t i v e displacement compressor (15 cfm.) when i t was found that the pressure drop through the apparatus was very great. In order to obtain maximum flow rates, both compressors were run at the same time. A i r pressure to the apparatus was regu-l a t e d by a BBL type Pisher c o n t r o l l e r . Prom the c o n t r o l l e r the a i r passed through a calib r a t e d o r i f i c e assembly and thence to the entrance of the experimental section. The upstream pressure of the a i r at the o r i f i c e and the pressure at the entrance to the heating section could be measured on the same mercury manometer or on the c a l i b r a t e d 6 i n . diameter, 0 - 30 p s i . , Bourdon pressure gauge i f the pressures were too high. The temperature T x of the a i r at the entrance to the heating section'was measured to the nearest 0.1 °P with a c T , S T E A M P R E S S U R E G A U G E 0 r O R I F I C E S T A N D A R D P R E S S U R . E T A P , y^ss. P I P E v ^ T r A I R P R E S S U R E R E G U L A T O R ^ 4 = S T E A M P R E S S U R E R E G U L A T O R A I R | V E N T S T E A M I N S U L A T I O N 0 J A C K E T Y/////A Y///////A YA//////A Y////A B I I N. S.S. P I P E \ f t S T A N D A R D P R E S S U R E T A P V E N T =tx3= S T E A M T R A P ^ J) / O R I F I C E M A N O M E T E R U P S T R E A M P R E S S U R E G A U G E E X P E R I M E N T A L S E C T I O N C O N D E N S A T E ik u U P S T R E A M P R E S S U R E M A N O M E T E R S E C T I O N M A N O M E T E R F I G . I S C H E M A T I C D I A G R A M O F A P P A R A T U S 12 c a l i b r a t e d 3 i * * . Kimble immersion thermometer. The pressure drops through the o r i f i c e and through the experimental section were measured on the d i f f e r e n t i a l o r i f i c e and section mano-meters. The outlet a i r temperature T2 was measured on another ca l i b r a t e d thermometer to 0.2 °P. The a i r was then vented to the atmosphere. Two brass, standard square-edge o r i f i c e p l a t e s (1) of 1/tf. In. and 3/8 i n . bore were cal i b r a t e d at the same time as the isothermal runs were performed with a lf.00 c f h r . B. C. E l e c t r i c diaphragm gasmeter which had been calibr a t e d to within 2% accuracy. The c a l i b r a t i o n curves f o r the o r i f i c e plates are given i n Appendix l a . The o r i f i c e pressure taps were of the vena contracta type, constructed according to the standards of the Am. Soc. Mech. Engrs. (1) from aluminum discs, as were the s t a t i c pressure taps at the entrance and e x i t of the experimental section. The bore of the taps was made to conform as c l o s e l y as possible to the actual in s i d e diameter of the pipe i n which they were placed. The a i r flow rates were calculated from the - L o r i f i c e discharge equation (33): w = 0 oYS o /2 gc(Pi - P 2 T 5 [ (16) A l l terms i n the equation are obtainable from the physical dimensions of the system or from c a l i b r a t i o n data except Y, which may be calculated from the expression f o r vena contracta and radius taps (33) s 13 = fesf)loJ«1 + ° - 3 5 A ) U 7 ) or estimated from the p l o t given by Stearns et a l (ij.6) which , i s based on Equation 17. The a i r temperature thermometers were calibr a t e d against each other and against a standard thermometer, but no p l o t i s given because they were accurate to the degree of p r e c i s i o n to which they could be read. Both thermometers were Kimble 3 i n . immersion thermometers, the scales being graduated from -10 to 120 and 0 to 300°F»» res p e c t i v e l y . Appendix l b . i s a c a l i b r a t i o n curve f o r the 6 i n . , 0-30 p s i g . Bourdon pressure gauge. The gauge was c a l i b r a t e d against a Barnet No. OI31 dead-weight t e s t e r . A calming length of 8 i n . preceded the experimental section, although i n turbulent flow t h i s should not be necessary. The heating section i t s e l f was 5*17 f t . long. B. The Steam System Steam from the 30 p s i g i b u i l d i n g supply passed through a condensate eliminator and a Mueller pressure reducer to the I f i n . insulated steam jacket. A vent at the upper surface allowed the escape of non-condensable gases. The jacket was i n c l i n e d very s l i g h t l y so that condensate would run in t o a steam-trap, passed through a water-cooled condenser, collected, and weighed. Steam temperatures T^, Tg> and Tq; were read from three c a l i b r a t e d thermometers. Corresponding Ik steam pressures were checked on a 3 i n . diameter Bourdon gauge. 2. Experimental Method The experimental section i n every case except that of the Karbate graphite pipe was cut to length (5.17 f t . ) from a piece of new pipe, the outside polished on an emery sander, threaded on both ends, coated with o l e i c acid, and mounted i n the experimental apparatus. The o l e i c acid was applied to ensure that steam would condense i n a drop-wise manner (16), thus giving a n e g l i g i b l y small resistance to heat transfer on the steam side of the exchanger. The 1/2 i n . Karbate pipe could not be treated i n the same way because of the d i f f i c u l t y encountered i n threading such a b r i t t l e material. The pressure taps f o r t h i s pipe were made i n the form of a sleeve which f i t t e d over the end of the graphite pipe, a t i g h t seal being made with a rubber gasket and a sealing compound. The steam jacket was sealed at the ends by means of rubber gaskets tightened on with locknuts. The seven pipes examined were: 1. 1/8 i n . standard galvanized. 2. l/k. i n . standard galvanized 3. 1/2 i n . (actual diameter) Karbate Graphite. ij.. 3/8 i n . standard galvanized. 5. l/Ij. i n . standard s t e e l . 6. 3/8 l n« standard s t e e l . 