The University of Texas Publication June 22, 1943 YE HEAT TRANSFER AND PRESSURE DROP IN HEAT EXCHANGERS (Revision of Bulletin No. 3819) By BYRON E. SHORT lV Engineering Research Series No. 37 Bureau of Engineering Research PUBLISHED BY THE UNIVERSITY OF TEXAS AUSTIN Publications of The University of Texas PUBLICATIONS COMMITTEE E. J. MATHEWS R. H. GRIFFITH c. F. ARRoWOOD c. D. LEAKE D. CONEY A. SCHAFFER A. C. WRIGHT General Publications R. H. GRIFFITH H. R. HENZE LoUISE BAREKMAN A. SCHAFFER FREDERIC DUNCALF E. G. SMITH FREDERICK EBY M. J. THOMPSON Administrative Publications E. J. MATHEWS B. MCLAURIN C. F • .ARROWOOD C. D. SIMMONS R. J. WILLIAMS The University publishes bulletins four times a month, so numbered that the first two digits of the number show the year of issue and the last two the position in the yearly series. (For example, No. 4301 is the first publication of the year 1943.) These bulletins comprise the official publica­tions of the University, publications on humanistic and scientific subjects, and bulletins issued from time to time by various divisions of the University. The following bureaus and divisions distribute publications issued by them; communications concerning publications in these fields should be addressed to The University of Texas, Austin, Texas, care of the bureau or division issuing the publication : Bureau of Business Research, Bureau of Economic Geology, Bureau of Engineering Research, Bureau of Industrial Chemistry, Bureau of Public School Service, and Division of Extension. Communications con­cerning all other publications of the University should be addressed to University Publications, The University of Texas. Additional copies of this publication may be procured from the Bureau of Engineering Research, The University of Texas Austin 12, Texas THI VlllYERSITY OF T!IAS PU5' ~ The University of Texas Publication No. 4324: June 22, 1943 HEAT TRANSFER AND PRESSURE DROP IN HEAT EXCHANGERS (Revision of Bulletin No. 3819) By BYRON E. SHORT .. ,..r~ .-\~\_,, _ .. 1Jwkww*1 ., i -·· ""' ~tf~Tn~ Engineering Reaearch Seriea No. 37 Bureau of Engineering Reaearch PUa&.l•HllD aY THIE UNIVERSITY OF' TEXAS AU8TIN The benefits of education and of useful knowledge, generally diffused through a community, are essential to the preservation of a free govern· ment. Sam Houston Cultivated mind is the guardian genius of Democracy, and while guided and controlled by virtue, the noblest attribute of man. It is the only dictator that freemen acknowledge, and the only security which freemen desire. Mirabeau B. Lamar COPYRIGHT, 1943 BY THE BOARD OF REGENTS OF THE UNIVERSITY OF TEXAS TABLE OF CONTENTS Topic Page Table of Symbols................................................................................................ 5 Preface and Introduction.................................................................................... 7 Acknowledgments ...................................... ........................... ............................... 8 Summary .............................................................................................................. 9 Object ---------------------------------------------------------------------···························---·----------------10 Scope ··················································--····--·--·--------··-···-·····----------------········-········· 10 Apparatus and Experimental Procedure .......................................................... 11 Discussion and Correlation of Results, Heat Transfer Coefficients................ 19 Discussion and Correlation of Results, Pressure Drop.................................... 29 General Comparison -------------·-------------------------------------------------··----·--·--··-··--.......... 33 Bibliography ··----------------------------········-··--·····--·-······--·-----·--------------------------------------· 37 Appendix (Data) ····-----·-----------·············------------················································ 38 LIST OF FIGURES Fig. No. Title Page 1 Section through Heat Exchanger with Half-Moon Bailes.................................. 12 2 Sizes and Types of Bailes and Sizes and Arrangements of Tubes ................ 14 3 Effect of Different Degrees of Cleanliness on Transfer Rate ............................ 15 4 Thermal Conductivity of Water and Oil... ............................................................. 16 5 Viscosity of Water and Oils...................................................................................... 17 6 Wilson Plot for Half-Moon Baffled Bundle .......................................................... 20 7 Flow Sections for Different Baffle Types................................................................ 22 8 Effect of Baile Spacing on Nusselt Number........................................................ 23 9 Effect of Tube Spacing on Nusselt Number.......................................................... 