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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 t h i s t h e s i s as conforming t o the standard r e q u i r e d  from c a n d i d a t e s f o r the  degree o f MASTER OF APPLIED SCIENCE  Members o f the Department o f CHEMICAL ENGINEERING THE UNIVERSITY OF BRITISH COLUMBIA September, 1955  ABSTRACT Heat t r a n s f e r and f r i c t i o n data were o b t a i n e d f o r a i r f l o w through  seven commercial p i p e s w i t h e q u i v a l e n t sand  roughness r a t i o s v a r y i n g from 0.020 to 0.000lj.l i n the Reynolds number range 10,000 - 80,000.  Heat t r a n s f e r f o r a g i v e n  power l o s s decreased w i t h i n c r e a s i n g roughness r a t i o  except  at v e r y h i g h power l o s s e s , where t h i s t r e n d was t o some extent reversed.  The r e s u l t s f o r the Karbate p i p e were somewhat out  o f l i n e w i t h those f o r standard p i p e s .  T h i s i s a t t r i b u t e d to  a d i f f e r e n c e i n the n a t u r e o f the Karbate  roughness.  I n the p l o t s o f f r i c t i o n f a c t o r and Reynolds number, the experimental d a t a show  versus  that J  H  continues  to decrease w i t h Reynolds number when f r i c t i o n f a c t o r has become constant f o r a rough p i p e . o n l y Reynolds'  T h i s £act c o n t r a d i c t s n o t  simple t u r b u l e n c e analogy and Colburn's m o d i f i -  c a t i o n t h e r e o f , which are i n other r e s p e c t s i n a p p l i c a b l e , but i s a l s o at odds w i t h the more r i g o r o u s analogy o f T a y l o r and P r a n d t l and the s i m i l a r ,  semi-empirical equation of P i n k e l .  I t i s , however, i n agreement w i t h t h e Karman analogy, also g i v e s a good absolute p r e d i c t i o n o f the heat data.  which  transfer  ACKNOWLEDGMENTS  I wish t o acknowledge the a s s i s t a n c e o f Mr. B. C. Almaula, who i n i t i a t e d c o n s t r u c t i o n o f the apparatus, and o f Dr. Norman E p s t e i n , under whose guidance the work was performed. I am a l s o indebted  to the N a t i o n a l Research  C o u n c i l f o r a Bursary and f o r supplementary g r a n t s d u r i n g the summers o f 1951+- and 1955•  financial  TABLE OP CONTENTS  ACKNOWLEDGMENTS ABSTRACT INTRODUCTION CRITICAL REVIEW OP PREVIOUS PERTINENT WORK 1. 2. 3. I).. 5. 6. 7.  C o r r e l a t i o n o f Isothermal Data i n Rough P i p e s C o r r e l a t i o n o f Non-isothermal F r i c t i o n Data C o r r e l a t i o n o f Heat T r a n s f e r Data P r e v i o u s I n v e s t i g a t i o n s o f the E f f e c t o f Surface Roughness on Heat T r a n s f e r T h e o r e t i c a l Heat T r a n s f e r - Momentum T r a n s f e r Analogies E m p i r i c a l Heat T r a n s f e r - Momentum T r a n s f e r Equations C o n c l u s i o n s Based on the L i t e r a t u r e Survey  DESCRIPTION OP APPARATUS AND EXPERIMENTAL METHOD 1. 2. 3.  The Apparatus A. The A i r System B. The Steam System E x p e r i m e n t a l Method Treatment o f Data A. C a l c u l a t i o n o f Flow Rate B. C a l c u l a t i o n o f Isothermal Data C. C a l c u l a t i o n o f Heating Data  i Ij. 6 8 9 10 10 10 13 lL lo 16 16 17 19  RESULTS AND CONCLUSIONS Table I - Comparison o f j C a l c u l a t e d from Reynoldsi Analogy and from E x p e r i mental Curves H  31a  SUMMARY  3k  NOMENCLATURE  35  BIBLIOGRAPHY AND REFERENCES  38  APPENDIX 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 o f P r e s s u r e Gauge  k-2  to  Appendix 2  - Approximate T o l e r a n c e s f o r O r i f i c e Meter  Appendix 3  - R e s u l t s of Heat Balance Runs  Appendix J+a  - P h y s i c a l Dimensions o f P i p e s  Appendix i+b  - R e s u l t s o f Isothermal Runs  Appendix i+c  - C a l c u l a t e d Values o f R e l a t i v e Roughness and D e v i a t i o n s  Appendix i^-d  - R e s u l t s o f H e a t i n g Runs  Appendix 5  - Heat T r a n s f e r and F r i c t i o n E f f i c i e n c y Data  Appendix 6  - E x p e r i m e n t a l Non-isothermal Data  LIST OF FIGURES  Figure  1.  F i g u r e 2. F i g u r e 3. F i g u r e I+.  Schematic Diagram o f Apparatus 1/8 i n . G a l v a n i z e d  Pipe -  Heat T r a n s f e r and F r i c t i o n Data 1/lj. i n . G a l v a n i z e d  11  20  Pipe -  Heat T r a n s f e r and F r i c t i o n Data  21  1/2 i n . Karbate P i p e Heat T r a n s f e r and F r i c t i o n Data 3/8 i n . G a l v a n i z e d P i p e Heat T r a n s f e r and F r i c t i o n Data l A i n . Standard S t e e l P i p e Heat T r a n s f e r and F r i c t i o n Data  2I4.  7.  3/8 i n . Standard S t e e l P i p e Heat T r a n s f e r and F r i c t i o n Data  25  F i g u r e 8.  i n . Copper P i p e Heat T r a n s f e r and F r i c t i o n Data  26  F i g u r e 9*  7 Commercial  F i g u r e 5» F i g u r e 6. Figure  F i g u r e 10. Figure  11.  22 23  Pipes  Heat T r a n s f e r and F r i c t i o n Data  27  Heat T r a n s f e r - F r i c t i o n E f f i c i e n c y  29  Test o f von Karman's Analogy  32  1  INTRODUCTION Although e x t e n s i v e l i t e r a t u r e on the e f f e c t o f s u r f a c e roughness  on f l u i d f r i c t i o n i s a v a i l a b l e (7,  few i n v e s t i g a t i o n s o f the e f f e c t o f roughness have been made.  30, 39, ii.2),  on heat .transfer  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 p i p e s ( 8 , 1+-0), the t i o n b e i n g a study o f the performance  excep-  of a s i l i c o n carbide  tube by Sams and Desmon (ill.). T h i s i n v e s t i g a t i o n was of normal w a l l roughness  I n i t i a t e d to study the e f f e c t  i n commercial p i p e s on heat  transfer  r a t e s ; to determine whether rough p i p e s are more or l e s s efficient  heat t r a n s m i t t e r s than smooth p i p e s f o r a g i v e n  power e x p e n d i t u r e ; and to t e s t some o f the t h e o r e t i c a l equat i o n s which have been developed (I4., 19*  35* 37* M*)  for  p r 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 p i p e s (1/8,  l/Lf., 3/8 I n . standard  g a l v a n i z e d ; 1/lj., 3/8 i n . standard s t e e l ; l/Lf. i n . standard copper; and 1/2  i n . "Karbate" g r a p h i t e ) were i n v e s t i g a t e d .  The data on each p i p e were c o r r e l a t e d u s i n g the f i l m  temper-  ature concept, which had p r e v i o u s l y been found to c o r r e l a t e both f l u i d f r i c t i o n  and heat t r a n s f e r d a t a most c o n s i s t e n t l y  by Humble, Lowdermilk and Desmon (15) • number a t t a i n a b l e (80,000) was supply o f h i g h p r e s s u r e a i r .  The maximum Reynolds  l i m i t e d by an inadequate  2  CRITICAL REVIEW OF PREVIOUS PERTINENT WORK  1,  C o r r e l a t i o n o f Isothermal F r i c t i o n Data i n Rough P i p e s Numerous c o r r e l a t i o n s are a v a i l a b l e 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 p i p e s , a term which may  be a p p l i e d  to most commercial p i p e o t h e r than drawn t u b i n g . An e a r l y e q u a t i o n of Drew and Genereaux  =  3.2  r e p r e s e n t s the average f l o w i n rough p i p e .  log(Re-Vf)  •  (11)  1.2  (1)  of widely scattered data f o r turbulent  T h i s e q u a t i o n n e g l e c t s the e f f e c t of  v a r y i n g w a l l roughness r a t i o s which I s taken i n t o account i n the t h e o r e t i c a l equation f o r t u r b u l e n t flow d e r i v e d by  von  K arm an (19a)»  -L-  -  4.06  log(D /e) w  • 2.02  (2)  and the e q u i v a l e n t e m p i r i c a l e q u a t i o n of Nikuradse  -JLVf Colebrook  -  1|. l o g ( D / e ) w w  (7) used Nikuradse's  •  2.28  (32)J  (3)  d a t a t o d e r i v e an e q u a t i o n  applying i n the t r a n s i t i o n r e g i o n between laminar and t u r b u l e n t flow,  = V?  k log(D /e) w  •  2.28  -  k log/l • k M ^ l ) \ Re-Vv e  (k)  which reduces to E q u a t i o n 3 a t l a r g e Reynolds numbers. Moody (30) and Rouse (39) have p r e s e n t e d 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 E q u a t i o n s 3 and ij..  Moody  i n c l u d e s a c h a r t from which, f o r any g i v e n commercial p i p e , e/D  may be o b t a i n e d , and the c o r r e s p o n d i n g f r i c t i o n f a c t o r  w  f may be o b t a i n e d a t any Reynolds number from the f r i c t i o n factor p l o t .  2•  C o r r e l a t i o n o f Non-isothermal F r i c t i o n Data Methods o f c o r r e l a t i n g non-Isothermal f r i c t i o n  d a t a have been i n v e s t i g a t e d by McAdams (29)» E p s t e i n and P h i l l i p s (lljl), Sams (I4.O), and Humble, Lowdermilk (15).  and Desmon  These workers conclude t h a t i f the f i l m temperature  (average o f b u l k f l u i d  and w a l l temperatures) i s used f o r  e v a l u a t i n g the f l u i d p r o p e r t i e s , good c o r r e l a t i o n may obtained w i t h n o n - i s o t h e r m a l f r i c t i o n d a t a .  