1$ 7. lA± i n . standard copper. Ten or more isothermal runs were made on each pipe to determine the f r i c t i o n f a c t o r curve from which e/Dw, the r e l a t i v e roughness, could be determined. At the same time, i f desired, a check on the o r i f i c e c a l i b r a t i o n curve could be made on the B. C. E l e c t r i c gasmeter. A l l pressures ( i n c -luding barometric pressure), pressure drops, and temperatures were recorded during these runs. An attempt was made to obtain a range of Reynolds numbers from 10,000 to as high as the equipment and a i r supply would allow. The procedure followed during the heating runs was such that the system was as close to steady state as possible when readings were taken. Runs were not made u n t i l at l e a s t one hour after the steam had been turned on. Ten or more runs of 15 minutes duration were made on each pipe; a l l thermometers, pressure gauges and manometers being read every f i v e minutes. Cooled condensate was co l l e c t e d during each run and weighed to permit a heat balance. At l e a s t f i v e minutes were allowed to elapse between runs, although, i n general, apparent equilibrium was achieved i n less than one minute. A range of Reynolds numbers from 10,000 to the maxi-mum capacity attainable (60,000 -80,000) was covered, f o r each pipe. 16 3. Treatment of Data In a l l calculations D_, the inside diameter of the w pipe i n question^ was assumed to be equivalent to the insi d e diameter s p e c i f i e d by the manufacturer. As a check, the diameter of the 1/L|. i n . standard steel pipe was measured by volumetric displacement. The difference between the measured and s p e c i f i e d diameters was l e s s than 0,6%. A. Calculation of the Flow Rate The a i r flow rated was calculated from Equations l 6 and 17 using the p h y s i c a l dimensions of the o r i f i c e meter, experimentally observed data and the c a l i b r a t i o n curves appearing i n Appendix l a . A consideration of the tolerances (Appendix 2) reveals that the approximate o v e r a l l tolerance of the meter i s l . l f j $ , which indicates that the o r i f i c e meter should have an accuracy of ,at l e a s t 2% f o r non-pulsating flows. B. Calculation of Isothermal Data The Fanning f r i c t i o n f a c t o r and Reynolds number f o r each run were calculated from Equations 5> and- 6> r e s p e c t i v e l y . From these values, the value of e/Dw, the r e l a t i v e roughness, was calculated for each point using Equation Ij.. The geo-metric average of the values f o r D w/e f o r each pipe was then calculated, and t h i s value i n turn used to p l o t a smooth curve of f versus Re f o r each pipe, according to Equation ij.. 17 G. Calculation of Heating Data A l l heating data were correlated using the f i l m temperature f o r evaluating the physical properties of the a i r , as recommended by Humble et a l (lf>) and previously described. The f i l m f r i c t i o n f a ctors, calculated from Equation 5>, served as a check that the pipe wall roughness had not changed during long i n t e r v a l s between runs. The f i l m Reynolds number and jg were calculated from Equations 6 and 7» respect-i v e l y . The s p e c i f i c heat of a i r was assumed to be 0.2ij. Btu/(lb) (°P), but i t i s r e a d i l y seen that since C_ appears i n both the numerator ( i n h) and i n the denominator of the Stanton modulus, C p w i l l have no e f f e c t on the Stanton modulus St. The f i l m Prandtl number Prj. was evaluated from a p l o t of Pr versus temperature given i n the paper by Sams (1+0). Throughout the entire i n v e s t i g a t i o n Pr^ seldom deviated from the value O.69. A recent t h e o r e t i c a l analysis of L i n , Moulton and Putnam (&£)» which introduces a small amount of eddy i n what i s normally considered the boundary layer, indicates that better agreement could be obtained i f the index of the Prandtl modulus i n J H were made a variable with Reynolds number. Weisman (I4.9) reports that the index may be written: n = 1.22 R e " 0 , 7 (18) The difference, however, has very l i t t l e e f f e c t on jjj when the Prandtl modulus i s close to unity, as i s the case with gases. I t was decided, therefore, to r e t a i n the o r i g i n a l value of 2/3 18 used by Colburn (6). In t h e i r c o r r e l a t i o n of turbulent heat transfer data using the f i l m concept, Humble et a l (15) eliminate the influence of entrance and ex i t conditions by, i n e f f e c t , multiplying j H by the f a c t o r ( L / D w ) 0 , 1 .. Since i n the present study L/D w varies only from I2I4. to 170, the maximum possible v a r i a t i o n i n J H due to t h i s factor i s only 3.$%. The actual v a r i a t i o n was probably even smaller, because of the r e l a t -^ i v e l y low and p r a c t i c a l l y constant wall surface temperature employed. End eff e c t s were therefore ignored i n co r r e l a t i n g the present data. The c a l c u l a t i o n of the heat balance was based on the t o t a l energy balance: q + w g = M * * 2 - r Y U £ A Z ( 1 9 ) 2gc Sc which, f o r the present setup, reduces to: q = AH Because of the extremely low and variable steam qu a l i t y , good heat balances were not obtained during regular runs. However, special heating runs with well-dried steam were made i n which the maximum deviation was reduced to l e s s than 10% {l.k%, 9»$% and 3.k%)> which i s considered good f o r th i s type of balance (see Appendix 3). Calculation of heat trans-f e r c o e f f i c i e n t s was based on heat actually received by the a i r , as given by i t s flow rate and temperature r i s e . 19 RESULTS AND CONCLUSIONS The calculated values f o r the heat transfer and f r i c t i o n f a c t o r data f o r each pipe are tabulated In Appendix k. and are shown gra p h i c a l l y on Figures 2 to 8. On the graphs, f r i c t i o n f actor curves are drawn through the isothermal points using Equation 2 and the logarithmic (geometric) average r e l a t i v e roughness ( e / D w ) & . The tendency of the f i l m temp-erature method to overcompensate f o r r a d i a l temperature gradients at Re l e s s than 20-30,000, noted by Humble, Lowder-milk and Desmon (15) and by Sams (lj.0), has been corroborated i n t h i s work. At higher Re, the isothermal and heating f r i c t i o n data l i e on the same curve. A comparison of f r i c t i o n factors f o r the various pipes i n Figure 9 shows that, i n order of decreasing roughness, the pipes are: Pipe e/°w e (calc.) e (Moody) A - 1/8 i n . galv. 0.01958 ... 