24 10 Effect of Prandtl Number on Transfer Rate ........................................................ 25 11 Heat Transfer Rate for Half-Moon Baffles ............................................................ 26 12 Heat Transfer Rate for Disk-and-Doughnut Bailes .............................................. 27 13 Heat Transfer Rate for Orifice Bailes, and Bundles with No Bailes, and with Large Baile Spacings ................................................................................ 28 14 Coefficients for Pressure Drop for Cross-Flow for Half-Moon and Disk-and- Doughnut Baffles --------------------------------------·············----------------------------------------------· 31 15 Effect of Prandtl Number on Pressure Drop........................................................ 32 16 Coefficients for Orifices of Half-Moon Baffles ........................................................ 33 17 Coefficients for Orifices of Disk-and-Doughnut Bailes ........................................ 34 18 Coefficients for Orifices of Orifice Baffles ................................................................ 35 THE UNIVERSITY OF TEXAS BUREAU OF ENGINEERING RESEARCH STAFF Homer Price Rainey .................................................................................. President W.R. Woolrich ........................ Director and Dean of the College of Engineering Raymond F. Dawson .................................... Assistant Director-Testing Engineer H. E. Degler ··-·······-·················-····-·····························-··-···Mechanical Engineering S. P. Finch ······-········--·--···········-········-······-····-···················-···········Civil Engineering H. H. Power ·······--·-··············-··················-···-·······-···············Petroleum Engineering B. E. Short ········-----·······-··············-······-··-···-···-·······-·····-······Mechanical Engineering R. W. Warner ...................................................................... Electrical Engineering Hugo Leipziger ·······-··--··-············································-······-···················Architecture Luis H. Bartlett ··-·······-··-······--·····················-·-··········-·····Mechanical Test Engineer Leland Antes .............................................................................. Research Assistant G. A. Parkinson ·········-·-······---················--··············-······Assistant Testing Engineer TABLE OF SYMBOLS D C a = ( p ) o.s= correlating factor for pressure drop for orifice baffles. Do-Dt Aa =free or net area of flow between baffles along tubes in exchanger in orifice baffles or along tubes of bundles without baffles, sq. ft. (See Fig. 7.) AA =free or net area of annular ring of disk-and-doughnut baffles, sq. ft. (See Fig. 7.) Ab =free or net area at baffle of half-moon baffles, sq. ft. (See Fig. 7.) AH =free or net area of hole of disk-and-doughnut baffles, sq. ft. (See Fig. 7.) Am =maximum area between tube rows perpendicular to fluid path be­ tween baffles of half-moon baffles, sq. ft. (See Fig. 7.) Arna =maximum area between tube rows perpendicular to fluid path be­ tween baffles of disk-and-doughnut baffles, sq. ft. (See Fig. 7.) A 0 =total net area of annular orifices in baffles of orifice baffles, sq. ft. (See Fig. 7.) AP =minimum area between tubes perpendicular to fluid path for half­ moon baffles, sq. ft. (See Fig. 7.) Aa =minimum area between tubes perpendicular to fluid path for disk­ and-doughnut baffles, sq. ft. (See Fig. 7.) Bh = baffle height, ft., from edge of shell to baffle edge around which fluid flows. =specific heat of fluid, B.t.u. per lb. deg. F. CA =head loss coefficient for annular ring of disk-and-doughnut baffles. Cb =head loss coefficient for orifice of half-moon baffles. CH =head loss coefficient for hole of disk-and-doughnut baffles. 0 = head loss coefficient for orifice of orifice baffles. C0 1 =head loss coefficient for small orifice of "half-orifice" baffles. C02 =head loss coefficient for large orifice of "half-orifice" baffles. cp =head loss coefficient for flow perpendicular to tubes of half-moon baffles. Ca =head loss coefficient for flow perpendicular to tubes of disk-and-dough­nut baffles. 0 = diameter of orifice of orifice baffles, ft. D. =inside diameter of shell of exchanger, ft. Dt =outside diameter of tube of exchanger, ft. g =acceleration due to gravitational force; taken as 32.2 ft. per sec.2 • Ga =mass velocity parallel to tubes of tube bundles without baffles and between baffles of orifice baffled bundles, lb. per hr. sq. ft. (See Fig. 7.) GA =mass velocity through net area of annular ring of disk-and-doughnut baffles, lb. per hr. sq. ft. Gb =mass velocity through net opening at baffle of half-moon baffles, lb. per hr. sq. ft. The University of Texas Publication GH = mass velocity through net opening of hole in doughnut baffles, lb. per hr. sq. ft. G Gm =mass velocity through maximum area perpendicular to tubes, half­moon or disk-and-doughnut baffles, lb. per hr. sq. ft. (See Fig. 7.) 