be  Thus, the f i l m  Fanning f r i c t i o n f a c t o r may be c a l c u l a t e d from the e q u a t i o n  and the f i l m Reynolds number from the e q u a t i o n  Re  f  =  D V e /fc w  b  f  (6)  f  Humble, Lowdermilk and Desmon (15)  and Sams (lf.0)  found t h a t h e a t i n g d a t a c a l c u l a t e d i n t h i s manner l i e on the curve r e p r e s e n t e d by i s o t h e r m a l d a t a , except at Re^  less  than 20,000, where the method appears to overcompensate f o r r a d i a l temperature g r a d i e n t s .  k 3. C o r r e l a t i o n of Heat T r a n s f e r Data Standardized  methods o f c o r r e l a t i n g heat t r a n s f e r  dataare g i v e n i n many e x c e l l e n t works, i n c l u d i n g those of McAdams (29),  Kern (21),  and Jakob (17).  The  j„ f a c t o r i s ii  f r e q u e n t l y used f o r c o r r e l a t i n g heat t r a n s f e r d a t a because o f the simple, Re  approximate r e l a t i o n between the  curves noted by Colburn (6)  H  and f v e r s u s  f o r smooth t u b i n g .  Humble, Lowdermilk and Desmon (1^) found t h a t the b e s t  j  c o r r e l a t i o n between J  and  Sams (l|JL)  and Reynolds  H  number r e s u l t e d i f , as i n the c a l c u l a t i o n o f the n o n - i s o 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 p r o p e r t i e s were e v a l u ated at the f i l m temperature T f . from E q u a t i o n 6 and  • Previous  j  h  from the  v f e M f  Thus, R e  f  may  be c a l c u l a t e d  equation:  -  s t  ^/3  I n v e s t i g a t i o n s of the E f f e c t o f Surface  Roughness  on Heat T r a n s f e r The  e a r l y work o f Cope (8) on the e f f e c t o f  artif-  i c i a l , m i l l e d roughness on heat t r a n s f e r r a t e s i n d i c a t e d t h a t the i n c r e a s e i n the heat t r a n s f e r r a t e i s not n e a r l y as as the i n c r e a s e i n f r i c t i o n , He  at l e a s t i n the t u r b u l e n t  concluded t h a t the smooth p i p e i s a more e f f i c i e n t  m i t t e r of heat than the a r t i f i c i a l l y roughened p i p e on  great region.  transthe  b a s i s of heat t r a n s f e r r e d f o r equal power l o s s . Colburn (6),  u s i n g the d a t a of K i n g (22)  and  of  5  Nagaoka and Watanabe (31)» m e t a l l i c turbulence  who  s t u d i e d the e f f e c t o f i n t e r n a l  promoters, appears to c o n t r a d i c t  c o n c l u s i o n o f Cope that rough p i p e s smooth tubes.  are l e s s e f f i c i e n t  than  However, t h i s c o n t r a d i c t i o n i s p r o b a b l y more  apparent than r e a l ,  s i n c e the turbulence  a c t i n g as extended s u r f a c e s . Drexel  the  and McAdaras (12)  n a t u r e of the  surface  promoters may  be  A s i m i l a r c o n c l u s i o n reached by  f o r wavy s u r f a c e s may  be duetto  the  studied.  Leva and^Grummer (2i|.a) s t u d i e d the e f f e c t o f p a r t icle  c h a r a c t e r i s t i c s , i n c l u d i n g surface roughness, on heat  t r a n s f e r 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 t h a t  f o r smooth  p a r t i c l e s (2i|b), the corresponding i n c r e a s e i n the heat fer  r a t e was  only  trans-  10$.  A r n i and Meyers (2)  i n v e s t i g a t e d the e f f e c t o f  i n t e r n a l roughness on heat t r a n s f e r and p r e s s u r e i n t e g r a l f i n n e d tubes, but f e l t  drop i n  t h a t the 10$ i n c r e a s e i n  f over the t h e o r e t i c a l smooth curve d i d not m e r i t  an  estimation  of the i n c r e a s e i n the heat t r a n s f e r c o e f f i c i e n t . Sugawara and  Sato (1|7), s t u d y i n g  grooves and p r o j e c t i o n s on the  surface of a f l a t p l a t e  heat t r a n s f e r r a t e s , found that t h i s an a p p r e c i a b l e  e f f e c t but  the e f f e c t of  type of roughness  on had  d i d not c a l c u l a t e f r i c t i o n f a c t o r s .  They a l s o found that at h i g h Re h e a t t r a n s f e r 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«  T h e o r e t i c a l Heat T r a n s f e r - Momentum T r a n s f e r  Analogies  S e v e r a l attempts have been made to deduce the form o f the f u n c t i o n <|) i n the e x p r e s s i o n St  =  (8)  $(Re, Pr)  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 t u r b u l e n t f l o w by comparing the exchange o f momentum and h e a t .  Reynolds (38) d e a l t  a p u r e l y t u r b u l e n t 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 o f f l u i d s was p o s t u l a t e d Pr r 1 ) .  J  The e q u a t i o n r e p r e s e n t i n g  § (Pr)  s H  Colburn i n t r o d u c e d  with  t h i s system i s  ( I . e.,  simply:  (9)  2 / 3  a m o d i f i c a t i o n o f t h i s analogy which was  found to f i t the data f o r smooth tubes b e t t e r and on which the d e f i n i t i o n o f j i s based: H J  H  =  §  =  St ( P r ) / 2  (10)  3  P r a n d t l (35) and G. I . T a y l o r (I4.8) extended the analogy t o other v a l u e s o f the P r a n d t l modulus by i n t r o d u c i n g the concept o f a laminar  sublayer  and a t u r b u l e n t c o r e .  T h e i r d e r i v a t i o n can  be expressed a s : ,  .  t  (Pr)  2 / 3  Von Karman (19b) d e f i n e d a b u f f e r l a y e r o f p a r t i c u l a r c t e r i s t i c s between the laminar  l a y e r and the t u r b u l e n t  chara-  7  core.  H i s equation may be w r i t t e n : yf(pp) J  H  4 5PD + 0.5 l a g / f ]  5[Pr f i n d  =  2 / 3  B o e l t e r , M a r t i n e l l i and Jonassen  (  1  2  )  extended the Karman  analogy to i n c l u d e the cases where the p h y s i c a l p r o p e r t i e s o f the f l u i d v a r y across the diameter o f the tube. obtained  the e x p r e s s i o n : ( F r ) *2/3 /J  £ J  H  They  W  m  e  a  n  5Pr) + 0 . 5 l a ^ / ^  $[Pr • l n ( l  S  A T Z f f  +  U  3  )  M a r t i n e l l i s (27) f u r t h e r m o d i f i c a t i o n o f von Karman»s analogy 1  i n c l u d e s the e f f e c t o f the eddy d i f f u s i v i t i e s o f heat and momentum (assumed e q u a l ) . j  H  =  71  (  P  r  )  2  The f i n a l equation i s : /  3  ^max/AT ean m  5 [ P r * l n ( l + 5Pr) + 0.$D.R. l n | § / | ]  where D.R. I s a f u n c t i o n o f the eddy and m o l e c u l a r d i f f u s i v i t i e s o f heat.  M a r t i n e l l i t e s t e d h i s analogy w i t h the  data o f Cope (8)and obtained  a r e a s o n a b l y good c o r r e l a t i o n .  He used t h i s f a c t t o i n f e r t h a t a laminar sublayer e x i s t s I n rough p i p e . (28)  and R e i c h a r d t  also  Other i n v e s t i g a t o r s , such as M a t t i o l i  (37), have p r e s e n t e d more i n v o l v e d  rela-  t i o n s h i p s between heat and momentum t r a n s f e r . An o b j e c t i o n t o these analogies  has been made by  Cavers e t a l (5)* who note t h a t i n a l l the a n a l o g i e s  the r a t i o  o f eddy c o n d u c t i v i t y t o eddy d i f f u s i v i t y i s u n i t y , whereas experimental measurements i n d i c a t e t h a t t h i s i s not so f o r Pr near 1, except p o s s i b l y a t h i g h Re.  8  6.  E m p i r i c a l Heat T r a n s f e r  - Momentum T r a n s f e r  Equations  P r a t t (36) has proposed t h a t turbulence  promoters  and p a c k i n g s should be c h a r a c t e r i z e d by a f a c t o r B r e l a t i n g t h e i r performance from the p o i n t o f view o f h e a t o r mass t r a n s f e r t o t h a t i n a smooth tube.  He p o i n t s out t h a t  sur-  f a c e roughness may p o s s i b l y a c t as a t u r b u l e n c e promoter and therefore may a l s o be c l a s s i f i e d by the f a c t o r B.  However,  t h i s method has a maximum e r r o r o f 2%<f , which i s p r o b a b l y 0  as g r e a t  as the h e a t t r a n s f e r v a r i a t i o n s caused by v a r i a t i o n s  i n w a l l roughness, PInkel  (3I+,) extended the concepts developed by  D e i s s l e r (10) t o i n c l u d e rough p i p e s . can be rearranged  His final  equation  to f (Pr)*/  3  f  where O . 9 I and 1370 were determined from e x p e r i m e n t a l and y  Q  data  i s a measure o f the e f f e c t i v e h e i g h t o f the i n f l u e n c e  o f the roughness.  E q u a t i o n 15 i s q u i t e s i m i l a r I n form t o  the analogy o f P r a n d t l  and T a y l o r  (Equation  11).  Pinkel  used E q u a t i o n 15 t o o b t a i n e x c e l l e n t c o r r e l a t i o n o f d a t a w i t h w i d e l y v a r y i n g f i l m temperatures and degrees o f a r t i ficial  roughness.  9  7.  C o n c l u s i o n s Based on the L i t e r a t u r e  Survey  The g e n e r a l c o n c l u s i o n s 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 o f a r t i f i c i a l roughness on heat t r a n s f e r i s t h a t roughness  does n o t have n e a r l y the  same e f f e c t on heat t r a n s f e r t h a t i t has oh f l u i d and t h a t d i f f e r e n t types o f roughness  friction,  o r t u r b u l e n c e promoters  may have a p p r e c i a b l y d i f f e r e n t e f f e c t s f o r the same power l o s s p e r u n i t area o f heat t r a n s f e r  surface.  