0.000^39 0.0005 B - l/k i n . galv. 0.01150 0'0003^9 0.Q005 C - 1/2 i n . Karbate 0.00702 0.0002Q3 D - 3/8 i n . Galv. O.OO63I 0.000260 0.0005 E - l A i n . s t . s t e e l 0.00362 0.000110 0.00015 F - 3/8 i n . s t . s t e e l 0.002^6 0.000105 0.00015 G - l A i n . copper O.OOOlf.1 0.000013 0.000005 A l l values of the roughness index e appear to be lower than those given by Moody (30} except the value of e f o r the copper pipe. Such differences might be expected, however, because of changes and differences i n manufacturing techniques, o n _ i i i I I i l l FIGURE 2. g IN. GALVANIZED PIPE _ U F A T T R A M Q F F R A F R I P . T I H N D A T A -. O -CD O s ° CD m O G 0 IS s VI "vD—(t EATING RUNS n • — - O o — — i — ~ von K. • 8 10 1.5 2 3 4 F ILM R E Y N O L D S NUMBER DvM>Qf 8 I0 = 1.5 . - A - 1 - -! 1 l \—i—i i FIGURE 3. 3 IN. GALVANIZED PIPE U C T A - T T D A M C P C D Q . F P I P T i n M H A T A nc_M l < -u • 1 MM CD IS O w OTHEI E A T I N R M A L RU G R U N S NS — — . . . . _ . |— iD Xfc* w n . . . . — — . . . • i -•  • 1 i ! G O - ' ' 1 \ i i 1 1 ! ' - von K 8 1 0 4 1.5 2 3 4 FILM R E Y N O L D S N U M B E R DwVbef 8 I 0 5 1.5 FIGURE 4. ^|N. KARBATE GRAPHITE PIPE HEAT TRANSFER a FRICTION DATA ® I S O T H E R M A L R U N S O H E A T I N G R U N S F I L M R E Y N O L D S N U M B E R DwVDef Wt CM _l|Q 8 csJirO *-ol o * 3 FIGURE 5. | IN. GALVANIZED PIPE HEAT TRANSFER a FRICTION DATA (D I S O T H E R M A L R U N S O H E A T I N G R U N S ro F I L M R E Y N O L D S N U M B E R FIGURE 6, 5 IN. STANDARD S T E E L PIPE! HEAT TRANSFER S FRICTION DATA i i <D I S O T H E R M A L R U N S i i — O H E A T I N G R U N S i I ! o -— M 1 - 4 1 1 1 1 — 1 — 1 — I — | FIGURE 7. | l N . STANDARD S T E E L PIPE U C A T T D A M C C C D Q. C D I f T I O M H A T " A • CD IS O T H E R M A L R U NS w n c A i i n i D ( n — i ~~~~~~ - ~ ^ y o n K . i i ! 1 ! 1 8 10 L5 2 3 F I L M REYNOLD 'S N U M B E R 8 10' 1.5 CVJ > o r _1|Q .CM ^ lO2 0_' II OJ|tO •3] 0> O II X 1 1"" 1 1 1 1 1 1 1 1 -1 1 1 ; 1 1 1 1 1 1 1 FIGURE 8. J|IN. COPPER PIPE i i r - A T - r r - i A M f r r n o r n i O T i r \ M r i A T A n c . M i -\i^or t_r r rA 1 \Jl\ 1 L • ® -is O u »OTHEI E A T IN R M A L R U G R U N S NS ' o -> O C ) C) r C i 1 ) . von K. i 8 I 0 4 1.5 ro F I L M R E Y N O L D S N U M B E R 8 |Q5 —\ 1- ----- I - . 1 - I - I ( H-T--FIGURE 9. 7 COMMERCIAL PIPES HEAT TRANSFER & FRICTION DATA A i IN GALV. f 2 8 and because of normal differences i n i n d i v i d u a l samples of pipe. The curves of j H versus Re f have been f i t t e d i n the straight l i n e region by the method of averages to equations of the form: J H • - ' K ( R e f ) m ( 2 0 ) Values of K and m are included with the tabulated data i n Appendix If.. These values show no s i g n i f i c a n t trend, probably because the range of Reynolds numbers investigated was not large enough f o r a l l the pipes. A comparison of the heat transfer e f f i c i e n c i e s of the various pipes i s given i n Figure 1 0 , where a modified form of the heat transfer c o e f f i c i e n t h / C p t P r ) ^ ^ i s p l o t t e d against the power loss per square foot of heat transfer area E. The data from which the graph was plotted are tabulated i n Appendix This method of p l o t t i n g the data i s si m i l a r to one presented by Colburn ( 6 ) f o r comparing turbulence promoters. The graph shows that f o r the same heat transfer c b e f f i c i e n t , l e s s pumping power per square foot of heat transfer area i s required f o r smooth tubing than f o r rough piping. This agrees with the conclusion of Cope ( 8 ) , who found the same r e s u l t f o r a r t i f i c i a l l y roughened pipes. The f a c t that a l l the curves except the curve f o r copper pipe i n t e r s e c t at a power loss of about 3 2 0 foot-pounds per second per square foot of transfer area i s an i n t e r e s t i n g phenomenon. Apparently, beyond t h i s point, the very rough pipes become more e f f i c i e n t than i i iii m—i—r " FIGURE 10. HEAT TRANSFER - FRICTION EFFICIENCY 30 those of intermediate roughness, but s t i l l not as e f f i c i e n t as the copper pipe, at l e a s t within the l i m i t s of the i n v e s t i -gation. Possibly some new . a w turbulent heat transfer mech-anism which i s not a d i r e c t function of flow rate becomes dominant at t h i s point. Another Interesting point i s that although the Karbate pipe i s rougher than the 3/8 i n . galv., l/k i n . s t . steel and 3/8 i n . s t . steel pipes, at power losses of l e s s than 320 i t i s more e f f i c i e n t than these pipes, i n d i c a t i n g that the nature of the surface roughness of the Karbate pipe may have been d i f f e r e n t . A microscopic examination ( of the four types of surfaces investigated ("smooth" copper, standard s t e e l , galvanized steel and Karbate graphite) rev-ealed that: 1. The copper surface was smooth, with only a few l o n g t i t u d i n a l scratches, the c r y s t a l structure being e a s i l y d i s c e r n i b l e . 2. The galvanized surface was extremely rough, jagged and i r r e g u l a r , as i f the surface of a r a p i d l y b o i l i n g l i q u i d had suddenly been frozen. 3. The standardized steel surface was l i k e the galv-anized surface, the roughness being random and i r r e g u l a r , but on a much smaller scale. if.. The Karbate graphite pipe, on the other hand, d i s -played a very regular, geometrically patterned surface, l i k e the surface of a double-cut f i l e , with the v a l l e y s running normal to and i n the d i r e c t i o n of flow. 31 I t i s quite reasonable,then, to expect that the nature of the surface i t s e l f may have an appreciable e f f e c t on heat transfer rates. The values of J H predicted by Reynolds 1 analogy (Equation 9) a**© compared with the experimentally observed values at Re f = 20,000, 50,000, and 100,000 i n Table I. That these values are not i n accord i s not surprising when one considers the simple turbulent core basis of the Reynolds* analogy. Taylor's and Prandtl's analogy (Equation 11) as well as Pinkel's equation (Equation 15) p r e d i c t