0 =mass velocity through orifices of orifice baffles, lb. per hr. sq. ft. (See Fig. 7.) GP =mass velocity through minimum area perpendicular to tubes of half­moon baffles, lb. per hr. sq. ft. (See Fig. 7.) GR =mass velocity through minimum area perpendicular to tubes of disk­ and-doughnut baffles, lb. per hr. sq. ft. (See Fig. 7.) Gav =average velocity for each particular baffle type, lb. per hr. sq. ft. h = film coefficient on outside surface of tubes, B.t.u. per hr. sq. ft. deg. F. 6H = head loss per repeating section of exchanger, ft. lb. per lb. 6 Ht =total head loss across exchanger, ft. lb. per lb. k or k. =thermal conductivity of shell fluid at average fluid temperature, B.t.u. ft. per hr. sq. ft. deg. F. p. or /Ls =absolute viscosity of shell fluid at average fluid temperature, lb. per hr. ft. n = number of tube rows between baffle edges perpendicular to path of fluid. N =number of baffles in exchanger. NA =number of disk baffles in exchanger with disk-and-doughnut baffles. NH =number of doughnut baffles in exchanger with disk-and-doughnut baffles. P =tube pitch, center to center of tubes, ft. Q. =heat given up by shell fluid, B.t.u. per hr. S = baffle spacing, ft. U =overall transfer coefficient, B.t.u. per hr. sq. ft. deg. F. VA =fluid velocity through free area of annular ring in disk-and-doughnut baffles, ft. per sec. vb =fluid velocity through net orifice opening of half-moon baffles, ft. per sec. VH = fluid velocity through net opening of hole in doughnut baffle, ft. per sec. Vo = fluid velocity through annular shaped orifices of orifice baffles, ft. per sec. Vo=fluid velocity through small orifice of "half-orifice" baffles, ft. per sec. 1 Vo2 =fluid velocity through large orifice of "half-orifice" baffles, ft. per sec. VP = fluid velocity perpendicular to tubes through minimum area between tubes for half-moon baffles, ft. per sec. VR = fluid velocity perpendicular to tubes through minimum area between tubes for disk-and-doughnut baffles, ft. per sec. W. =weight of fluid flowing through shell, lb. per hr. =clearance between tubes, perpendicular to path of flow (P-Dt), ft. y =total distance across shell between tube rows, ft. PREFACE AND INTRODUCTION This bulletin is a revision of Bulletin No. 3819, published by the Bureau of Engineering Research of the College of Engineering of The University of Texas in 1938, the printed supply of which was exhausted early in 1942. There have been so many requests for Bulletin 3819 by companies and indi­viduals engaged in War Work that the Bureau of Engineering Research con­sidered it desirable to have more copies printed but the cost of reprinting was so high in comparison with the cost for a new publication of the same size that it was found desirable to make a revision before re-issuing the material. The data on which the analyses and discussions were based have been such a vital part of the utility of the material that the bulletin form of publication has been retained. In this revision of Bulletin 3819, an effort has been made to simplify the correlation procedures which were used by the writer in previous analyses of this material. Although the present analysis is largely empirical, it is not empirical to the extent that the previous correlations have been. Initially, in this revision, the resistance of the tube wall and tube side (inside of tube) resistances were obtained by means of the Wilson plotting method instead of by means of dimensionally arranged equations with empirical coefficients and exponents which were employed in Bulletin 3819. As has been previously pointed out, the normal equations for flow inside of tubes for Reynolds numbers greater than 6,000 to 8,000 gave results that were not reasonable and the writer had resorted to an empirical scheme of alteration which was open to questioning even though the results were close to those obtained by the Wilson method. The Wilson method had been applied to a portion of the data in 1935 and 1936, in which the tube fluid rate was varied for the purpose of establishing a relation for the tube side coefficients for this case, but the results were not satisfactory. The cause of this discrepancy cannot be explained but the major portion of the experimental work was carried out with a fixed tube fluid rate in the transition region and it is possible that this caused the difference. The second major difference in this revision from previous analyses is the average or effective velocity for the shell side fluid that was used. In this case, a direct average of the flow rates has been used, whereas, in previous analyses, an empirically weighted average of the local flow rates was used. Although, in most cases, the empirically weighted average gave better correlations than is now obtained, simplicity has been gained without a great sacrifice in close­ness of correlation and the criticism of factors being included in the weighting that should not affect