The l a c k o f d a t a on heat t r a n s f e r i n commercial p i p e s ; the p o s s i b i l i t y that commercial  rough p i p e s may be  more e f f i c i e n t heat t r a n s m i t t e r s p e r u n i t area heat  transfer  than smooth t u b i n g ; and the d e s i r a b i l i t y o f t e s t i n g the heat - momentum t r a n s f e r a n a l o g i e s 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  1.  The  EXPERIMENTAL METHOD  Apparatus The apparatus c o n s i s t s o f a double p i p e h e a t ex-  changer  (Pig. 1).  A i r passes through the Inner experimental  p i p e where i t i s heated by steam contained i n the o u t e r p i p e (steam j a c k e t ) . the  The equipment may  be d i v i d e d i n t o two  systems,  a i r system and the steam system, each o f 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  compressor  s u p p l i e d at 20 p s i g . by the b u i l d i n g Nash  (ijOO cfm.), o r a t 80 p s i g . by a s m a l l p o s i t i v e  displacement compressor  (15  cfm.) when i t was found t h a t the  p r e s s u r e drop through the apparatus was  very great.  In order  to o b t a i n maximum f l o w r a t e s , b o t h compressors were run at the same time. l a t e d by a BBL  A i r p r e s s u r e to the apparatus was  type P i s h e r 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 c a l i b r a t e d o r i f i c e  to  the entrance o f the experimental s e c t i o n .  p r e s s u r e o f the a i r at the o r i f i c e  regu-  assembly The  and  thence  upstream  and the p r e s s u r e a t the  entrance to the h e a t i n g s e c t i o n c o u l d 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 p r e s s u r e gauge i f the p r e s s u r e s were too high.  The temperature T  x  o f the a i r a t the entrance to the  h e a t i n g section'was measured to the n e a r e s t 0.1  °P w i t h a  S T E A M  AIR  ORIFICE  y^ss. T  STANDARD PRESSUR.E TAP,  P R E S S U R E  PIPE  v  P R E S S U R E  |  r  STEAM  PRESSURE  REGULATOR  STEAM JACKET  REGULATOR AIR  I  VENT  r  Y///////A  0  ^4=  ^  INSULATION  Y/////A  GAUGE  I N. S.S. P I P E \ f t STANDARD  0 B  P R E S S U R E TAP  YA//////A  VENT  Y////A  c T,  J) EXPERIMENTAL  =tx3= T R A P ^  MANOMETER  UPSTREAM PRESSURE GAUGE  ORIFICE C  ik u  SECTION  STEAM  /  SECTION  ONDENSATE  MANOMETER  UPSTREAM  P R E S S U R E MANOMETER  FIG.  I  SCHEMATIC OF  DIAGRAM  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. drops through the o r i f i c e  and through the experimental  were measured on the d i f f e r e n t i a l meters.  The p r e s s u r e  orifice  The o u t l e t a i r temperature  c a l i b r a t e d thermometer t o 0 . 2 ° P .  section  and s e c t i o n mano-  T2 was measured on another The a i r was then vented  to the atmosphere. Two b r a s s , standard square-edge o r i f i c e p l a t e s (1) of 1/tf. I n . and 3/8 i n . bore were c a l i b r a t e d a t the same time as the i s o t h e r m a l runs were performed Electric  w i t h a lf.00 c f h r . B. C.  diaphragm gasmeter which had been c a l i b r a t e d t o  w i t h i n 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  p l a t e s a r e g i v e n i n Appendix l a .  The o r i f i c e p r e s s u r e taps  were o f the vena c o n t r a c t a type, c o n s t r u c t e d a c c o r d i n g t o the standards o f the Am. Soc. Mech. Engrs. (1) from  aluminum  d i s c s , as were the s t a t i c p r e s s u r e taps a t the entrance and e x i t o f the experimental s e c t i o n .  The bore o f the taps was  made to conform as c l o s e l y as p o s s i b l e to the a c t u a l i n s i d e diameter o f the p i p e i n which they were p l a c e d . The  a i r f l o w r a t e s were c a l c u l a t e d from the - L  o r i f i c e discharge equation (33): w  =  0 YS o  o  /2 g c ( P i - P T 5 [ 2  (16)  A l l terms i n the e q u a t i o n are o b t a i n a b l e from t h e p h y s i c a l dimensions  o f the system o r from c a l i b r a t i o n d a t a except Y,  which may be c a l c u l a t e d from the e x p r e s s i o n f o r vena c o n t r a c t a and r a d i u s taps (33) s  13  fesf)l «  =  oJ  1  +  °-35A)  U7)  or estimated from the p l o t g i v e n by Stearns e t a l (ij.6) which , i s based on E q u a t i o n  17.  The a i r temperature  thermometers were c a l i b r a t e d  a g a i n s t each other and a g a i n s t a standard thermometer, but no p l o t i s g i v e n because they were accurate to the degree p r e c i s i o n to which they c o u l d be r e a d . were Kimble  of  Both thermometers  3 i n . immersion thermometers, the s c a l e s b e i n g  graduated from -10  to 120  and 0 to 300°F»»  respectively.  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 p r e s s u r e gauge. a g a i n s t a B a r n e t No. OI31  The gauge was  calibrated  dead-weight t e s t e r .  A calming l e n g t h o f 8 i n . preceded the experimental s e c t i o n , although i n t u r b u l e n t f l o w t h i s should not be necessary.  B.  The h e a t i n g s e c t i o n i t s e l f was 5*17  f t . long.  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  e l i m i n a t o r and a M u e l l e r p r e s s u r e reducer  to the I f i n . i n s u l a t e d steam j a c k e t .  A vent at the upper  s u r f a c e allowed the escape o f non-condensable gases. j a c k e t was  i n c l i n e d v e r y s l i g h t l y so t h a t condensate  run i n t o a steam-trap, passed through a water-cooled c o l l e c t e d , and weighed.  Steam temperatures  T^, Tg>  were r e a d from three c a l i b r a t e d thermometers.  The would condenser, and  Tq  ;  Corresponding  Ik  steam p r e s s u r e s were checked  on a  3 i n . diameter Bourdon  gauge.  2.  Experimental Method The experimental s e c t i o n i n every case except t h a t  of  the Karbate g r a p h i t e p i p e was c u t t o l e n g t h (5.17 f t . )  from a p i e c e o f new p i p e , the o u t s i d e p o l i s h e d on an emery sander,  threaded on b o t h ends, coated w i t h o l e i c  mounted i n the experimental apparatus. a p p l i e d to ensure  a c i d , and  The o l e i c a c i d was  t h a t steam would condense i n a drop-wise  manner ( 1 6 ) , thus g i v i n g a n e g l i g i b l y s m a l l r e s i s t a n c e to heat t r a n s f e r on the steam s i d e o f the exchanger.  The 1/2  i n . Karbate p i p e c o u l d n o t be t r e a t e d i n the same way because of  the d i f f i c u l t y encountered  material.  i n t h r e a d i n g such a b r i t t l e  The p r e s s u r e taps f o r t h i s p i p e were made i n the  form o f a sleeve which f i t t e d over the end o f the g r a p h i t e p i p e , a t i g h t s e a l b e i n g made w i t h a rubber gasket and a s e a l i n g compound.  The steam j a c k e t was s e a l e d a t the ends  by means o f rubber gaskets t i g h t e n e d on w i t h l o c k n u t s . The  seven p i p e s examined were:  1.  1/8 i n . standard g a l v a n i z e d .  2.  l/k. i n . standard g a l v a n i z e d  3.  1/2 i n .  ij..  3/8 i n . standard g a l v a n i z e d .  5.  l/Ij. i n . standard  steel.  6.  3/8 l « standard  steel.  n  ( a c t u a l diameter) Karbate  Graphite.  1$ 7.  lA± i n . standard copper. Ten o r more i s o t h e r m a l r u n s were made on each p i p e  to determine the f r i c t i o n f a c t o r curve from which e/D , the w  r e l a t i v e roughness,  c o u l d be determined.  A t the same time,  i f d e s i r e d , a check on the o r i f i c e c a l i b r a t i o n curve c o u l d be made on the B. C. E l e c t r i c gasmeter.  A l l pressures (inc-  l u d i n g b a r o m e t r i c p r e s s u r e ) , p r e s s u r e drops, and temperatures were r e c o r d e d d u r i n g these r u n s .  An attempt was made to  o b t a i n a range o f Reynolds numbers from 10,000 to as h i g h as the equipment and a i r supply would a l l o w . The procedure f o l l o w e d d u r i n g the h e a t i n g runs was such that the system was as c l o s e t o steady s t a t e as p o s s i b l e when r e a d i n g s were taken. one hour  Runs were n o t made u n t i l  at l e a s t  a f t e r the steam had been turned on. Ten o r more  runs o f 15 minutes d u r a t i o n were made on each p i p e ; a l l thermometers, f i v e minutes.  p r e s s u r e gauges and manometers b e i n g read every Cooled condensate was c o l l e c t e d d u r i n g each  run and weighed to p e r m i t a heat b a l a n c e .  At l e a s t  five  minutes were allowed to e l a p s e between r u n s , although, i n g e n e r a l , apparent e q u i l i b r i u m was achieved i n l e s s than one minute.  A range o f Reynolds numbers from 10,000 to the maxi-  mum c a p a c i t y a t t a i n a b l e each p i p e .  (60,000 -80,000) was covered, f o r  16  3.  Treatment of Data In a l l c a l c u l a t i o n s D_, w  p i p e i n question^ was diameter  the i n s i d e diameter  of the  assumed to be e q u i v a l e n t to the i n s i d e  s p e c i f i e d by the manufacturer.  As a check, the  diameter o f the 1/L|. i n . standard s t e e l p i p e was measured by v o l u m e t r i c displacement.  The d i f f e r e n c e between the measured  and s p e c i f i e d diameters was A.  l e s s than  0,6%.  C a l c u l a t i o n o f the Flow Rate The  a i r f l o w r a t e d was  c a l c u l a t e d from E q u a t i o n s  and 17 u s i n g the p h y s i c a l dimensions e x p e r i m e n t a l l y observed  l6  of the o r i f i c e meter,  data and the c a l i b r a t i o n curves  appearing i n Appendix l a . A c o n s i d e r a t i o n of the t o l e r a n c e s (Appendix  2)  r e v e a l s t h a t the approximate o v e r a l l t o l e r a n c e of the meter i s l . l f j $ , which i n d i c a t e s t h a t the o r i f i c e meter should have an accuracy of ,at l e a s t 2% f o r n o n - p u l s a t i n g f l o w s . B.  C a l c u l a t i o n 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 c a l c u l a t e d from Equations 5> and- 6> r e s p e c t i v e l y . From these v a l u e s , the value o f e/D , w  was  the r e l a t i v e  c a l c u l a t e d f o r each p o i n t u s i n g E q u a t i o n Ij..  m e t r i c average  of the v a l u e s f o r D /e w  The  roughness, geo-  f o r each p i p e was  then  c a l c u l a t e d , and t h i s v a l u e i n t u r n used to p l o t a smooth curve o f f versus Re f o r each p i p e , a c c o r d i n g t o E q u a t i o n ij..  17  G.  C a l c u l a t i o n o f Heating Data A l l heating  data were c o r r e l a t e d u s i n g  the  film  temperature f o r e v a l u a t i n g the p h y s i c a l p r o p e r t i e s o f a i r , as recommended by Humble et a l (lf>) and described. 5>, served  The  f i l m f r i c t i o n f a c t o r s , c a l c u l a t e d from E q u a t i o n  changed during l o n g i n t e r v a l s between runs.  ively.  previously  as a check t h a t the p i p e w a l l roughness had The  The  s p e c i f i c h e a t o f a i r was  assumed to be  B t u / ( l b ) (°P), but i t i s r e a d i l y seen that s i n c e C_ b o t h the numerator ( i n h) Stanton modulus, C St.  The  p  not  f i l m Reynolds  j g were c a l c u l a t e d from Equations 6 and 7»  number and  the  and i n the denominator o f  respect-  0.2ij. appears i n the  w i l l have no e f f e c t on the Stanton modulus  f i l m P r a n d t l number Prj. was  evaluated  Pr versus temperature g i v e n i n the paper by  from a p l o t of  Sams (1+0).  Throughout the e n t i r e i n v e s t i g a t i o n P r ^ seldom d e v i a t e d the v a l u e  O.69. A recent  Putnam (&£)»  t h e o r e t i c a l a n a l y s i s o f L i n , Moulton  which i n t r o d u c e s  i s normally considered  modulus i n J  H  the boundary l a y e r , i n d i c a t e s t h a t i f the index o f the  The  Prandtl  were made a v a r i a b l e w i t h Reynolds number.  Weisman (I4.9) r e p o r t s t h a t the index may =  and  a small amount o f eddy i n what  b e t t e r agreement c o u l d be o b t a i n e d  n  from  1.22  Re"  be  written: (18)  0 , 7  d i f f e r e n c e , however, has  very l i t t l e e f f e c t on jjj when the  P r a n d t l modulus i s c l o s e to u n i t y , as i s the case w i t h gases. I t was  decided,  t h e r e f o r e , to r e t a i n the o r i g i n a l v a l u e  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 o f t u r b u l e n t heat t r a n s f e r d a t a u s i n g the f i l m concept, Humble e t a l (15) e l i m i n a t e the i n f l u e n c e o f entrance and e x i t c o n d i t i o n s 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 p r e s e n t  study L / D v a r i e s o n l y from I2I4. to 170, the maximum p o s s i b l e w  variation i n J  H  due t o t h i s f a c t o r i s o n l y 3.$%.  The a c t u a l  v a r i a t i o n was p r o b a b l y even s m a l l e r , because o f t h e r e l a t ^  i v e l y low and p r a c t i c a l l y constant w a l l s u r f a c e temperature employed.  End e f f e c t s were t h e r e f o r e i g n o r e d i n c o r r e l a t i n g  the p r e s e n t d a t a . The c a l c u l a t i o n o f the h e a t balance was based on the t o t a l energy b a l a n c e : q+w  g  =  M  *  * 2 -r  2gc  Y  U  £  A  Z  (  1  9  )  Sc  which, f o r the p r e s e n t setup, reduces t o : q  =  AH  Because o f the extremely low and v a r i a b l e steam q u a l i t y , good heat b a l a n c e s were n o t o b t a i n e d d u r i n g r e g u l a r r u n s . However, s p e c i a l h e a t i n g runs w i t h w e l l - d r i e d steam were made i n which the maximum d e v i a t i o n was reduced to l e s s than 10%  {l.k%,  9»$% and 3.k%)>  which i s c o n s i d e r e d good f o r t h i s  type o f balance (see Appendix 3 ) .  C a l c u l a t i o n o f heat  trans-  f e r c o e f f i c i e n t s was based on heat a c t u a l l y r e c e i v e d by the air,  as g i v e n by i t s f l o w r a t e and temperature  rise.  19  RESULTS AND  CONCLUSIONS  The c a l c u l a t e d v a l u e s f o r the heat t r a n s f e r and friction  f a c t o r d a t a f o r each p i p e are t a b u l a t e d I n  k. and are shown g r a p h i c a l l y on F i g u r e s 2 to 8 . friction  Appendix  On the graphs,  f a c t o r curves are drawn through the i s o t h e r m a l p o i n t s  u s i n g E q u a t i o n 2 and the l o g a r i t h m i c (geometric) average r e l a t i v e roughness  (e/D ) . w  The tendency o f the f i l m temp-  &  e r a t u r e method t o overcompensate  for radial  temperature  g r a d i e n t s at Re l e s s than 20-30,000, noted by Humble, Lowderm i l k and Desmon (15) i n t h i s work. friction  and by Sams (lj.0), has been c o r r o b o r a t e d  At h i g h e r Re,  the i s o t h e r m a l and h e a t i n g  d a t a l i e on the same curve. A comparison o f f r i c t i o n  f a c t o r s f o r the v a r i o u s  p i p e s i n F i g u r e 9 shows t h a t , i n o r d e r o f d e c r e a s i n g roughness, the  pipes are: Pipe  A B C D E F G  -  1/8 l/k 1/2 3/8 l A 3/8 l A  e  i n . galv. i n . galv. i n . Karbate i n . Galv. i n . st. steel i n . st. steel i n . copper  /°w  0.01958 0.01150 0.00702 O.OO63I 0.00362 0.002^6 O.OOOlf.1  ...  e (calc.)  e (Moody)  0.000^39 0'0003^9 0.0002Q3 0.000260 0.000110 0.000105 0.000013  0.0005 0.Q005 0.0005 0.00015 0.00015 0.000005  A l l v a l u e s o f the roughness index e appear to be lower than those g i v e n by Moody (30} except the v a l u e o f e f o r the copper p i p e .  Such d i f f e r e n c e s might be expected, however,  because o f changes  and d i f f e r e n c e s i n manufacturing t e c h n i q u e s ,  i  n _  i  i  I  I  i l l  FIGURE 2. g IN. GALVANIZED PIPE  o  _ UFAT TRAMQFFR  A  FRIP.TIHN  -  DATA -  .  O CD  O  s  VI  CD  m  °  OG  0  "vD—(t  IS n  s  EATING R U N S  •  —  - O ~  o  —  — — 8  10  1.5  2  3  i  4  FILM REYNOLDS NUMBER  DvM>Qf  von K.  8  •  I0  =  1.5  -1-  . -A  -!  1  l  i  \—i—i  FIGURE 3. 3 IN. GALVANIZED PIPE TDAMCPCD  UCTA-T  nc_M  l  FPIPTinM  Q.  1  <  u  •  -  — —  ....  |—  _ .  iD  HATA  CD IS OTHEIR M A L R U NS  MM  Xfc*  ....  ...  i • •  O w EATIN G R U N S w n  ——  •  •  1 i !  1 G O -  '  \ i  '  1 i  -  1  von K  !'  8  10 4  1.5  FILM  2  REYNOLDS  3  4  NUMBER  DwV ef b  8  I0  5  1.5  FIGURE 4. ^|N. KARBATE GRAPHITE HEAT  PIPE  TRANSFER a FRICTION DATA  FILM REYNOLDS NUMBER  DwV e D  Wt  f  ®  ISOTHERMAL  O  HEATING  RUNS  RUNS  FIGURE 5. | IN. GALVANIZED PIPE HEAT TRANSFER a FRICTION  DATA  CM _l|Q  (D  ISOTHERMAL RUNS  O  HEATING  RUNS  8  csJirO *ol *  o  3  ro  FILM REYNOLDS  NUMBER  FIGURE 6, 5 IN. STANDARD  STEEL  PIPE!  HEAT TRANSFER S FRICTION DATA i  i  <D I S O T H E R M A L  o  i —  i  I  RUNS  i  !  O  HEATING  RUNS  — M  1  - 4  1  1  1  FIGURE 7. | l N . STANDARD  -  U C A T  T D A M C C C D  Q.  1—1—1—I—|  STEEL  CDI f T I O M  PIPE •  H AT" A  CD IS O T H E R M A L R U NS w  D  (  n—  ncAiini  i  ~~~~~~ - ~ i  ^yonK.  8  10  L5  2  3  FILM REYNOLD'S N U M B E R  8  10'  i ! ! 1.5  1 1  1 1  1  1"" 1  1  ;  1  1  1  1  1  1  FIGURE 8. J|IN. COPPER  -  i i r - A T  nc.Mi  -rr-i A M f r r n  -\i^or t_r  o  1  1  1 11  1  PIPE  r n i O T i r \ M 1 \Jl\  r  1  1  rA  r i A T A  1  L  •  CVJ  >  ® -is»OTHEIR M A L R U N S  or  _1|Q .CM  ^ lO 0_'  O  2  II  '  o  u E A T IN G R U N S  -  > O C)  C) r C i1  OJ|tO  •3] 0> O  )  II  X  ro .  8  I0  4  1.5  FILM  8  REYNOLDS  NUMBER  |Q5  von K.  i  —\  1-  FIGURE 9.  -----  I-  .1-  -I  I  ( H-T--  7 COMMERCIAL PIPES  HEAT TRANSFER & FRICTION DATA A  f  i IN G A L V .  