that when f has become constant i n rough pipes at high Re, J H should also be constant. Data obtained during t h i s i n v e s t i g a t i o n do not confirm t h i s r e s u l t , although Pinkel obtains good c o r r e l a t i o n with h i s equation using some NACA data f o r a r t i f i c i a l l y roughened tubes. The explanation f o r the constancy of f at large Re i n rough tubes given by Coulson and Richardson (9) i s : "With rough pipes, however, an additional drag known as form drag r e s u l t s from the eddy currents caused by impact of the f l u i d on obstructions, and, when the surface i s "very rough, i t becomes large compared with the skin f r i c t i o n . Since form drag involves d i s s i p a t i o n of k i n e t i c energy, the losses are proportional to the square of the v e l o c i t y of the f l u i d . . . " When t h i s happens, f becomes independent of Re. One would surmise, however, that heat transfer rates are not d i r e c t l y influenced by the form drag, so that the simple r e l a t i o n between f and j H indicated by the Prandtl and Taylor analogy and by the Pinkel equation Is not v a l i d . 31a TABLE 1 Comparison of j H Calculated from Reynolds' Analogy and from Experimental Curves Pipe Reynolds Number J h (Experimental) J h (Reynolds) 1/8 Galv. 1/4 Galv. 1/2 Karbate 3/8 Galv. 1/4 S. Steel 3/8 S. Steel 1/4 Copper 20,000 50,000 100,000 20,000 50,000 100,000 20,000 50,000 100,000 20,000 50,000 100,000 20,000 50,000 100,000 20,000 50,000 100,000 20,000 50,000 100,000 0.00185 0.00280 0.00233 0.00338 0.00268 0.00215 0.00329 0.00270 0.00231 0.00295 0.00239 0.00200 0.00295 0.00238 0.00194 0.00291 0.00239 0.00202 0.00323 0.00255 0.00498 0.00473 0.00473 0.00410 0.00392 0.00391 0.00355 0.00340 0.00340 0.00351 0.00335 0.00328 0.00314 0.00293 0.00281 0.00307 0.00273 0.00254 0.00264 0.00222 0.00196 5 0 FIGURE II. TEST. OF VON KARMAN'S ANALOGY Pr = 0.69 4 0 3 0 20 10 + . + - — ' * - m D O-^ - - * b e A o ^ I N GALV. © ^IN GALy. e . i | N K A R B A T E +• | l N GALV . X i - IN ST. S T E E L • | l N S T . S T E E L A ^ I N C O P P E R V O N K A R M A N D O O 1500 2 0 0 0 3 0 0 0 R e f V f i 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 33 The a p p l i c a b i l i t y of von Karman's analogy was tested by p l o t t i n g V f f / J H versus -/f fRe f on Figure 11 f o r data points where j H versus Re f was i n the str a i g h t l i n e region. This method of p l o t t i n g should give a straight l i n e i f Karman's analogy holds. The data points f a l l on or near the theoret-i c a l curve with a maximum deviation of 15$. Lack of temper-mature gradient data prevented a test of the refinements incorporated into von Karman's derivation by Boelter et a l (Equation 13) and M a r t i n e l l i (Equation llj.) . However, the refinement introduced by Boelter et a l to compensate f o r r a d i a l temperature gradients ( i . e., r a d i a l v a r i a t i o n s i n f l u i d properties) should be rendered superfluous by the use of the f i l m temperature concept, which i s an empirical attempt to compensate f o r these v a r i a t i o n s . M a r t i n e l l i ' s refinement (the e f f e c t of the eddy d i f f u s i v i t i e s of heat and momentum) r e s u l t s i n p r a c t i c a l l y the same curve as von Karman's at high Re, but at lower Re predic t s that A/f^/jjj should be lower than predicted by von Karman's analogy. The experimental data seem to support t h i s p r e d i c t i o n . The jg curves calcu-lated by von Karman's analogy are also p l o t t e d f o r each pipe i n Figures 2 to 8 (dashed l i n e ) . Although the a p p l i c a b i l i t y of the von Karman analogy and i t s modifications has not been d e f i n i t e l y proved by t h i s investigation, i t i s shown to conform more to the f a c t s concerning the e f f e c t of wall roughness on heat transfer than do the simple analogies, the models f o r which either exclude the laminar layer completely or exclude the e f f e c t of the buffer l a y e r . 3k SUMMARY 1. Heat transfer and f r i c t i o n data f o r a i r i n 7 commercial pipes have been obtained i n the Reynolds number range 10,000 - 8 0 , 0 0 0 , e/D w varying from 0.020 to 0.000ij.l. These data have been correlated using the f i l m temperature concept described by Humble, Lowdermilk and Desmon (l£) by c a l c u l a t i n g J H * Re f, and f f f o r a l l pipes. The data are presented i n tabular and graphical form. 2. The e f f i c i e n c i e s of the pipes have been compared by p l o t t i n g h / C p t P r ) 2 / 3 against E, the power loss per square foot of heat transfer area. The p l o t shows that at l e a s t f o r E l e s s than 320 f t - l b s / ( s e c ) ( s q f t ) , smoother pipes are more e f f i c i e n t than rough pipes. An exception was the Karbate pipe, which, though le s s e f f i c i e n t than the smooth copper pipe, was more e f f i c i e n t than other pipes of lowererelative roughness. This f a c t i s attributed to the difference i n the nature of the surface of the graphite pipe. 3 . A t e s t of the Reynolds analogy has revealed, as expected, that i t does not hold for rough pipes. The analogy of Prandtl and Taylor and Pihkel's semi-empirical equation have the -common f a i l i n g of p r e d i c t i n g that when, at s u f f i c i e n t l y high ROfj-ff has become constant, jjj must also become constant, which i s not confirmed by these experimental data. The von Karman analogy, however, has been found to predict the data quite accurately and consistently within the range of Reynolds numbers investigated. 