the velocity should not now occur. The criticism that has been made in this connection is that one should be able to design a unit length of an exchanger and establish the transfer rate and then fix the length to suit the total load. In the present case, the local flow rates at all sections of each exchanger has not been used in the averaging because this is almost impossible but by a compromise between the use of specific rates readily The University of Texas Publication determined and an empirical scheme, the approach to the true average is more easily obtained. The third major difference between this revision and previous analyses is in the correlation of the pressure drop. For the present analysis, it was assumed that each exchanger was made up of a series of orifices, at the baffles and between the tubes, rather than to assume that the flow passage was a pipe y2 with varying roughness conditions. In doing this the coefficient of -was de­ 2g termined which would give the loss in head for each restriction. An assump­tion was made in some cases to simplify the calculation of the coefficients and this assumption was made in spite of a sacrifice in accuracy. ACKNOWLEDGMENTS The writer wishes to acknowledge the assistance in the form of suggestions and critical comments from many people that have been utilized in the re­working of the material from Bulletin 3819. In particular he has attempted to utilize the criticisms and comments of Mr. R. A. Bowman of Westinghouse Electric and Manufacturing Company, Mr. R. H. Norris of the General Elec­tric Company, Professor W. H . McAdams of Massachusetts Institute of Technology, Professor A. P. Colburn of the University of Delaware, Dr. Max Jacob of the Illinois Institute of Technology, and Professor George Hawkins of Purdue University, and has utilized a timely suggestion of Dr. A. C. Mueller of E. I. du Pont de Nemours Company, who has been working with this data during the last several months. The writer also wishes to acknowledge the assistance of Mr. Charles K. Leeper in computation and drawing work, and the Bureau of Engineering Research and the College of Engineering of The University of Texas in funds for assistance and printing. SUMMARY The material in this bulletin presents in both a graphical and analytical manner the results of a series of experiments with water and several grades of oil being cooled in a shell-and-tube heat exchanger. The heat exchanger was first used without baffles or turbulence promoters, then with half-moon (cross-flow or cut-out) type, then orifice type, and finally disk-and-doughnut type baffles. Both the heat transfer coefficients for the outside of the tubes in the bundles and the pressure drop on this same side are treated. An average velocity is used that consists of an arithmetic averaging of specific local flow rates along and across the tube bundles for the half-moon and disk­and-doughnut baffled bundles and a weighted average for the orifice baffle bundles that is empirically obtained so as to approach the flow conditions usually found on the discharge side of orifices. A comparison is shown, where data were available, with exchangers other than the experimental unit. In order to make such a comparison, use was made of data supplied by the Westinghouse Electric and Manufacturing Com­pany (R. A. Bowman), the Foster-Wheeler Corporation (E. N. Sieder), Ross Heater and Manufacturing Company (J. W. Gudgel), and Ingersoll-Rand Company (G. G. Riddle). These data were for oil on the shell side in all cases except those of Ingersoll-Rrand Company which were for air. A com­parison is also made with the results of others on flow along and across single pipes as well as across banks of pipes. The results are also compared with Colburn's equation and with Grimison's work. The pressure drop relations given present, graphically, coefficients for the velocity head at the principal points of restriction in the flow path so that the total head loss for a repeating section is given by an equation of the general type, The effect on the pressure drop of cooling the fluid during flow is, as has been done previously, shown as a function of Prandtl's number. OBJECT This experimental study was made to determine the possibility of establish­ing a relation that would permit both the film coefficient of heat transfer and the pressure drop to be calculated for a particular heat exchanger irrespective of the type, size and spacing of the baffles used, or of the size and spacing of the tubes in the bundle, or of the fluid used. SCOPE This paper covers the results of experimental work that was done on a shell­and-tube heat type exchanger in which three different forms of baffles (turbu­lence promoters) were used and, also, in which the spacing of these baffles and the size and spacing of the tubes were varied. The fluid used on the inside of the tubes as the coolant was water, while water and three different grades of oil were used on the