28  and because o f normal d i f f e r e n c e s i n i n d i v i d u a l samples o f pipe. The  curves o f j  H  versus Re  f  have been f i t t e d i n the  s t r a i g h t l i n e r e g i o n by the method of averages of  to equations  the form: J  H  • -  ' K(Re )  (20)  m  f  Values o f K and m are i n c l u d e d w i t h the t a b u l a t e d d a t a i n Appendix If..  These v a l u e s show no  s i g n i f i c a n t trend, probably  because the range o f Reynolds numbers i n v e s t i g a t e d was  not  l a r g e enough f o r a l l the p i p e s . A comparison o f the heat t r a n s f e r e f f i c i e n c i e s of the v a r i o u s p i p e s i s g i v e n i n F i g u r e 1 0 ,  where a m o d i f i e d  form o f the heat t r a n s f e r 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 a g a i n s t the power l o s s p e r square f o o t of heat t r a n s f e r E.  area  The data from which the graph was p l o t t e d are t a b u l a t e d i n  Appendix  T h i s method of p l o t t i n g the d a t a i s s i m i l a r to  one p r e s e n t e d by Colburn ( 6 ) f o r comparing turbulence  promoters.  The graph shows t h a t f o r the same heat t r a n s f e r c b e f f i c i e n t , l e s s pumping power p e r square f o o t o f heat t r a n s f e r area i s r e q u i r e d f o r smooth t u b i n g than f o r rough p i p i n g . w i t h the c o n c l u s i o n o f Cope ( 8 ) , who for  a r t i f i c i a l l y roughened p i p e s .  T h i s agrees  found the same r e s u l t  The f a c t t h a t a l l the  curves except the curve f o r copper p i p e i n t e r s e c t at a power l o s s o f about 3 2 0 foot-pounds  per second p e r square f o o t of  t r a n s f e r area i s an i n t e r e s t i n g phenomenon.  Apparently, beyond  t h i s p o i n t , the very rough p i p e s become more e f f i c i e n t  than  i i iii HEAT  m—i—r  " FIGURE 10. TRANSFER - FRICTION EFFICIENCY  30  those o f i n t e r m e d i a t e roughness, b u t  s t i l l not as  efficient  as the copper p i p e , at l e a s t w i t h i n the l i m i t s o f the gation.  investi-  P o s s i b l y some new . a w t u r b u l e n t heat t r a n s f e r mech-  anism which i s not a d i r e c t f u n c t i o n of f l o w r a t e becomes dominant at t h i s p o i n t . Another I n t e r e s t i n g p o i n t i s t h a t although Karbate p i p e i s rougher than the 3/8 s t e e l and 3/8 than 320  the  i n . g a l v . , l/k i n . s t .  i n . s t . s t e e l p i p e s , at power l o s s e s of l e s s  i t i s more e f f i c i e n t than these p i p e s ,  indicating  t h a t the nature o f the s u r f a c e roughness of the Karbate p i p e may  have been d i f f e r e n t .  A microscopic  examination (  of  the f o u r types of s u r f a c e s i n v e s t i g a t e d ("smooth" copper, standard  s t e e l , g a l v a n i z e d s t e e l and Karbate g r a p h i t e )  rev-  ealed that: 1.  The  copper s u r f a c e was  smooth, with o n l y a  few  l o n g t i t u d i n a l s c r a t c h e s , the c r y s t a l s t r u c t u r e b e i n g easily 2.  The  discernible. g a l v a n i z e d s u r f a c e was  extremely rough,  jagged  and i r r e g u l a r , as i f the s u r f a c e o f a r a p i d l y b o i l i n g l i q u i d had 3.  The  suddenly been f r o z e n .  standardized  s t e e l surface was  l i k e the g a l v -  a n i z e d s u r f a c e , the roughness b e i n g random and  irregular,  but on a much s m a l l e r s c a l e . if..  The Karbate g r a p h i t e p i p e , on the o t h e r hand, d i s -  p l a y e d a very r e g u l a r , g e o m e t r i c a l l y p a t t e r n e d l i k e the s u r f a c e of a double-cut  surface,  f i l e , w i t h 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 f l o w .  31 I t i s q u i t e reasonable,then,  to expect t h a t the nature o f the  s u r f a c e i t s e l f may have an a p p r e c i a b l e e f f e c t on h e a t  transfer  rates. The v a l u e s o f J  H  p r e d i c t e d by Reynolds  analogy  1  ( E q u a t i o n 9) a**© compared w i t h the e x p e r i m e n t a l l y observed values at Re  f  = 20,000, 5 0 , 0 0 0 ,  and 100,000 i n Table I .  these v a l u e s are n o t i n accord i s n o t s u r p r i s i n g  That  when one  c o n s i d e r s the simple t u r b u l e n t core b a s i s o f the Reynolds* analogy. T a y l o r ' s and P r a n d t l ' s analogy  ( E q u a t i o n 11) as  w e l l as P i n k e l ' s e q u a t i o n ( E q u a t i o n 15) p r e d i c t that when f has become constant i n rough p i p e s a t h i g h Re, J be c o n s t a n t .  H  should a l s o  D a t a o b t a i n e d d u r i n g t h i s i n v e s t i g a t i o n do n o t  c o n f i r m t h i s r e s u l t , although P i n k e l o b t a i n s 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 e x p l a n a t i o n f o r the constancy o f f i n rough tubes g i v e n by Coulson and Richardson  a t l a r g e Re  (9) i s :  "With rough p i p e s , however, an a d d i t i o n a l drag known as form drag r e s u l t s from the eddy c u r r e n t s caused by impact o f the f l u i d on o b s t r u c t i o n s , and, when the s u r f a c e i s "very rough, i t becomes l a r g e compared w i t h the s k i n f r i c t i o n . S i n c e form drag i n v o l v e s d i s s i p a t i o n of k i n e t i c energy, the l o s s e s are p r o p o r t i o n a l t o the square o f the v e l o c i t y o f the f l u i d . . . " When t h i s happens, f becomes independent  o f Re.  One would  surmise, however, t h a t heat t r a n s f e r r a t e s are n o t d i r e c t l y i n f l u e n c e d by the form drag, so t h a t the simple r e l a t i o n between f and j  H  i n d i c a t e d by the P r a n d t l and T a y l o r analogy  and by the P i n k e l equation I s n o t v a l i d .  31a  TABLE 1 Comparison of j Calculated from Reynolds' H  Analogy and from Experimental Curves  Pipe  Reynolds Number  J (Experimental) h  J  h  (Reynolds)  1/8 Galv.  20,000 50,000 100,000  0.00185 0.00280 0.00233  0.00498 0.00473 0.00473  1/4 Galv.  20,000 50,000 100,000  0.00338 0.00268 0.00215  0.00410 0.00392 0.00391  1/2 Karbate  20,000 50,000 100,000  0.00329 0.00270 0.00231  0.00355 0.00340 0.00340  3/8 Galv.  20,000 50,000 100,000  0.00295 0.00239 0.00200  0.00351 0.00335 0.00328  1/4 S. Steel  20,000 50,000 100,000  0.00295 0.00238 0.00194  0.00314 0.00293 0.00281  3/8 S. Steel  20,000 50,000 100,000  0.00291 0.00239 0.00202  0.00307 0.00273 0.00254  1/4 Copper  20,000 50,000 100,000  0.00323 0.00255  0.00264 0.00222 0.00196  FIGURE II. TEST. OF VON KARMAN'S ANALOGY Pr = 0.69  50  ' *  40  + .+ -  ^ --  - m D  O-  *  b  o  ^IN  ©  ^IN GALy.  e .  i|N  KARBATE  +•  |lN  GALV.  X  i-IN ST. S T E E L  •  |lN  A  ^IN  —  e  A  30  20  10  GALV.  ST. S T E E L COPPER  VON DOO  1500  3000  2000  Re Vfi f  4000  5000  6000  KARMAN  7000  33  The by p l o t t i n g  a p p l i c a b i l i t y o f von Karman's analogy was t e s t e d  Vf /J  p o i n t s where j  f  H  H  versus  versus R e  f  -/f Re f  on F i g u r e 11 f o r d a t a  f  was i n the s t r a i g h t l i n e r e g i o n .  T h i s method o f p l o t t i n g should g i v e a s t r a i g h t l i n e i f Karman's analogy h o l d s .  The d a t a p o i n t s f a l l on o r near the t h e o r e t -  i c a l curve w i t h a maximum d e v i a t i o n o f 15$.  Lack o f temper-  mature g r a d i e n t d a t a prevented a t e s t o f the refinements i n c o r p o r a t e d i n t o von Karman's d e r i v a t i o n by B o e l t e r e t a l ( E q u a t i o n 13) and M a r t i n e l l i  ( E q u a t i o n llj.) .  However, the  refinement i n t r o d u c e d by B o e l t e r e t a l to compensate f o r r a d i a l temperature  g r a d i e n t s ( 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 p r o p e r t i e s ) should be rendered s u p e r f l u o u s by the use of the f i l m temperature  concept, which i s an e m p i r i c a l  to compensate f o r these v a r i a t i o n s .  attempt  M a r t i n e l l i ' s refinement  (the e f f e c t o f the eddy d i f f u s i v i t i e s o f 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 a t h i g h Re, but a t lower Re p r e d i c t s t h a t  A / f ^ / j j j should be lower  than p r e d i c t e d by von Karman's analogy. data seem to support t h i s p r e d i c t i o n .  The experimental The j g curves c a l c u -  l a t e d by von Karman's analogy are a l s o p l o t t e d f o r each p i p e i n F i g u r e s 2 to 8 (dashed  line).  Although the a p p l i c a b i l i t y o f the von Karman analogy and i t s m o d i f i c a t i o n s has n o t been d e f i n i t e l y proved by t h i s i n v e s t i g a t i o n , i t i s shown to conform more to the f a c t s concerning the e f f e c t o f w a l l roughness on heat t r a n s f e r do the simple a n a l o g i e s , the models f o r which e i t h e r  exclude  the l a m i n a r l a y e r completely o r exclude the e f f e c t o f the buffer layer.  than  3k  SUMMARY 1.  