35 NOMENCLATURE i a - constant i n Equation 11, dimensionless A - heat transfer surface area, sq f t B - characterization f a c t o r , dimensionless C Q - o r i f i c e discharge c o e f f i c i e n t , dimensionless C - s p e c i f i c heat of a i r at constant pressure, p Btu/(lb)(°F) D Q - diameter of o r i f i c e , f t D w - in s i d e diameter of pipe, f t D. R. - d i f f u s i v i t y r a t i o Eg/(Eg + k/ C p ) , dimensionless e - equivalent sand roughness, f t Eg - eddy d i f f u s i v i t y f o r heat, sq f t / h r f - Panning f r i c t i o n f a c t o r , dimensionless f f ' - f i l m Panning f r i c t i o n f a c t o r , f l u i d properties evaluated at T^, dimensionless g - acceleration of gravity, f t / s q sec g c - conversion factor, ( l b ) ( f t ) / ( s e c ) 2 ( l b - f o r c e ) G - mass flow G = ev , lb/(see)(sq f t ) h - average heat transfer c o e f f i c i e n t , Btu/(sec)(sq ft)(°P) AH - enthalpy gained by a i r = wC p(T 2 - T j ) , Btu/sec j - " j - f a c t o r " f o r heat transfer a St P r 2 ^ , dimens-ionless k - thermal conductivity, ( B t u ) ( f t ) / ( s e c ) ( s q ft)(°P) K - constant c o e f f i c i e n t , Equation 20 L - tube length, f t m - index of Re i n Equation 20, dimensionless 3 6 n - index of Pr i n j ^ , Equation 18, dimensionless P - absolute pressure, lb-force/sq f t P^ - absolute pressure at i n l e t , lb-force/sq f t P 2 - absolute pressure at outlet, lb-force/sq f t AP - t o t a l pressure drop, lb-force/sq f t £&fr - pressure drop through section due to sk£zf f r i c t i o n , lb-force/sq f t = ? 1 - P 2 - G 2 ( v 2 - V i ) / g e q - heat supplied by steam, Btu/sec Pr - Prandtl number - GpW/k, dimensionless P r f - f i l m Prandtl number = (CJ*/k) , evaluated at T-, dimensionless P r Re - Reynolds number = DwV€//{, dimensionless Re^ - f i l m Reynolds number = ^•n^\>^fMft dimensionless S - cross-sectional area of pipe, sq f t S 0 - cross-sectional area of o r i f i c e , sq f t St - Stanton number = h/c pVe, dimensionless Stf. - f i l m Stanton number • h/CpV^S^, dimensionless T. _ _ - steam temperature, °R . A,x3,C - temperature of i n l e t air,. °R T 2 - temperature of outlet a i r , °R T b - temperature of bulk of f l u i d » (T^ + T 2)/2, °R T f - f i l m temperature - ( T b + T g)/2, °R T - average surface temperature of experimental pipe = T A = T B = T C, °R A T m a x - difference between temperature of pipe wall and center of pipe, °R ^Tmean " difference between temperature of pipe wall and average (mixed) temperature of f l u i d , °R V- - v e l o c i t y of a i r , f t / s e c 37 V-JL - s p e c i f i c volume of a i r at entrance, cu f t / l b v 2 - s p e c i f i c volume of a i r at outlet, cu f t / l b w - weight rate of a i r flow, lb/sec Y - expansion f a c t o r , Equation 17, dimensionless y e - e f f e c t i v e thickness of layer associated with roughness, f t A Z - difference i n elevation, f t /3 - r a t i o of o r i f i c e diameter to pipe diameter, dimen s i onless U - absolute v i s c o s i t y of f l u i d , l b / ( s e c ) ( f t ) € - density of f l u i d , lb/cu f t § - func t i o n a l r e l a t i o n s h i p Subscripts: a - average b - bulk, based on average of mean i n l e t and outlet temperatures f - f i l m , based on temperature s - surface, based on temperature T s 1,2 - entrance and e x i t of experimental section, r e s p e c t i v e l y 38 BIBLIOGRAPHY AND REFERENCES (1) Am. 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L., "Turbulence and D i f f u s i o n , " Ind. Eng. Chem, 21, 416 (1939). 39 (lif.) Epstein, N., and P h i l l i p s , J . B., "Non-isothermal Press-ure Drop f o r a Gas, " Can. J . of Research," F26, 503-12 (19i+8). (15) Humble,,. L. V., Lowdermilk, W. G., and Desmon, L. G», "Measurements of Average Heat Transfer and F r i c t i o n C o e f f i c i e n t s f o r Subsonic Flow of A i r at High Surface and F l u i d Temperatures," NACA TR 1020, 1951. (16) Hampson, H. "The Condensation of Steam on a Metal Surface," Inst. Mech. Engrs., General Discussion on Heat Transfer, 1951• (17) Jakob, M., "Heat Transfer," Wiley, New York, 19^9. (18) Johnson, H. A., and Rube s i n , M. W., " Aerodynfbni c Heating and Convective Heat Transfer - Summary of a Literature Survey," Trans. ASME 71, kkl-$b (19^9). (19a.) Karman, T. von, "Mechanical Similitude and Turbulence," NACA TM 611, 1931. (l9b) Karman, T. von, "The Analogy between F l u i d F r i c t i o n and Heat Transfer, 1 1 Trans. ASME, 6 l , 705 (1939). (20) Kays, W. M., London, A. L., and Johnson, D. W., "Gas Turbine Plant Heat Exchangers," Am. Soc. Mech. Engrs., New York, 1950. ;(:21) Kern, D. Q., "Process Heat Transfer," McGraw-Hill, New York, 1950. (22) King, W. J., and Colburn, A. P., Ind. Eng. Chem., 2^, 919-23 ( 1 9 3 D . (23) Knudsen, J. G., and Katz, D. L., " F l u i d Dynamics and Heat Transfer," U. of Michigan Press, Ann Arbor, 19f&-» (2l|.a) Leva, M. and Grummer, M., "Heat Transfer to Gases through Packed Tubes," Ind. Eng. Chem., 1±0, lp.5-19 (19^8). (21+b) Leva, M. and Grummer, M., Chem. Eng. Progress, ijJJ, 633 (I9I4J (25) Lin, C. S., Moulton, R. W., and Putnam, G. L., Ind. Eng. Chem., h£, 636 (1953). (26) L i g h t h i l l , M. J., "The Theory of Heat Transfer through a Laminar Boundary Layer," Proc. Roy. Soc. (London), A202, 350-77 (1950). (27) M a r t i n e l l i , R. C , "Heat Transfer to Molten Metals," Trans. ASME, 62., 9*1-7-53 (19^7). (29) McAdams, W. H., "Heat Transmission," 3rd ed., McGraw-H i l l , New York, 1954". (30) Moody, L. P., " F r i c t i o n Factors f o r Pipe Flow," Trans. A S M E , 66, 671 (1944). (31) Nagaoka, J., and Watanabe, A.,, Proc. 7th Intern. Congr. Re f r i g . The Hague-Amsterdam No. 16, J3» 221-45 (1937). (32) Nikuradse, J., "Stromungsgesetze In Rauhen Rohren," V. D. I. Forschungschaft, 361, (1933). (33) Perry, J. H., "Chemical Engineer's Handbook," 3rd ed., McGraw-Hill, New York, 403, 467 (1950). (34) Pinkel, B., "A Summary of NACA Research on Heat Transfer and F r i c t i o n f o r A i r Flowing through a Tube with large Temperature Difference," Trans. ASME, 76, 305-17 (1954). (351 Prandtl, L., "Bermerkung uber den Warmeubertragung i n Rohr," Phys. Z.eitschrift, 23, 487-89 (1928).