shell side. In case of the half-moon baffles, Table I shows the different arrangements (tube sizes, tube spacing, and baffle spacing) that were used: TABLE I HALF-MOON BAFFLES Baffie Spacing Tube Diameter Tube Pitch % (inches) 11 0.d. %" 2.33, 3.01, 4.24, 7.11, 21.44 %"o.d. 11/16" 2.33, 3.01, 4.24, 7.11, 21.44 %" o. d. 19/32" 2.33, 3.01, 4.24, 8.11, 21.44 %" 0 . d. 11/16" 2.33, 4.24, 21.44 1h"o. d. 25/32" 2.33, 4.24, 21.44 % 11 0. d. 1" 2.33, 4.24, 21.44 %" 0. d. 1 3/32" 2.33, 3.01, 4.24, 7.11, 21.44 % 11 % 0.d. %" 2.33, 4.24, 21.44 11 0. d. %" 2.33, 3.01, 4.24, 7.11, 21.44 % 11 0.d. 11/16" 2.33, 4.24, 21.44 while in the case of the orifice baffles, Table II shows the different arrangements that were used: TABLE II ORIFICE BAFFLES Baffie Spacing Tube Dia. Tube Pitch Orifice Dia. (inches) % 11 0.d. 11/16" 7/16" 2.33, 4.24, 21.44 1h"o. d. 25/32" 17/32" 2.33, 3.01, 4.23, 7.11, 21.44 1h"o. d. 25/32" 9/16" 2.33, 4.24, 21.44 1h"o. d. 25/32" %" 2.33, 4.24, 21.44 %" o. d. 1 3/32" 9/16" 2.33, 4.24, 21.44 % 11 0.d. 11/16" 11/16" 2.33, 4.24, 21.44 while for the disk-and-doughnut baffles Table III shows the variation in con­struction of the unit; and for the bundles without baffles Table IV shows the arrangements: Heat Transfer and Pressure Drop in Heat Exchangers TABLE III DISK-AND-DOUGHNUT BAFFLES Diameter Diameter Bame Spacing Tube Dia. Tube Pitch of Disk of Hole (inches) %"o.d. 11/16" 4.5" 4.0" 2.33, 4.24, 21.44 %" o. d. 25/32" 4.5" 4.0" 2.33, 4.24, 7.11, 21.44 112" 0 . d. 25/32" 4.95" 3.5" 2.33, 4.24, 21.44 1h"o. d. 25/32" 5.5" 2.5" 2.33, 4.24, 21.44 112" 0. d. 1 3/32" 4.5" 4.0" 2.33, 4.24, 21.44 %"o.d. 11/ 16" 4.5" 4.0" 2.33, 4.24, 21 .44 TABLE IV NO BAFFLES Tube Dia. Tube Pitch %"o. d. 1h" %"o.d. 11/16" 1h"o. d. 19/32" 112" o. d. 25/32" 112" 0. d. 1 3/32" %"o. d. %" For practically all of these investigations the rate of tube fluid was main­tained at 2 ft. per sec. while the shell fluid was varied from a minimum of 2,000 lb. per hour to 45,000 lb. per hour. The total range in Reynold's number was approximately 10,000 fold and, in Prandtl's number, approxi­mately 3 to 2,000. APPARATUS AND EXPERIMENTAL PROCEDURE The heat exchanger used in this series of investigations consisted, as shown by Fig. 1, of a 6-inch steel pipe shell with inlet and outlet for the shell fluid placed on the top side near each end. The tube plate on one end was attached to the shell flange and then the "water box" placed over this, while, on the other end, the tube plate was attached to a "floating water box" which had an inlet connection extending through a stuffing box in the shell end-housing to the outside. The tube bundles that were used were made of No. 18 B.W.G. brass tubes, 5 ft. long, attached to % inch thick brass plates at each end. The holes in the tube plates were drilled 1/ 64 inch larger in diameter than the outside diameter of the tubes and, in assembling, the tubes extended Ys inch beyond the inner (water box side) face of the plates and were soldered to these plates. The baffles were made from 1/ 16 inch thick brass plate. These baffles were cut from the flat plate to a size slightly in excess of the inside diameter of the exchanger shell and then the tube holes were drilled before the baffles were fitted to the shell. For the half-moon and disk-and-doughnut baffles, the tube holes were drilled 1/ 64 inch in diameter larger than the tubes with which they were to be used, whereas, the tube holes for the orifice baffles were drilled to a size shown by Table II for each particular tube bundle. After the tube holes had been drilled in the circular plates that were to be used for half-moon baffles, a portion was cut off along a horizontal line % inch above or below the center line, depending on whether it was desired to have ...... N> I ,, 4'-0! 4 211 PIPE 2· PIPE ~ O' ..... .... ~ .... c ~ SECT. AT A-A Fm. 1. Section through Heat Exchanger with Half-Moon Baffies. Heat Transfer and Pressure Drop in Heat Exchangers the fluid flow under or over the baffle. In the case of the disk-and-doughnut baffles, the outer portion was cut off so as to leave a disk of the desired size for those plates from which the disks were made, and the inner portion cut out so as to leave an annular shaped plate of the desired size for those plates from which the "doughnuts" were made. Fig. 2 shows the dimensions of all of these baffles as well as showing the tube pattern. After the baffles had been cut to the desired shape, they were assembled as a group (19 for each particular tube size and spacing) and filed so as to allow them to be forced through the shell. Then after a group of tubes has been assembled with 19 baffles and the tubes had been soldered to the end plates, the baffles were fitted into the shell in such a manner, that the assembled bundle could be drawn in or out of the shell with very slight effort. The initial and final baffles were always at the same points relative to the shell inlet and exit connections and the distance