Heat t r a n s f e r and f r i c t i o n d a t a f o r a i r i n 7  p i p e s have been obtained - 8 0 , 0 0 0 , e/D  i n the Reynolds number range 1 0 , 0 0 0  v a r y i n g from 0.020 to 0.000ij.l.  w  commercial  These d a t a  have been c o r r e l a t e d u s i n g the f i l m temperature concept d e s c r i b e d by Humble, Lowdermilk and Desmon (l£) by c a l c u l a t i n g J * Re , H  f  and f  f  for a l l pipes.  The d a t a are p r e s e n t e d  in  t a b u l a r and g r a p h i c a l form. 2.  The  e f f i c i e n c i e s o f the p i p e s have been compared by  plotting h/CptPr) / 2  3  against E, the power l o s s p e r  f o o t of heat t r a n s f e r 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 ) , e f f i c i e n t than rough p i p e s .  square  smoother p i p e s are more  An e x c e p t i o n was  the Karbate p i p e ,  which, though l e s s e f f i c i e n t than the smooth copper p i p e ,  was  more e f f i c i e n t than other p i p e s o f l o w e r e r e l a t i v e roughness. T h i s f a c t i s a t t r i b u t e d to the d i f f e r e n c e i n the nature  of  the  surface of the g r a p h i t e p i p e . 3.  A t e s t of the Reynolds analogy has r e v e a l e d ,  t h a t i t does not h o l d f o r rough p i p e s . and T a y l o r and P i h k e l ' s s e m i - e m p i r i c a l  The  as expected,  analogy of P r a n d t l  equation have the  -common f a i l i n g o f p r e d i c t i n g t h a t when, at s u f f i c i e n t l y R O f j - f f has become constant, which i s not confirmed  jjj must a l s o become  by these experimental  high  constant,  data.  The  Karman analogy, however, has been found to p r e d i c t the  von data  q u i t e a c c u r a t e l y and c o n s i s t e n t l y w i t h i n the range of Reynolds numbers i n v e s t i g a t e d .  35  NOMENCLATURE i  a  - c o n s t a n t i n E q u a t i o n 11, d i m e n s i o n l e s s  A  - heat t r a n s f e r s u r f a c e area, sq f t  B  - characterization factor,  CQ  - o r i f i c e discharge c o e f f i c i e n t ,  C  - s p e c i f i c h e a t o f a i r a t constant p r e s s u r e , Btu/(lb)(°F)  p  dimensionless  D  Q  - diameter o f o r i f i c e , f t  D  w  - i n s i d e diameter o f p i p e , f t  dimensionless  D. R.  - d i f f u s i v i t y r a t i o Eg/(Eg + k/ C ) , d i m e n s i o n l e s s  e  - e q u i v a l e n t sand roughness, f t  Eg  - eddy d i f f u s i v i t y f o r heat,  f  - Panning  f  f  g g  '  p  f r i c t i o n factor,  sq f t / h r  dimensionless  - f i l m Panning f r i c t i o n f a c t o r , f l u i d p r o p e r t i e s e v a l u a t e d at T^, d i m e n s i o n l e s s - a c c e l e r a t i o n o f g r a v i t y , f t / s q sec  c  - conversion f a c t o r ,  (lb)(ft)/(sec) (lb-force) 2  G  - mass f l o w G = e v , l b / ( s e e ) ( s q f t )  h  - average heat t r a n s f e r B t u / ( s e c ) ( s q ft)(°P)  AH  - enthalpy gained b y a i r = w C ( T  coefficient,  p  2  - T j ) , Btu/sec  j  - " j - f a c t o r " f o r heat t r a n s f e r a St P r ^ , ionless  k  - thermal c o n d u c t i v i t y , ( 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 , E q u a t i o n 20  L  - tube l e n g t h , f t  m  -  2  dimens-  index o f Re i n E q u a t i o n 20, dimensionless  36  n  - index o f Pr i n j ^ , E q u a t i o n 18, d i m e n s i o n l e s s  P  - absolute pressure, l b - f o r c e / s q f t  P^  - absolute p r e s s u r e a t i n l e t , l b - f o r c e / s q f t  P  - absolute p r e s s u r e a t o u t l e t , l b - f o r c e / s q f t  2  AP  - t o t a l p r e s s u r e drop, l b - f o r c e / s q f t  £&f  r  - p r e s s u r e drop through s e c t i o n due to sk£zf f r i c t i o n , lb-force/sq f t = ? - P - G ( v - V i ) / g 2  1  2  2  e  q  - heat s u p p l i e d by steam, Btu/sec  Pr  - P r a n d t l number - GpW/k, d i m e n s i o n l e s s  Pr  - f i l m P r a n d t l number = (CJ*/k) , e v a l u a t e d a t T-, dimensionless P r  f  Re  - Reynolds number = D V€//{, dimensionless  Re^  - f i l m Reynolds number = ^• ^\ ^fMft  S  - c r o s s - s e c t i o n a l area o f p i p e , sq f t  S  w  n  - cross-sectional  0  dimensionless  >  a r e a o f o r i f i c e , sq f t  St  - Stanton number = h / c V e ,  Stf.  - f i l m Stanton number • h/CpV^S^, d i m e n s i o n l e s s  T. _ _ . A,x3,C  - steam temperature,  p  dimensionless  °R  - temperature  o f i n l e t a i r , . °R  T  2  - temperature  o f o u t l e t a i r , °R  T  b  - temperature  o f b u l k o f f l u i d » ( T ^ + T ) / 2 , °R  T  f  - f i l m temperature  T  - (T  b  + T ) / 2 , °R g  - average s u r f a c e temperature = T = T = T , °R A  AT  2  T  V-  C  - d i f f e r e n c e between temperature center o f p i p e , °R  m a x  ^ mean  B  o f experimental p i p e  "  o f p i p e w a l l and  d i f f e r e n c e between temperature o f p i p e w a l l and average (mixed) temperature o f f l u i d , °R  - v e l o c i t y of a i r , ft/sec  37  V-JL  - s p e c i f i c volume o f a i r a t entrance, cu f t / l b  v  - s p e c i f i c volume of a i r at o u t l e t , cu f t / l b  2  w  - weight r a t e o f a i r flow, l b / s e c  Y  - expansion f a c t o r , E q u a t i o n 17,  y  e  dimensionless  - e f f e c t i v e thickness of layer associated roughness, f t  AZ  - difference i n elevation, f t  /3  - r a t i o of o r i f i c e dimen s i o n l e s s  with  diameter to p i p e diameter,  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  §  - functional  relationship  Subscripts: a  - average  b  - b u l k , based on average o f mean i n l e t temperatures  f  - f i l m , based on  s  - surface,  1,2  - entrance and e x i t of experimental s e c t i o n , respectively  and o u t l e t  temperature  based on temperature  T  s  38  BIBLIOGRAPHY AND  REFERENCES  (1)  Am. Soc. Meeh. Engrs., " F l u i d Meters - T h e i r A p p l i c a t i o n and P r a c t i c e , " ASME, 4 t h ed., 1937.  (2)  A r n i , V. R. S., and Meyers, J . E., " E f f e c t s o f I n t e r n a l Roughness on Pressure Drop and Heat T r a n s f e r of I n t e g r a l Finned Tubes," R e f r i g . Eng. 6 l , 757 (1953).  (3)  A v e r i n , E. V., " E f f e c t s of M a t e r i a l and Mechanical Working on a s u r f a c e upon Heat T r a n s f e r , " I z v e s t . Akad. Nauk S .S. S. R., O t d e l Tekh Nauk, H 6 - 2 2 (1954).  (4)  B o e l t e r , L. M. K., M a r t i n e l l i , R. C , and Jonas sen, F i n n , "Remarks on the Analogy between Heat T r a n s f e r and Momentum T r a n s f e r , " T r a n s . ASME, 6 j , 447"55» U 9 4 l ) '  (5.) > Cavers, S. D., Hsu, T., S c h l i n g e r , G., Sage, B. H., "Temperature G r a d i e n t s i n T u r b u l e n t Gas Streams," Ind. Eng. Chem., * £ , 2139"45 (1953). (6)  Colburn, A. 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The Hague-Amsterdam No. 16, J3» 221-45 (1937).  (32)  Nikuradse, J . , "Stromungsgesetze I n Rauhen Rohren," V. D. I . Forschungschaft, 361, (1933).  (33)  P e r r y , J . H., "Chemical Engineer's Handbook," 3 r d ed., McGraw-Hill, New York, 4 0 3 , 467 (1950).  (34)  P i n k e l , B., "A Summary o f NACA Research on Heat T r a n s f e r and F r i c t i o n f o r A i r Flowing through a Tube w i t h l a r g e Temperature D i f f e r e n c e , " Trans. ASME, 76, 305-17 (1954).  (351  P r a n d t l , L., "Bermerkung uber den Warmeubertragung i n Rohr," Phys. Z . e i t s c h r i f t , 23, 487-89 (1928).*'  (36)  P r a t t , H. R. C , "The A p p l i c a t i o n o f T u r b u l e n t Flow Theory to T r a n s f e r Processes I n Tubes C o n t a i n i n g Turbulence Promoters and P a c k i n g s , " Trans. I n s t . Chem. Engrs., (London), 28, 177 (1950).  (37)  R e i c h a r d t , H., "Heat T r a n s f e r through T u r b u l e n t F r i c t i o n L a y e r s , " NACA TM 1047, Sept. 1943.  (38)  Reynolds, Osborne, "On the E x t e n t and A c t i o n o f the Heating S u r f a c e f o r B o i l e r s , " P r o c . Manchester S o c , l£, 7-12 (1874).  (39)  Rouse, H., " F l u i d Mechanics f o r H y d r a u l i c E n g i n e e r s , " McGraw-Hill, New York, 1938.  (40)  Sams, E . W., "Experimental I n v e s t l n g a t i o n o f Average Heat T r a n s f e r 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 F l o w i n g 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 T r a n s f e r from High Temperature S u r f a c e s to F l u i d s - I I I C o r r e l a t i o n o f Heat T r a n s f e r Data f o r A i r Flowing i n A S i l i c o n Carbide Tube w i t h Rounded Entrance," NACA RM E9 D12, June 23, 1949-  (42)  S c h l i c h t i n g , H., "Boundary Layer Theory - P a r t I I Turbulent Flows," NACA TM 1208, A p r i l , 1949-  (43)  Schubauer, G. B., "Turbulent Processes as Observed i n the Boundary Layer o f a P i p e , " J . App. Phys., 2£, I88-96 (1954)  hi  Seban, R. A., and Shimazki, T. T., "Temperature D i s t r i b u t i o n s f o r A i r Plowing T u r b u l e n t l y i n a Smooth Heated P i p e , " Trans. ASME 21, 803-809 ( 1 9 5 D . Sherwood, T. K., "Heat T r a n s f e r , Mass T r a n s f e r , and F l u i d F r i c t i o n - R e l a t i o n s h i p s 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 w i t h O r i f i c e Meters," Van Nostrand, New York, 1951• Sugawara, S., and Sato, T., "Heat T r a n s f e r on the S u r f a c e of a F l a t P l a t e i n the F o r c e d Flow," Mem. F a c u l t y Eng. Kyoto Univ., lij., No. 1, 21-37 (1952). T a y l o r , G. I . , " C o n d i t i o n s a t the Surface o f a Hot Body Exposed t o the Wind," G. B. Adv. Comm. f o r A e r o n a u t i c s Reports and Memoranda, 272, V o l . 