*' (36) Pratt, H. R. C , "The Application of Turbulent Flow Theory to Transfer Processes In Tubes Containing Turb-ulence Promoters and Packings," Trans. Inst. Chem. Engrs., (London), 28, 177 (1950). (37) Reichardt, H., "Heat Transfer through Turbulent F r i c t i o n Layers," NACA TM 1047, Sept. 1943. (38) Reynolds, Osborne, "On the Extent and Action of the Heating Surface for B o i l e r s , " Proc. Manchester S o c , l£, 7-12 (1874). (39) Rouse, H., "F l u i d Mechanics f o r Hydraulic Engineers," McGraw-Hill, New York, 1938. (40) Sams, E. W., "Experimental Investlngation of Average Heat Transfer and F r i c t i o n C o e f f i c i e n t s f o r A i r Flowing i n C i r c u l a r Tubes Having Square-Thread Type Rqughness," NACA RM E52 2D17, June 27, 1952. (41) Sams, E. W., and Desmon, L. G., "Heat Transfer from High Temperature Surfaces to Fl u i d s - I I I Correlation of Heat Transfer Data for A i r Flowing i n A S i l i c o n Carbide Tube with Rounded Entrance," NACA RM E9 D12, June 23, 1949-(42) Schlichting, H., "Boundary Layer Theory - Part II -Turbulent Flows," NACA TM 1208, A p r i l , 1949-(43) Schubauer, G. B., "Turbulent Processes as Observed i n the Boundary Layer of a Pipe," J. App. Phys., 2£, I88-96 (1954) hi Seban, R. A., and Shimazki, T. T., "Temperature D i s t r i -butions f o r A i r Plowing Turbulently i n a Smooth Heated Pipe," Trans. ASME 21, 803-809 ( 1 9 5 D . Sherwood, T. K., "Heat Transfer, Mass Transfer, and F l u i d F r i c t i o n - Relationships i n Turbulent Flow," Ind. Eng. Chem., ^2, 2077 (1950). Stearns, R. F., Johnson, R. P . J a c k s o n , R. M., and Larson, G. A., "Flow Measurements with O r i f i c e Meters," Van Nostrand, New York, 1951• Sugawara, S., and Sato, T., "Heat Transfer on the Surface of a F l a t Plate i n the Forced Flow," Mem. Faculty Eng. Kyoto Univ., lij., No. 1, 21-37 (1952). Taylor, G. I., "Conditions at the Surface of a Hot Body Exposed to the Wind," G. B. Adv. Comm. f o r Aeronautics -Reports and Memoranda, 272, Vol. 2, I4.23-29 (I916-I7). Weisman, Joel, "Effect of Void Volume and Prandtl Modulus on Heat Transfer i n Tube Banks and Beds," Preprint 17 -Heat Transfer Symposium AIChE, March 1955-k2 APPENDIX A PPENC 1 i i A MX la . I 3 . . 1 1 i • r Q I N U K I M U t r L A 1 t \ J- i M r i D i c i r r ni A T C ! i i • i o \ \ 4 ' ^ to" d>N o U> CI) CALIBRAT ION CUI W E S FOR ORI FICE PI _ATES 15000 2 0 0 0 0 . 3 0 0 0 0 5 0 0 0 0 7 0 0 0 0 ORIFICE R E Y N O L D S N U M B E R M W 3 0 2 5 Q. L VPP •FN my i i ! " CALIBRATION OF PRESSURE GAUGE • i 1 i 1 i i 1 1 • i • f 0 ' i i 1 i . J • 1 1 i i 1 1 i i )• i ! i i i i i • i 1 1 1 i i ! i i i I i j i i or CD CO U J a: a. U J I O o < CD 15 10 15 2 0 25 A C T U A L P R E S S U R E P S l 3 0 APPENDIX 2  Tolerances for Orifice Meter Factor Tolerance (%) Square Do 0.4 x 2 0.64 1 0.2 x 1/2 0.01 Co 0.6 x 1 0.36 Y 0.12 x 1 0.14 P x 0.2 x 1/2 0.01 Pi - P 2 0.25 x 1/2 0.15 T-L 0.1 x 1/2 0.00 Sum of squares: 1.31 Overall approximate tolerance 1.15$ U6 APPENDIX 3  Results of Heat Balance Runs Run No. 1 2 2 Time of run, min 15 20 20 W,lbs/sec 0.00475 0.0159 0.0158 Wt.cond, lbs/sec 0.000201 0.000674 0.000632 WCpCTg-Tj) jg£ 0.1968 0.5773 0.5745 Latent heat 938 939 939 Heat supplied BTU/sec 0.1995 0.632 0.594 % Unaccounted 1.37 9.49 3.39 APPENDIX 4a  Physical Dimensions of Pipes Pipe Dw L S A ft f t sq.ft sq.ft 1/8 Galv. 0.0224 5.17 0.000394 O.364 1/4 Galv. 0.0303 5.17 0.000721 0.492 1/2 Karbate 0.0416 5.17 0.00136 0.677 3/8 Galv. 0.0411 5.17 0.00333 0.668 1/4 S. Steel 0.0303 5.17 0.000721 0.492 3/8 S. Steel 0.0411 5.17 0.00133 0.668 1/4 Copper 0.0313 5.17 0.000767 0.5076 APPENDIX 4b  Results of Isothermal Runs l/8 in. Galvanized Pipe Run No. W Re f Dw/.e Co lb/sec — — — 201 0.001808 8490 0.01247 60.39 0.5957 202 0.002581 12120 0.01297 49.18 0.5962 203 0.003145 14760 0.01370 40.77 0.6015 204 0.004030 18920 0.01283 48.24 0.6040 205 0.004676 21950 0.01269 48.77 0.6030 206 0.005745 26990 0.01247 50.17 0.6040 207 0.006843 32130 0.01212 53.70 0.6070 208 0.008308 39020 0.01187 56.51 0.6047 209 0.009703 45570 0.01196 54.72 0.6019 l / 4 in. Galvanized Pipe 25 0.01815 63100 0.01020 67.64 26 0.01890 65700 0.00998 91.16 27 0.02450 84700 0.00986 93.19 28 0.01236 42800 0.01072 75.55 Rl 0.00325 11280 0.0111 87.28 R2 0.00506 17590 0.01042 94.22 R3 0.00700 24300 0.00996 103.20 R4 0.00906 31420 0.01065 79.29 R5 0.01050 36450 0.01032 86.05 86 0.01242 43200 0.01005 91.95 R7 0.01368 47500 0.00999 92.88 R8 0.01459 50700 0.01121 65.15 R9 " 0.01652 57500 0.00993 93.75 RIO 0.01752 60850 0.00956 104.7 111 0.01093 38000 0.01082 73.27 R12 0.01298 45200 0.00928 115.00 R13 0.01270 47600 0.01005 91.11 R14 0.01450 50200 0.01062 76.52 R15 0.00900 31250 0.01030 88.31 k9 APPENDIX kb  Results of Isothermal Runs 1/2 in. "Karbate" Graphite Pipe Run No. W Re f Dw/e lb/sec — — 137 0.02230 56300 0.008495 152 133 0.01985 50100 0.008657 146 139 0.01760 44500 0.008480 166 140 0.01484 37400 0.00881 148 141 0.01240 31250 0.00874 160 142 0.01021 25750 0.00919 137 143 0.00908 22900 0.00899 154 144 0.00734 18500 O.OO965 125 145 0.00604 15220 0.01420 (omitted) 146 0.00481 12150 0.01063 97.5 158 0.02912 73680 0.00881 154 3/8 in. Galvanized Pipe 181 0.004893 12500 0.01025 112 182 0.006975 17830 0.00977 120 183 0.008960 22900 0.00932 134 184 0.004143 29220 0.008998 148 185 0.01341 34300 0.008901 145 186 0.01561 39920 0.00848 169 187 0.01755 44850 0.00838 173 188 0.01948 49810 0.00823 182 189 0.02143 54770 0.00796 204 190 0.02343 59870 0.00766 234 1/4 in. Standard Steel Pipe 7 0.00610 21000 0.00720 312 8 0.00663 22850 0.00770 341 10 0.00653 22550 0.00870 181 11 0.00663 22850 0.00773 302 12 0.007415 25600 0.00780 309 13 0.00818 28250 0.00775 284 14 0.00844 29200 0.00798 245 15 0.00923 31800 0.00783 254 16 0.00919 31600 0.00813 231 17 0.01752 69800 0.00698 357 18 0.01651 65800 0.00722 271 19 0.01501 59800 O.OO722 277 50 APPENDIX 4b Results of Isothermal Runs 3/3 in. Standard Steel Pipe Run No. W lbs/sec Re Dw/e 159 160 161 162 163 164 165 166 167 168 179 180 0.00506 0.00691 0.00899 0.01039 0.01231 0.01415 0.01557 0.01714 0.01873 0.01990 0.02330 0.02815 12960 17700 23000 26600 31500 36200 39800 43400 48000 55900 60900 71900 0.00860 0.00775 0.00789 0.00767 0.00734 0.00718 0.00717 0.00692 0.00684 0.00673 0.00634 0.00620 278 421 294 314 362 380 361 414 425 441 573 602 1/4 in. Copper Pipe 45 0.00431 14500 0.00809 386.9 46 0.00515 17310 0.00749 608.4 47 0.00654 22000 0.00677 1557.5 48 0.00776 26100 0.00628 2780 49 0.00895 30150 0.00631 1430 50 0.01080 36400 0.00589 2530 51 0.01228 41400 0.00569 3170 52 0.01480 49900 0.00529 13900 53 0.01738 58500 0.00514 13100 54 