between these end baffles was 43 inches and all intermediate baffles were evenly distributed within this distance. All baffles were held at a particular location on the tube bundle by "tacking" the baffles to the tubes with solder at three or four uniformly dis­tributed points around each baffle. In changing the arrangement of a bundle so that it would have less than 19 active baffles, the solder holding each baffle to the tubes was removed and the excess baffles moved to the end zones next to the tube plates. The remaining baffles were then distributed within the 43-inch space, with the initial and final baffles being located in the same position with respect to the inlet and exit shell connections as before. The inactive baffles in the end zones were "tacked" to keep them from moving toward the active baffles. Fig. 1 shows a tube bundle with 11 half-moon baffles in place with 8 inactive baffles in the end zones. Preliminary investigations showed that the overall transfer coefficient varied with time and a weak solution of hydrochloric acid was used as a bath for the tube bundles in order to have the same degree of cleanliness for each series of tests. Fig. 3 shows the effects of the fouling and cleaning. Weighing tanks and calibrated platform scales were used to determine the rates of flow of the liquids, the procedure being to note the time required for a particular weight of tube or shell fluid to flow through the unit. Mercurial thermometers in mercury-filled, steel wells were used to determine the inlet and exit temperatures in each case, and a mercury-filled U-tube manometer was used for the pressure drop determination. For all tests where the shell fluid was water, direct connection was made from the manometer to the "piezometer manifold"; but for the tests with oil, glass reservoirs were placed between the manometer and the "piezometer manifold" and oil was allowed to extend to the middle of the reservoirs with water occupying the lower half of each reservoir and the copper tubing which connected them to the manom­eter. The size of the reservoirs was such that the change in elevation of the oil-water separation level with manometer deflection was negligible. The initial temperature of the shell fluid entering the exchanger was main­tained at approximately 140 deg. F. and the entering tube fluid temperature ,_. ti::.. ,.. 2.5" ·at-T&P f t-f§eP e-t 11€,P ft -;')E p Et -3E p Et-3e_ P e-t-~p rt-~~..p D1SK-A ND-DOUGHNUT B A FFLES ,t-:;.rz:.e. ~"Dia Orihc.e ~"oia.Or\hc.t! ORIFICE. ElAFFLE.~ ~ ~rze_. FIG. 2. Sizes and Types of Baffles and Sizes and Arrangements of Tubes as Used in the Tests. 11" I" 11" I" -16 p e:t -16p ~t .. J"p H ALF-MOON BAFFLE."1 S c..ALE. -~ 5 1£E ~OTE All holf-rnoon. ba.~fle~ a.re ;,.88.. fr-om tla.t ed.qe oppo~i t'e !>ide n1 co.5 v.r-ed. o.lon~ 4. o S-Lh': c.1rc...l e.J 4.0"Dla. Hole 4.0" Oto..Hole c.5" Ola.. Hole 4.0' Dia..Hole 4.5" Ola.Disk 3.S"Dla. Hole 5.5" Dia.Disk Y II" I'' 3" 5" I " , .. c.s" ,.. C..5" I C.5" - gt -Tb p. {i' DlCl . Or-~ S ic.e 5" 3" 5" 1" ""':! at-4 P 5t-\l(,P ;;:s­ ~ No•e ln o.ll ca'.)ES the :5haded po.rlj [ ~ repre5enb the ba ffle at: that se:c.tion-J ~­ ;i ~ -~ ~ 0 ~ ~ ~ lt -I 3z. p S" I" et -li6P ~ aOio... OriHc...c ~ .... .... <:':I ~ C)· ~ 450 400 350 300 eso ZDO ~ i ~ "1 [ ~ ~ ~ ~ ~ ~ t::l "1 ~ ~· ::t:: ~ t:i ..... t:t.l ~ ~ ~ ~ ~ ~ ...... Ol ,.... 0) 0.40 0.38 u.: o.~6 0 )... I J-: t lL o.~4 > . -(J ~ \() \,) I 0.~£! ::> . o~ "Z 0 Ql \I..)~ ·~ t0.054 ·~I &.. :s Ol r lJ Qj0.08C. ~ 0.080 "":! ~ ~ ~ ~· ~ ~ -~ ~ c ~ ~ ~ ~ ~ O" ..... ... ~ .,... C)• ~ ::i:: ~ l ~ c ~ l.&..: • 15 I ~ w ~ J· ~ ~ Clo ~10 Clo Ci ~ ~ ~ 8 ~ ~ "i ~ ~­ ~ 10 30 40 so Go e.o 100 cOO 300 500 1000 ~000 ::i:: 1.0 1.5 3.0 ...-(Seo.le ~or Wo.ter:) ~ ~ .,.... ~ <:'; .FIG. 5. Viscosity Variation with Temperature for Water and the Three Oils that Were Used. ~ <:t" ~ (Cl ~ ~ ~ -::i The University of Texas Publication remained approximately constant for each series. The tube fluid inlet tempera­ture was around 60 deg. F. for the earlier series but had increased to about 80 deg. F. before the final tests were made. The rate of flow of the shell fluid was varied from a minimum of 2,000 to 3,000 lb. per hour to a maximum of 35,000 to 45,000 lb. per hour. The mini­mum rate was governed by the stability of pumping and heating conditions while the maximum was governed by the range of the pressure drop manom­eter in some cases (the manometer had a range of 40 inches) and by accurate weighing ranges in other cases. Sufficient intermediate tests were made be­tween these extreme limits to permit definite trends of results to be ascer­tained. Plots of the overall trans£ er coefficients against rate of flow and pressure drop were used as a means of control on the experimental procedure. The heat absorbed by the tube fluid was balanced against the heat given up by the shell fluid for each set of data recorded and this was used as a verification of the fluid temperature determinations. As