2, I4.23-29 ( I 9 1 6 - I 7 ) . Weisman, J o e l , " E f f e c t o f V o i d Volume and P r a n d t l Modulus on Heat T r a n s f e r i n Tube Banks and Beds," P r e p r i n t 17 Heat T r a n s f e r Symposium AIChE, March 1955-  k2  APPENDIX  1i i  A PPENC MX l a . A  Q I NUKIMUt  \ U>  CALIBRAT ION  15000  CI)  1 1  3..  r  o  I  r L A1 t  J- i M r i D i c i r r ni A T C \ \ 4' o d>N ^ to"  C U IW E S  FOR  i  •  !  i  i  •  i  ORI FICE PI_ATES  20000 . 30000 ORIFICE R E Y N O L D S N U M B E R  50000 M  W  70000  my  LV P P • F N  i i  !  " CALIBRATION OF PRESSURE GAUGE  • i 1  30  i 1 i  1  i  1  25  • i  •f  i  Q.  0  '  or CD CO UJ  1  15  i  i  .J i  a: a. UJ I O  i  • 1 1  o  i  CD  i •  i  i 1  I  ACTUAL  i  1 1 i i  !  j i  i  i  15  i  i  i  10  i  i  !  <  )•  1 1 i i  20  25  PRESSURE PSl  30  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  0.2 x 1/2  0.01  0.25 x 1/2  0.15  0.1 x 1/2  0.00  P  x  Pi - P  2  T-L  Sum of squares:  1.31  Overall approximate tolerance  1.15$  U6  APPENDIX 3 Results of Heat Balance Runs  Run No.  Time of run, min  1  15  2  2  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  938  939  939  Latent heat 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 ft  L ft  S sq.ft  A 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 i n . Galvanized Pipe Run No.  W lb/sec  Re  f  —  —  Dw/.e  Co —  201 202 203 204 205  0.001808 0.002581 0.003145 0.004030 0.004676  8490 12120 14760 18920 21950  0.01247 0.01297 0.01370 0.01283 0.01269  60.39 49.18 40.77 48.24 48.77  0.5957 0.5962 0.6015 0.6040 0.6030  206  0.005745 0.006843 0.008308 0.009703  26990 32130 39020 45570  0.01247 0.01212 0.01187 0.01196  50.17 53.70 56.51 54.72  0.6040 0.6070 0.6047 0.6019  67.64 91.16 93.19  207 208 209  l / 4 i n . Galvanized Pipe 25 26 27 28 Rl  0.01815 0.01890 0.02450 0.01236 0.00325  63100 65700 84700 42800 11280  0.01020 0.00998 0.00986 0.01072 0.0111  R2 R5 86  0.00506 0.00700 0.00906 0.01050 0.01242  17590 24300 31420 36450 43200  0.01042 0.00996 0.01065 0.01032 0.01005  94.22 103.20 79.29 86.05 91.95  R7 R8 R9 " RIO 111  0.01368 0.01459 0.01652 0.01752 0.01093  47500 50700 57500 60850 38000  0.00999 0.01121 0.00993 0.00956 0.01082  92.88 65.15 93.75 104.7 73.27  R12  0.01298 0.01270 0.01450 0.00900  45200 47600 50200 31250  0.00928 0.01005 0.01062 0.01030  115.00 91.11 76.52 88.31  R3 R4  R13  R14 R15  75.55  87.28  k9 APPENDIX kb Results of Isothermal Runs 1/2 i n . "Karbate" Graphite Pipe Run No.  W lb/sec  Re  f  —  —  56300  Dw/e  0.008495 0.008657  152 146  0.00874  160  137 133 139 140 141  0.02230  0.01985 0.01760 0.01484  50100 44500  142 143 144 145 146  0.01021 0.00908 0.00734 0.00604 0.00481  25750 22900 18500 15220 12150  0.00919 0.00899 O.OO965 0.01420 0.01063  (omitted) 97.5  158  0.02912  73680  0.00881  154  12500  0.01025  112 120 134 148  0.01240  37400 31250  0.008480 0.00881  166 148  137 154  125  3/8 i n . Galvanized Pipe 181 182 183  184 185 186  187 188 189  190  0.004893  0.01341  17830 22900 29220 34300  0.01561  39920  0.01948 0.02143 0.02343  49810 54770  0.006975  0.008960  0.004143  0.01755  44850  59870  0.00977 0.00932  0.008998 0.008901 0.00848  0.00838 0.00823 0.00796 0.00766  145  169  173 182 204  234  1/4 i n . Standard Steel Pipe 7  8 10 11 12 13 14 15 16 17 18 19  0.00610  0.00720  0.00663  21000 22850  0.00663 0.007415  22850 25600  0.00780  0.00818  28250 29200  0.00798  0.00653  0.00844 0.00923 0.00919  0.01752  0.01651  0.01501  22550  31800  31600 69800 65800 59800  0.00770  0.00870  312 341 181  0.00773  302 309  0.00775  284 245 254 231  0.00783  0.00813 0.00698 0.00722  O.OO722  357  271  277  50  APPENDIX 4b Results of Isothermal Runs 3/3 i n . Standard Steel Pipe Run No.  W lbs/sec  Dw/e  Re  159 160 161 162 163  0.00506 0.00691 0.00899 0.01039 0.01231  12960 17700 23000 26600 31500  0.00860 0.00789 0.00767 0.00734  278 421 294 314 362  164 165 166 167 168  0.01415 0.01557 0.01714 0.01873 0.01990  36200 39800 43400 48000 55900  0.00718 0.00717 0.00692 0.00684 0.00673  380 361 414 425 441  179 180  0.02330 0.02815  60900 71900  0.00634 0.00620  573 602  45 46 47 48 49  0.00431 0.00515 0.00654 0.00776 0.00895  14500 17310 22000 26100 30150  0.00809 0.00749  0.00628 0.00631  386.9 608.4 1557.5 2780 1430  50 51 52 53 54  0.01080 0.01228 0.01480 0.01738 0.01952  36400 41400 49900 58500 65700  0.00589 0.00569 0.00529 0.00514 0.00516  0.00775  1/4 i n . Copper Pipe  0.00677  2530 3170 13900 13100 13746  51  APPENDIX 4c Calculated Values of Relative Roughness and Deviations  Pipe  Log Average (Dw) ( ?a e  Log (Dw) ( e)a  Max.Devh (%)  Avg.Devh (%)  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 i n . Galvanized Pipe Run No.  Re*  210 211 212  7440  11970  16360  213 234  22170 28770  215 216  35000  38000 42000 44000 46400  217 218  219  220 221 222 223*  9100 15660  231  48860 51578 55750 58310  f. X  h  0.00232 0.001565  0.00557  0.001348  0.01604  0.001467 0.001412  0.001364 0.003340 0.001326  0.001212  0.001262  13210  17210 27290  230  232  233 234 235  -ECU • (sec)(sq.ft)(°F)  61200  0.00342  0.00810 0.01170  0.02010  *  H  =  0.05322 (Re j-°f:  2726  0.002380 O.OO24IO 0.002555  0.002725  0.002880  0.002965  0.02185  O.OO297O  0.02420 0.02542  0.002975  0.02725  0.003030  0.00383  0.002170  0.002980  0.007710 0.007633 0.008861 0.01642  0.002545 0.002980 0.002660  0.02645 O.O279O 0.02933 0.02983 0.03330  0.002795 0.002794 O.OO2699 0.002642 O.OO2642  Equation f i t t i n g curve i n turbulent region (method of Averages) J  n  :-S  Runs 224 - 229 were omitted because the outlet a i r temperature thermometer bulb was touching the tube wall.  0.003108  53  APPENDIX 4d Results of Heating Runs  l A i n . Galvanized Pipe  S  ;,(,sec)(fte)(°F)  J!  0.01301 0.01468 0.01511 0.01641 0.01721  0.002< 0.002975  37600 41100 43000  .0121 0.0121 0.0119 0.01152 0.01139 0.01218  34 35 36 37 38  46900 50600 53600 56000 59700  0.01152 0.01112 0.01092 0.01022 0.01092  0.01830 0.01912 0.01970 0.02077 0.02180  0.002730 0.002640 0.002569 0.002585 0.002554  39 40 41 42 43 44  64000 70400 10350 13270 15400 26700  0.01040 0.01097 0.01515 0.02250 0.01658 0.01231  0.02180 0.0226 0.00474 0.005185 0.006720 0.01059  0.002386 0.002320 0.003194 0.003218 0.003046 0.002765  30500  29 30 31 32 33  34200  Equation f i t t i n g curve i n turbulent region  •"0 ^O ^ 1  J  H  =  0.07160 (Re)  f  0.003000 0.002812 0.002784 0.002800  APPENDIX 4d Results of Heating Runs 1/2 in. Karbate Pipe Run No.  X  h  i  J3IIL_ :(ff )(°F)(sec) 2  h  147 148 149  42380 39200 35970 32390 26670  0.00876 0.00947 0.00930 0.00895 0.00957-  0.01238 0.01154  0.00280 0.00282  152  22540 16230  0.00927  0.00316 0.00350 0.00355 0.00274 0.00262  150 151  0.009963 0.009831 0.008457  0.00276 0.00291 0.00304  156  47780 55860  0.01157 0.00848 0.00971  0.00742 0.005933 0.004134 0.01367 0.01529  157  62000  0.00988  0.01653  0.00255  153 154 155  11910  0.01090  Equation f i t t i n g curve i n turbulent region: j  =  H  0.02348  Re "°? ? : 15  6?  f  3/8 i n . Galvanized Pipe 191 192 193 194 195  9590 13320 18070 22870 27290  0.01210 0.01163 0.0111?. 0.01022 0.00965  0.003053 0.004200 0.005665 0.006852 0.007891  0.003017 O.OO303O 0.002972 0.002839  196 197 198 199 200  31860 37180 39920 44560 52470  0.00942 0.00866 0.00904 0.00856 0.00820  0.008862 0.01003 0.01051 0.01129 0.01293  0.002636 0.002557 0.002495  Equation f i t t i n g curve i n turbulent region: J  H  =  -0.2" 0.03139 (Re ) • T f  0.002741  0i.002401 O.OO2323  55  APPENDIX 4d Results of Heating Runs 1/4 i n . Standard Steel Pipe Ref  Run No.  (f^)(°F)(sec)  H  J  7 8 9 10  11020 14420 16030 33380  0.03240 0.00885 0.01061 0.00934  0.00436 0.00605 0.00683 0.00802  0.00273 0.00290 0.00295 0.00301  11 12 33 14 15  23400 24700 26350 56800 54500  0.00906 0.00883 0.00859 0.00732 0.00745  0.00903 0.00998 0.01060 0.01612 0.01652  0.002930 0.002796 0.002780 0.001983 0.002324  16 22 23 24  52100 72700 76200 68500  0.00745 0.00730 0.00735 0.00722  0.01710 0.0216 0.0255 0.0203  0.002311 0.002077  0.002073  O.OO2070  Equation f i t t i n g curve i n turbulent region: J  r 0.04998  H  3/8 i n . Standard Steel Pipe 169 170 171 172 173  9764 13740 18910 21430 24640  0.009579 0.009121 0.008560 0.008353 0.008221  0.003240 0.004417 0.005891 0.006971 • 0.007225  0.003146 0.003040 0.002951 0.002862 0.002780  174 175 176 177 178  30400 35440 41590 45320 52950  0.007522 0.007047 0.007401 0.007056 0.006888  0.008588 0.009665 0.010882 0.031587 0.032963  0.002677 0.002585 0.002480 0.002433 0.002321  Equation f i t t i n g curve i n turbulent region: J  H  =  0.06382 (Re) "°f  ?2  56  APPENDIX kd Results of Heating Runs  l A i n . Copper Pipe Run No.  f  h  f  2-BTH HfS" )( F)(sec) 6  55 56 57 58 59  13350 18220 19800 24800 30600  0.00844 0.00707 0.00765 0.00727 0.00662  0.00560 0.00744 0.00786 0.01028 0.01090  0.00317 0.00309 0.00300 0.00313 0.00270  60 61 62 63 64  35450 39900 44700 49200 54300  0.00654 0.00658 0.00598 0.00587 0.00582  0.01199 0.01336 0.01385 0.01430 0.01522  0.00254 0.00253 0.00234 0.00220 0.00212  65 66 67  59100 64200 69700  0.00523 0.00552 0.00523  0.01620 0.01702 0.01772  0.00207 0.00201 0.00193  E q u a t i o n f i t t i n g curve i n t u r b u l e n t r e g i o n : •J  H  =  0.1622  (Re) -°'3971 f  57  APPENDIX 5 Heat Transfer & Friction Efficiency Data l/8 i n . Galvanized Pipe lbs. Run No. ^ f r - f t . 2  210 211 212 213 214 215  216  217 218 219  '  97.94 179.20 342.5 590.6 907.5 1254.5 1407.7 1616.5 1595.0 1778.  ft.-lbs . E (Sec)(ftr 6.677 20.61 58.72 133.23 255.20  V^e  f  lbs. f t . sec. 4.630  7.530  7^e  lbs. f t . sec. 2  f  0.01114  10.31 13.94 17.37  0.01815 0.02634 0.03799 0.05002  567.2 571.1 646.4  22.02 23.94 26.43 27.74 29.24  0.06529 0.071102 0.07863 0.08267 0.08860  396.7  466.8  IK i n . Galvanized Pipe  29 30 31 32 33  395 465 539 622 703  125.6 157.4 198.9 245.1 280.1  14.21 15.94 17.51 19.18 20.02  0.04227 0.04785 0.04924 0.05340 0.05606  34 35 36 37 33  773 843 913 987 1055  338.3 374.2 422.7 491.5 506.9  21.85 23.60 24.96 26.11 27.81  0.05965 0.06230 0.06480 0.06749 0.07103  39 40. 41 • 42 43  1130 1345 63.0 132.5 233.0  569.4 695.6 7.493 16.85 39.32  29.79 32.83 4.831 5.251 7.177  0.07108 0.07617 O.Q1543 0.01690 0.02186  315.0  89.29  12.46  0.03445  44  58  APPENDIX 5 Heat Transfer & Friction Efficiency Data  l / 2 i n , Karbate Graphite Pipe Run No.  lbs. "Ft. 2  E Ft. - lbs. (Sec.)(Ft.)  147 148 149 150 151  199.2 167.1 136.7 100.2 70.87  7.79 57.92 43.00 26.68 15.01  152 153 154 155 156 157  50.65 29.36 . 15.25 265.1 372.0 438.*:.  9.45 3.92 1.38 126.1 194.9 229.2  2  .  V i e . lbs. Pt.^Tec.  ,e lbs. H b fFt.^ec. r V :  J  14.38 13.31 12.21 10.99 9.05  0.0403 0.0375 0.0337 0.0320 0.0275  7.65 5.52 3.80 16.19 18.95 21.04  0.0242 0.01932 0.01349 0.0444 0.04965 0.0537  3/8 i n . Galvanized Pipe 191 192 193 194 195 196 197 198 199 200  13.19 24.28 43.14 65.27 87.05 120.3 157.0 190.5 216.3 273.6  1.113 2.827 6.876 13.54 21.37 35.82 56.83 74.72 91.03 128.60  3.293 4.573 6.202 7.851 9.367 10.94 12.76 13.70 15.30 18.10  0.009935 0.01386 0.01843 0.02227 0.02567 0.02884 0.03263 0.03418 0.03674 0.04205  59  APPENDIX 5 Heat Transfer & Friction Efficiency Data  1/4 i n . Standard Steel Pipe Run No.  JLbs. * fr-FtT* p  P  E Ft. - lbs, (Sec)(Ft)  2  6.229 11.06 17.57; 22.90  V e b  10  r  f  lbs. Ft.* (Sec)  5.22 6.80 7.545 8.653  t: Y/'e_ lbs. ° F t ~ Z sec. :  H  f  .01425 .01972 .02226 .02605  7 8 9 10  49.1 69.3 100.8 115.6  11 12 13 14 15  148.2 183.8 200.5 417. 443.  33.26 45.63 52.23 147.50 157.0  10.10 11.61 12.41 22.31 23.21  .02959 .03246 .03450 .04424 .04930  16 22 23 24  463. 855. 897 765  173.1 491.7 558.5 446.1  24.29 32.15 35.40 31.84  .05613 .06678 .07328 .06600  3/8 i n . Stainless Steel Pipe 169 170 171 172 173  10.52 20.12 36.23 46.12 60.95  174 175 176 177 178  87.78 116.62 168.70 184.20 231.90  0.8789 2.399 6.020 8.821 13.62 25.02 40.68 68.65 78.78 109.50  3.351 4.717 6.494 7.357 8.460 • 1 0.44 12.17 14.28 15.56 18.18  0.01054 0.01434 0.01916 0.02106 0.02352 0.02795 0.03146 0.03541 0.03786 0.04220  60  APPENDIX 5  Heat Transfer & Friction Efficiency Data  l A i n . Copper Pipe Run No. yip lbs. **** Ptr«  55 56 57 58 59  40.8 61.9 78.3 112.8 153.3  60 61 62 63 64  208.4 246.6 284.9 330.3 374.8  65 66 67  379. 448. 468.  E  Ft. - lbs. (Sec.)(Ft.)2  TEEf l b s . * (FUj2 ec. f  S  J  h  V'€ l b s . * ^FtT^ec.  5.732 7.824 8.515 10.65 13.11  0.01817 0.02418 0.02555 0.03333 0.03540  6.411 7.922 10.39 12.94 15.25  15.21 17.11 19.21 21.11 23.29  0.03863 0.04329 0.04495 0.04645 0.04937  15.89 19.33 20.66  25.38 27.56 29.85  0.05254 0.05540 0.05761  0.5113 1.019 1.382 2.421 4.009  61  APPENDIX 6 Experimental - Non-Isothermal Data  1/8 i n . Galvanized Pipe tun No. o  F  T2 Op  Pi i n Hg  ?2 i n Hg  T op s  W lb./sec,  210 211 212 213 214  68.5 68.5 68.2 67.8 67.5  240.6 242.0 244.1 246.0 247.6  37.94 36.89 35.23 38.64 42.32  36.51 34.22 30.05 28.46 27.36  255.9 255.5 255.3 255.4 256.1  0.001994 0.003213 0.004322 0.005913 0.007716  215 216 217 218 219  67.4 68.8 68.0 67.9 67.8  248.0 248.2 248.5 248.2 248.2  48.15 51.00 54.66 55.68 53.94  27.67 27.74 27.46 28.64 28.57  255.3 255.5 255.2 255.3 255.0  0.009371 0.01019 0.01125 0.01178 0.01244  ..220 221 223 230  93.2 94.2 83.2 75.0  242.0 246.5 247.0 250.2  38.75 36.00 35.65 33.67  37.37 31.90 30.06 29.95  256.2 256.2 256.4 256.1  0.002418 0.004148 0.004581 0.007274  231 232 233 234 235  72.8 72.5 72.4 72.7 72.8  247.2 246.5 246.0 245.5 245.2  60.93 61.34 66.02 67.45 70.89  28.50 28.36 28.22 28.07 27.39  255.7 255.4 255.4 255.5 255.2  0.01307 0.01379 O.OL490 0.01559 0.01636  62  Experimental Data, Continued 1/4 i n . Galvanized Pipe Run No.  Ti  T  Op  Op  29 30 31 32 33  79.0 80.0 81.0 84.0 81.0  34 35 36 37 38  2  Pi  p  2  T  s  W  i n Hg  i n Hg  op  243.0 242.0 240.0 240.0 238.0  36.2 38.0 39.4 41.1 42.9  29.9 30.6 30.7 31.0 31.3  259.0 259.0 258.0 259.0 258.0  80.0 80.0 80.0 75.0 75.0  238.0 237.0 '236.0 234.0 234.0  45.1 46.3 47.5 49.6 51.6  32.3 32.2 32.1 32.9 33.5  258.0 258.0 257.5 258.0 258.0  0.01730 0.01840 0.01942  39 40 41 42 43  74.0 73.0 72.0 71.0 71.0  231.0 229.0 246.0 246.0 244.0  53.3 58.3 30.5 31.5 33.2  33.6 34.7 29.5 29.5 29.7  257.0 257.0 259.0 260.0 259.5  0.02340 0.02575 0.00376 0.00409 0.00560  44  71.0  242.0  34.9  29.9  258.0  0.00970  .  lb./sec  0.01104  0.01234  0.01360 0.03489 0.01621  0.02045  0.02175  L/2 i n . Karbate Pipe 347 148 149 150 151  69.3 69.3 71.5 70.0 70.0  220.5 222.0 223.5 225.5 227.8  38.52 39.47 40.10 40.88 42.16  35.25 37.68 37.90 39.26 41.03  257.0 257.4 257.0 257.7 258.3  0.02338 0.01983 0.01833 0.01575 0.03311  152 153 154 155 156  70.1 70.2 70.1 70.6 71.2  229.7 232.2 235.1 219.1 216.1  41.70 41.91 42.42 36.43 39.33  40.89 41.44 42.18 31.99 33.09  258.3 258.8 259.0 256.8 256.2  0.01112 0.00855 0.005613 0.02413 0.02819  157  72.5  215.0  41.96  34.56  257.6  0.03335  63  Experimental Data. Continued  3/8 i n . Galvanized Pipe tun No.  T 1  T 2  Pi  op  op  in Hg  191 192 193 194 195  90.3 89.9 88.0 87.5 87.4  229.8 228.5 227.5 224.9 223.0  196 197 198 199 200  87.1 86.6 85.9 85.0 84.8  220.4 218.5 217.0 214.1 212.1  ?2  T  s  W  i n Hg  OF  lbs./sec,  39.24 39.54 39.26 38.34 38.76  39.04 39.17 38.59 37.32 37.39  257.3 256.2 256.1 256.0 256.0  0.004717 0.006613 0.008898 0.01128 0.01346  37.60 36.43 36.31 37.89 ' 40.50  35.69 33.89 33.23 34.36 35.96  255.8 255.6 255.6 255.2 255.2  0.002636 0.002557 0.002495 0.002401 0.002323  1/4 i n . Standard Steel 7 8 9 10  78.0 77.6 77.2 77.4  248.9 244.5 249.0 246.6  32.0 31.6 32.9 33.3  31.24 30.52 31.33 31.48  267.0 264.0 264.5 263.0  0.00273 0.00290 0.00295 0.00301  11 12 13 14 15  76.9 76.2 75.5 63.4 65.0  244.0 242.6 242.0 227.4 227.0  34.5 36.1 36.8 39.27 43.47  32.16 33.20 33.60 32.87 36.66  262.0 262.0 261.5 257.5 257.0  0.00293 0.002796 0.002780 0.001983 0.002124  16 22 23 24  65.9 75.6 74.0 75.0  225.8 225.8 229.0 225.00  41.52 39.12 39.64 38.34  33.92 31.00 34.3^  257.5 258.0 258.00 258.0  0.0023U 0.002Q7/7.0.002070 0.002073  6k  Experimental Data. Continued 3/8 i n . Standard Steel Run No.  W lbs./sec,  2 i n Hg r  i n Hg  169 170 171 172 173  89.0 87.0 85.4 84.7 84.0  230.0 228.2 225.9 224.2 223.3  40.24 39.72 39.30 38.73 38.23  40.08 39.40 38.73 38.00 37.23  256.6 255.2 255.3 255.2 255.5  0.00480 0.00677 0.00933 0.01058 0.01219  174 175 176 177 178  83.5 83.7 83.7 84.8 84.8  220.0 217.8 215.2 . 214.0 211.2  37.15 35.85 36.24 37.60 40.18  35.72 33.92 33.44 34.52 36.26  255.0 254.8 254.8 254.3 254.2  0.01503 0^01754 0.02060 0.02245 0.02630  258.0 258.0 258.0 258.0 258.0  0.00475 0.00647 0.00706 0.00883 0.01088  258.0 257.5 258.0 258.0 256.5  0.01256 0.01426 0.01597 0.01760 0.01942  256.5 256.5 257.0  0.02116 0.02302 0.02500  1/4 i n . Copper Pipe 5.5 56 57 58 59  70.0 70.65 74.0 74.7 74.0  242.5 241.5 240.5 238.00 236.0  35.55 36.63 37.23 38.64 39.39  33.90 35.63 36.00 36.82 36.86.  60 61 62 63 64  74.0 76.0 76.0 77.0 76.0  233.5 231.0 229.0 225.6 223.5  39.15 42.44 42.3 43.65 46.4  35.8 38.36 37.45 38.0 40.2  65 66 67  76.0 75.5 75.2  221.5 220.0 218.5  49.0 52.0 55.2.  42.3 44.25 46.9  ,  

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