0.01952 65700 0.00516 13746 51 APPENDIX 4c Calculated Values of Relative Roughness  and Deviations Pipe Log Average (Dw) Log (Dw) Max.Devh (%) Avg.Devh (%) ( e?a ( e)a 1/8 Galv. 51.07 1.7082 5.71 1.90 1/4 Galv. 87.00 1.9395 6.47 2.56 1/2 Karbate 142.1 2.1537 7.64 2.21 3/8 Galv. 158.2 2.1992 7.61 3.68 1/4 S. Steel 276.2 2.4411 7.51 2.24 3/8 S. Steel 391.0 2.5965 7.06 2.99 1/4 Copper 2465 3.3918 23.7 10.8 52 APPENDIX 4d  -Results of Heating Runs 1/8 in. Galvanized Pipe Run No. Re* f. h -ECU X • (sec)(sq.ft)(°F) n 210 7440 0.00232 0.00342 0.002380 211 11970 0.001565 0.00557 O.OO24IO 212 16360 0.001467 0.00810 0.002555 213 22170 0.001412 0.01170 0.002725 234 28770 0.001348 0.01604 0.002880 215 35000 0.001364 0.02010 0.002965 216 38000 0.003340 0.02185 O.OO297O 217 42000 0.001326 0.02420 0.002975 218 44000 0.001212 0.02542 0.002980 219 46400 0.001262 0.02725 0.003030 220 9100 0.00383 0.002170 221 15660 0.007710 0.002545 222 13210 0.007633 0.002980 223* 17210 0.008861 0.002660 230 27290 0.01642 0.003108 231 48860 0.02645 0.002795 232 51578 O.O279O 0.002794 233 55750 0.02933 O.OO2699 234 58310 0.02983 0.002642 235 61200 0.03330 O.OO2642 Equation fitting curve in turbulent region (method of Averages) J H = 0.05322 (Re f :j-°- 2 7 2 6:-S * Runs 224 - 229 were omitted because the outlet air temperature thermometer bulb was touching the tube wall. 53 APPENDIX 4d Results of Heating Runs l A in. Galvanized Pipe S ;,(,sec)(fte)(°F) J! .0121 0.01301 0.002< 29 30500 0 .002975 30 34200 0.0119 0.01468 0.003000 31 37600 0.01152 0.01511 0.002812 32 41100 0.01139 0.01641 0.002784 33 43000 0.01218 0.01721 0.002800 34 46900 0.01152 0.01830 0.002730 35 50600 0.01112 0.01912 0.002640 36 53600 0.01092 0.01970 0.002569 37 56000 0.01022 0.02077 0.002585 38 59700 0.01092 0.02180 0.002554 39 64000 0.01040 0.02180 0.002386 40 70400 0.01097 0.0226 0.002320 41 10350 0.01515 0.00474 0.003194 42 13270 0.02250 0.005185 0.003218 43 15400 0.01658 0.006720 0.003046 44 26700 0.01231 0.01059 0.002765 Equation fitting curve in turbulent region •"0 ^O1^ J H = 0.07160 (Re)f APPENDIX 4d  Results of Heating Runs 1/2 in. Karbate Pipe Run No. h J3IIL_ h X i :(ff2)(°F)(sec) 147 42380 0.00876 0.01238 0.00280 148 39200 0.00947 0.01154 0.00282 149 35970 0.00930 0.009963 0.00276 150 32390 0.00895 0.009831 0.00291 151 26670 0.00957- 0.008457 0.00304 152 22540 0.00927 0.00742 0.00316 153 16230 0.01090 0.005933 0.00350 154 11910 0.01157 0.004134 0.00355 155 47780 0.00848 0.01367 0.00274 156 55860 0.00971 0.01529 0.00262 157 62000 0.00988 0.01653 0.00255 Equation fitting curve in turbulent region: j H = 0.02348 Re f"°? 1 5? 6 ?: 3/8 in. Galvanized Pipe 191 9590 0.01210 0.003053 0.003017 192 13320 0.01163 0.004200 O.OO303O 193 18070 0.0111?. 0.005665 0.002972 194 22870 0.01022 0.006852 0.002839 195 27290 0.00965 0.007891 0.002741 196 31860 0.00942 0.008862 0.002636 197 37180 0.00866 0.01003 0.002557 198 39920 0.00904 0.01051 0.002495 199 44560 0.00856 0.01129 0i.002401 200 52470 0.00820 0.01293 O.OO2323 Equation fitting curve in turbulent region: -0.2" J H = 0.03139 (Ref) • T 55 APPENDIX 4d Results of Heating Runs 1/4 in. Standard Steel Pipe Run No. R e f (f^)(°F)(sec) JH 7 11020 0.03240 0.00436 0.00273 8 14420 0.00885 0.00605 0.00290 9 16030 0.01061 0.00683 0.00295 10 33380 0.00934 0.00802 0.00301 11 23400 0.00906 0.00903 0.002930 12 24700 0.00883 0.00998 0.002796 33 26350 0.00859 0.01060 0.002780 14 56800 0.00732 0.01612 0.001983 15 54500 0.00745 0.01652 0.002324 16 52100 0.00745 0.01710 0.002311 22 72700 0.00730 0.0216 0.002077 23 76200 0.00735 0.0255 O.OO2070 24 68500 0.00722 0.0203 0.002073 Equation fitting curve in turbulent region: J H r 0.04998 3/8 in. Standard Steel Pipe 169 9764 0.009579 0.003240 0.003146 170 13740 0.009121 0.004417 0.003040 171 18910 0.008560 0.005891 0.002951 172 21430 0.008353 0.006971 • 0.002862 173 24640 0.008221 0.007225 0.002780 174 30400 0.007522 0.008588 0.002677 175 35440 0.007047 0.009665 0.002585 176 41590 0.007401 0.010882 0.002480 177 45320 0.007056 0.031587 0.002433 178 52950 0.006888 0.032963 0.002321 Equation fitting curve in turbulent region: J H = 0.06382 (Re)f"°-?2 56 APPENDIX kd  Results of Heating Runs l A in. Copper Pipe Run No. f f h 2-BTH HfS" )( 6F)(sec) 55 13350 0.00844 0.00560 0.00317 56 18220 0.00707 0.00744 0.00309 57 19800 0.00765 0.00786 0.00300 58 24800 0.00727 0.01028 0.00313 59 30600 0.00662 0.01090 0.00270 60 35450 0.00654 0.01199 0.00254 61 39900 0.00658 0.01336 0.00253 62 44700 0.00598 0.01385 0.00234 63 49200 0.00587 0.01430 0.00220 64 54300 0.00582 0.01522 0.00212 65 59100 0.00523 0.01620 0.00207 66 64200 0.00552 0.01702 0.00201 67 69700 0.00523 0.01772 0.00193 Equation f i t t i n g curve i n turbulent region: • J H = 0.1622 (Re ) f - ° ' 3 9 7 1 57 APPENDIX 5 Heat Transfer & Friction Efficiency Data l/8 in. Galvanized Pipe lbs. ft.-lbs. lbs. lbs. Run No. ^ f r - f t . 2 ' E (Sec)(ftr V^e f f t . sec. 7^e f f t . 2 sec. 210 97.94 6.677 4.630 0.01114 211 179.20 20.61 7.530 0.01815 212 342.5 58.72 10.31 0.02634 213 590.6 133.23 13.94 0.03799 214 907.5 255.20 17.37 0.05002 215 1254.5 396.7 22.02 0.06529 216 1407.7 466.8 23.94 0.071102 217 1616.5 567.2 26.43 0.07863 218 1595.0 571.1 27.74 0.08267 219 1778. 646.4 29.24 0.08860 IK in. Galvanized Pipe 29 395 125.6 14.21 0.04227 30 465 157.4 15.94 0.04785 31 539 198.9 17.51 0.04924 32 622 245.1 19.18 0.05340 33 703 280.1 20.02 0.05606 34 773 338.3 21.85 0.05965 35 843 374.2 23.60 0.06230 36 913 422.7 24.96 0.06480 37 987 491.5 26.11 0.06749 33 1055 506.9 27.81 0.07103 39 1130 569.4 29.79 0.07108 40. 1345 695.6 32.83 0.07617 41 • 63.0 7.493 4.831 O.Q1543 42 132.5 16.85 5.251 0.01690 43 233.0 39.32 7.177 0.02186 44 315.0 89.29 12.46 0.03445 58 APPENDIX 5 Heat Transfer & Friction Efficiency Data l / 2 in, Karbate Graphite Pipe Run No. lbs. E Ft. - lbs. V i e . lbs. r V : , e lbs. " F t . 2 (Sec.)(Ft.) 2 Pt.^Tec. JH b f F t . ^ e c . 147 199.2 7.79 14.38 0.0403 148 167.1 57.92 13.31 0.0375 149 136.7 43.00 . 12.21 0.0337 150 100.2 26.68 10.99 0.0320 151 70.87 15.01 9.05 0.0275 152 50.65 9.45 7.65 0.0242 153 29.36 3.92 5.52 0.01932 154 . 