the shell was not insulated, the heat absorbed was usually ¥2 to 3 per cent less than that given up. The viscosity of each oil that was used was determined at several tempera­tures by means of a Saybolt Universal Viscosimeter and the viscosity of the water was based on the values given in the International Critical Tables. The thermal conductivities of the water and of the oils were based on the values given by McAdams.sa• The curves of these data are shown by Figs. 4 and 5. *Numbers refer to bibliography at end of text of Bulletin. DISCUSSION AND CORRELATION OF RESULTS Heat Transfer Coefficients The experimental work in this connection permitted only over-all transfer coefficients to be measured directly but the range of shell fluids rates was such that, with the constant tube fluid rate, the Wilson graphical method was used to determine the tube side and tube wall resistances. An example of this /J.s )0.6 scheme of plotting is shown by Fig. 6. In this plotting, the relation ( --DtW s 1 06 was used instead of (--) • so as to allow for the slight variation in fluid w. viscosity since the mean temperature of the shell fluid changed appreciably in going from the low rates of fl.ow to the highest ones. The tube fluid rates were reasonably constant and so were the mean temperatures of this tube fluid for all rates of shell fluid, so the tube side resistance was assumed to remain fixed throughout each tube bundle series. Also, greater consistency was obtained by working with each tube bundle as a unit and using the mean tube side resistance for all runs (i.e., all baffle spacings). The correlation of the shell side heat transfer coefficients was made with an average of specific local velocities for each baffle type. That is, for the half­ moon type baffles Gb+Gp+GmGav=-----­3 (1) for the disk-and-doughnut type baffles GA+ GH + 2 GR +2 Gm Gav=--------­6 (2) for the orifice type baffles 4Do (Go+ Ga)Gav=-­s 2 S-4Do+ Ga s (3) and for the tube bundles without baffles (4) In these equations Gb, Gp, Gm, GA, GH, G0 , and Ga represent the weight rate of flow at particular sections in the path of flow. For the case of the half-moon w baffles, Gb is the rate of flow, -, in the region beneath or above the baffles Ab w (Fig. 7), Gp is the rate of fl.ow, -, in the minimum area region in the flow AP *See table of symbols on first page of bulletin. t..:> 0 ~ ~ ~ ~ ~· 'i ~ c;,, ~ ~ c ....... 1-3 ~ ~ ~ -~ O' .... ~ .,... o· ~ r~f'r6 Fm. 6. Wilson Plot for %" D, -11 /16" P, Half-Moon Bailed Bundles. Heat Transfer and Pressure Drop in Heat Exchangers w across the tubes between each pair of baffles, and Gm is the rate of flow, -,Am in the maximum area region in the flow across the tubes between each pair of baffles (Fig. 7). For the disk-and-doughnut baffles, Ga is the rate of flow, w -, through the free annular space between the edge of the disk and the AA w shell, GH is the rate of flow,-, through the free area of the hole, GR is the AH w rate of flow, -, in a radial direction through the minimum area regionAR w between each pair of baffles (Fig. 7), and Gm is the rate of flow, --, in a AmR radial direction through the maximum area region between each pair of w baffles. For the orifice baffles, G0 is the rate of flow, -, through the orifices Ao w in each baffle, while Ga is the rate of flow,-, along the tubes in the region Aa between the baffles (Fig. 7). Ga is obtained for the bundles without baffles in the same manner as Ga for the orifice baffled bundles, Aa is the cross-sectional area of the shell (per pass) minus the gross cross-sectional area of the tubes (per pass). In the determination of these average rates of flow, it was assumed, in the case of the half-moon baffles, that the fluid passed through the baffle opening with the mass velocity Gb and then alternately became GP and Gm, respectively, as it passed through the minimum area regions and maximum area regions in flowing across the tubes. The maximum area regions would be at the points across the path of flow where tubes did not reduce the area, as indicated by distances, y, of Fig. 7. A similar assumption was made for the disk-and-dough­nut baffled bundles except, in this case, a repeating section would be from one doughnut baffle to the next so that the rates GR and Gm would each appear twice in the averaging. For the orifice baffled bundles it was assumed that it required 4 pipe diameters following the orifice for the fluid velocity to drop back to the velocity in the region between the baffles. The pipe diameter, in this case, was taken to be that of the orifice diameter since this seemed to be the governing dimension and since no data were found for annular orifices that covered the velocity variation or pressure recovery. It was also assumed, in this connection, that the fluid velocity dropped linearly from that which it had in the orifice to that which it possessed in the region between the baffles. So the average velocity would be made up of the average in the region where the velocity was decreasing and that where it was at the constant lower value. For the bundles without baffles, the velocity is simply that for flow along the tubes in the shell. The University of Texas Publication A v AA0A v vwv @()@00 .