15.25 1.38 3.80 0.01349 155 265.1 126.1 16.19 0.0444 156 372.0 194.9 18.95 0.04965 157 438.*:. 229.2 21.04 0.0537 3/8 in. Galvanized Pipe 191 13.19 1.113 3.293 0.009935 192 24.28 2.827 4.573 0.01386 193 43.14 6.876 6.202 0.01843 194 65.27 13.54 7.851 0.02227 195 87.05 21.37 9.367 0.02567 196 120.3 35.82 10.94 0.02884 197 157.0 56.83 12.76 0.03263 198 190.5 74.72 13.70 0.03418 199 216.3 91.03 15.30 0.03674 200 273.6 128.60 18.10 0.04205 59 APPENDIX 5 Heat Transfer & Friction Efficiency Data 1/4 in. Standard Steel Pipe Run No. p JLbs. E Ft. - lbs, V b e f lbs. t: : Y/'e_ lbs. * P f r - F t T * (Sec)(Ft) 2 1 0 r Ft.* (Sec) H ° f F t ~ Z sec. 7 49.1 6.229 5.22 .01425 8 69.3 11.06 6.80 .01972 9 100.8 17.57; 7.545 .02226 10 115.6 22.90 8.653 .02605 11 148.2 33.26 10.10 .02959 12 183.8 45.63 11.61 .03246 13 200.5 52.23 12.41 .03450 14 417. 147.50 22.31 .04424 15 443. 157.0 23.21 .04930 16 463. 173.1 24.29 .05613 22 855. 491.7 32.15 .06678 23 897 558.5 35.40 .07328 24 765 446.1 31.84 .06600 3/8 in. Stainless Steel Pipe 169 10.52 0.8789 3.351 0.01054 170 20.12 2.399 4.717 0.01434 171 36.23 6.020 6.494 0.01916 172 46.12 8.821 7.357 0.02106 173 60.95 13.62 8.460 • 0.02352 174 87.78 25.02 1 0.44 0.02795 175 116.62 40.68 12.17 0.03146 176 168.70 68.65 14.28 0.03541 177 184.20 78.78 15.56 0.03786 178 231.90 109.50 18.18 0.04220 60 APPENDIX 5 Heat Transfer & Friction Efficiency Data  l A in. Copper Pipe Run No. yip lbs. E Ft. - lbs. TEEf lbs. V'€ lbs. **** Ptr« (Sec.)(Ft.)2 * f ( F U j 2 Sec. J h * ^FtT^ec. 55 40.8 0.5113 5.732 0.01817 56 61.9 1.019 7.824 0.02418 57 78.3 1.382 8.515 0.02555 58 112.8 2.421 10.65 0.03333 59 153.3 4.009 13.11 0.03540 60 208.4 6.411 15.21 0.03863 61 246.6 7.922 17.11 0.04329 62 284.9 10.39 19.21 0.04495 63 330.3 12.94 21.11 0.04645 64 374.8 15.25 23.29 0.04937 65 379. 15.89 25.38 0.05254 66 448. 19.33 27.56 0.05540 67 468. 20.66 29.85 0.05761 61 APPENDIX 6  Experimental - Non-Isothermal Data 1/8 in. Galvanized Pipe tun No. T2 Pi ?2 T s W o F Op in Hg in Hg op lb./sec, 210 68.5 240.6 37.94 36.51 255.9 0.001994 211 68.5 242.0 36.89 34.22 255.5 0.003213 212 68.2 244.1 35.23 30.05 255.3 0.004322 213 67.8 246.0 38.64 28.46 255.4 0.005913 214 67.5 247.6 42.32 27.36 256.1 0.007716 215 67.4 248.0 48.15 27.67 255.3 0.009371 216 68.8 248.2 51.00 27.74 255.5 0.01019 217 68.0 248.5 54.66 27.46 255.2 0.01125 218 67.9 248.2 55.68 28.64 255.3 0.01178 219 67.8 248.2 53.94 28.57 255.0 0.01244 ..220 93.2 242.0 38.75 37.37 256.2 0.002418 221 94.2 246.5 36.00 31.90 256.2 0.004148 223 83.2 247.0 35.65 30.06 256.4 0.004581 230 75.0 250.2 33.67 29.95 256.1 0.007274 231 72.8 247.2 60.93 28.50 255.7 0.01307 232 72.5 246.5 61.34 28.36 255.4 0.01379 233 72.4 246.0 66.02 28.22 255.4 O.OL490 234 72.7 245.5 67.45 28.07 255.5 0.01559 235 72.8 245.2 70.89 27.39 255.2 0.01636 62 Experimental Data, Continued  1/4 in. Galvanized Pipe Run No. Ti T 2 Pi p2 T s W Op Op in Hg in Hg op lb./sec 29 79.0 243.0 36.2 29.9 259.0 0.01104 30 80.0 242.0 38.0 30.6 259.0 0.01234 31 81.0 240.0 39.4 30.7 258.0 0.01360 32 84.0 240.0 41.1 31.0 259.0 0.03489 33 81.0 238.0 42.9 31.3 258.0 0.01621 34 80.0 238.0 45.1 32.3 258.0 0.01730 35 80.0 237.0 46.3 32.2 258.0 0.01840 36 80.0 '236.0 47.5 32.1 257.5 0.01942 37 75.0 234.0 49.6 32.9 258.0 0.02045 38 75.0 234.0 51.6 33.5 258.0 0.02175 39 74.0 231.0 53.3 33.6 257.0 0.02340 40 73.0 229.0 58.3 34.7 257.0 0.02575 41 72.0 246.0 30.5 29.5 259.0 0.00376 42 71.0 246.0 31.5 29.5 260.0 0.00409 43 71.0 244.0 33.2 29.7 . 259.5 0.00560 44 71.0 242.0 34.9 29.9 258.0 0.00970 L/2 in. Karbate Pipe 347 69.3 220.5 38.52 35.25 257.0 0.02338 148 69.3 222.0 39.47 37.68 257.4 0.01983 149 71.5 223.5 40.10 37.90 257.0 0.01833 150 70.0 225.5 40.88 39.26 257.7 0.01575 151 70.0 227.8 42.16 41.03 258.3 0.03311 152 70.1 229.7 41.70 40.89 258.3 0.01112 153 70.2 232.2 41.91 41.44 258.8 0.00855 154 70.1 235.1 42.42 42.18 259.0 0.005613 155 70.6 219.1 36.43 31.99 256.8 0.02413 156 71.2 216.1 39.33 33.09 256.2 0.02819 157 72.5 215.0 41.96 34.56 257.6 0.03335 63 Experimental Data. Continued 3/8 in. Galvanized Pipe tun No. T 1 T 2 Pi ?2 T s W o p op in Hg in Hg OF lbs./sec, 191 90.3 229.8 39.24 39.04 257.3 0.004717 192 89.9 228.5 39.54 39.17 256.2 0.006613 193 88.0 227.5 39.26 38.59 256.1 0.008898 194 87.5 224.9 38.34 37.32 256.0 0.01128 195 87.4 223.0 38.76 37.39 256.0 0.01346 196 87.1 220.4 37.60 35.69 255.8 0.002636 197 86.6 218.5 36.43 33.89 255.6 0.002557 198 85.9 217.0 36.31 33.23 255.6 0.002495 199 85.0 214.1 37.89 ' 34.36 255.2 0.002401 200 84.8 212.1 40.50 35.96 255.2 0.002323 1/4 in. Standard Steel 7 78.0 248.9 32.0 31.24 267.0 0.00273 8 77.6 244.5 31.6 30.52 264.0 0.00290 9 77.2 249.0 32.9 31.33 264.5 0.00295 10 77.4 246.6 33.3 31.48 263.0 0.00301 11 76.9 244.0 34.5 32.16 262.0 0.00293 12 76.2 242.6 36.1 33.20 262.0 0.002796 13 75.5 242.0 36.8 33.60 261.5 0.002780 14 63.4 227.4 39.27 32.87 257.5 0.001983 15 65.0 227.0 43.47 36.66 257.0 0.002124 16 65.9 225.8 41.52 33.92 257.5 0.0023U 22 75.6 225.8 39.12 31.00 258.0 0.002Q7/7.-23 74.0 229.0 39.64 34.3^ 258.00 0.002070 24 75.0 225.00 38.34 258.0 0.002073 Experimental Data. Continued 3/8 in. Standard Steel 6k Run No. in Hg r2 in Hg W lbs./sec, 169 89.0 230.0 40.24 40.08 256.6 0.00480 170 87.0 228.2 39.72 39.40 255.2 0.00677 171 85.4 225.9 39.30 38.73 255.3 0.00933 172 84.7 224.2 38.73 38.00 255.2 0.01058 173 84.0 223.3 38.23 37.23 255.5 0.01219 174 83.5 220.0 37.15 35.72 255.0 0.01503 175 83.7 217.8 35.85 33.92 254.8 0^01754 176 83.7 215.2 36.24 33.44 254.8 0.02060 177 84.8 . 214.0 37.60 34.52 254.3 0.02245 178 84.8 211.2 40.18 36.26 254.2 0.02630 1/4 in. Copper Pipe 5.5 70.0 242.5 35.55 33.90 258.0 0.00475 56 70.65 241.5 36.63 35.63 258.0 0.00647 57 74.0 240.5 37.23 36.00 258.0 0.00706 58 74.7 238.00 38.64 36.82 258.0 0.00883 59 74.0 236.0 39.39 36.86. 258.0 0.01088 60 74.0 233.5 39.15 35.8 , 258.0 0.01256 61 76.0 231.0 42.44 38.36 257.5 0.01426 62 76.0 229.0 42.3 37.45 258.0 0.01597 63 77.0 225.6 43.65 38.0 258.0 0.01760 64 76.0 223.5 46.4 40.2 256.5 0.01942 65 76.0 221.5 49.0 42.3 256.5 0.02116 66 75.5 220.0 52.0 44.25 256.5 0.02302 67 75.2 218.5 55.2. 46.9 257.0 0.02500 

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