·.·:· .:·..· .:·::. .. e· o· ®®·:. .:: . ~ \;;,;;/ Fn?e/lrea OrificeQaf:F/es • bE>-/'w ,,,._,,,,.,,,,,. xx ./ .. ~ X" /."'/A J( IC '0 0 90 +~~~"x" 80 +/".'.y~ " ~1~ 7'0 0 " 'It ~.a " "'" 6­ i> !~ x/ ;0' "x 51... ++ ~ ~ x "x 40 +~+ ,,."" / "J( ,.,.,. ""' I 30--;,+ /)I. I 10~ 4x1oj 104 I 4"104, zo FIG. 9. Effect of Tube Spacing on Nusselt Number. similar to that used in previous correlations. For this correlation, the factor is shown to be P-Dt )o.4 ( --Dt p The effect of the Prandtl number on the transfer rate is shown graphically by Fig. 10 where the Nusselt number is plotted as a function of Reynolds number for three different oils and for water, the total range of the Prandtl number for this particular tube bundle being from 3.2 to 1,700. By assuming that the relation for the case with water can be extended to a Reynolds num­ber of 200, the effect of the Prandtl's number is obtained as a simple expo­nential function with, in this case, an exponent of 1/s. An exponent of 0.32 was used in the previous correlations. Figs. 11, 12, and 13 show the experimental data plotted for the half-moon, disk-and-doughnut, and orifice and zero baffled bundles respectively with the data for the bundles with the baffle spacing greater than 20 times the devia­. tion from the central path of flow (bundles with 3 baffles for the writer's data) shown on the same plot with the orifice and zero baffled bundles. The ~ l ~ ~ '"'! @ ~ ~ ~ i:.:> i:.:> ~ '"'! ~ b '"'! ~ ~· ::t: ~ ~ .,... t'.tj ~ ("> ;;:t< ~ ;::s FIG. 10. Effect of Prandtl Number on Transfer Rate. ~ ~ '"'! i:.:> ~ N) CJ) 400 ~ ;;s­ ~ C::l ~ ~· ~ ~ 100 ~ ~ "'-3 ~ ~ ~ 40 "'t:l ~ O' ...... .... ~ ~ ..... ~· 10 10 2 4x/02 10 3 4..r/03 /04 4x/Q~ D-c Cbv ~ F1G. 11. Composite Plot of Heat Transfer Rate for Half-Moon Baffies. ::i:: a l (I> ~ ~ ~ (I> Cl> Cl> ~ (I> b c ~ 'ti ~­ ::i:: (I> ~ .,.... t.?;l H <:'> ;:s-o ~ (I> ~ ~ -:J Nl 00 ~ (::!" (1> ~ ~· (1> ~ ~ ~ c ......... ~ (1> ~ ~ -~ O' .... ~ ..... C)· ~ Heat Transfer and Pressure Drop in Heat Exchangers data supplied by Westinghouse E. & M. Co. (R. A. Bowman), Foster-Wheeler Corporation (E. N. Sieder), and Ross Heater and Mfg. Co. (J. W. Gudgel) for oil and Ingersoll-Rand Co. (G. G. Riddle) for air are shown on the half­moon and orifice baffle plots points marked W, F, R, and I, respectively. Three of the Ingersoll-Rand data points fall within the zone of the data for water while two of the points fall slightly below. The resultant equations for the mean lines of these plots are as follows: Half-moon baffles hDt -=1.28 (5) k Disk-and-Doughnut baffles hDt -=1.45 (6)k Orifice, etc. (7) Pressure Drop The pressure drop or head loss due to the flow of the fluid through the exchanger has been considered on the basis that the exchanger is made up of a series of orifices or devices where the fluid is caused to be alternately contracted and expanded or accelerated and decelerated. On this basis, the loss at each restriction or point of velocity change may be determined as a constant multiplied by the velocity head so that the total loss for a repeating section is given for each case as follows. For the half-moon baffles vb2 vp2 6 H=Cb-+nCp-(8)2g 2g for the disk-and-doughnut baffles vA2 vH2 vR2 6 H= CA-+ CH-+ 2nCR-(9)2g 2g 2g and for the ori {ice baffles Vo2 6H=Co-(10) 2g In equation 8, a repeating section would be represented by a length equal to the baffle spacing since the flow conditions at each baffle should be geometrically similar. The symbol n, in this equation, represents the number of rows of The University of Texas Publication tubes from the edge of one baffle to the edge of the next baffle. For the disk­and-doughnut baffle, a repeating section would be from one doughnut baffle to the next doughnut baffle or from one disk baffle to the next disk baffle. For convenience in computing the experimental data, Eq. 9 was written in the form vA2 vH2 vR2 6.Ht=NACA-+NHCH-+ (N + 1) CR-, 2g 2g 2g and a further assumption that CA = CH was made. For the orifice baffle, a repeating section would be from one baffle to the next, except in the case where alternate baffles have tube holes with an appreciable clearance between the hole in the baffle and the tube and the baffle in between has a tube hole only large enough for reasonable ease in assembling. Such a baffle type is referred to by some as a half-orifice type. For the half-orifice type, the head loss for each repeating section (2 baffles in this case) would be given by but V01 = V02 and, hence, C01 = C02 according to normal orifice flow relations. Hence, Eq. 10 would apply to this case as well as to the regular orifice baffle type. In the case of the half-moon and disk-and-doughnut baffled bundles, cp and CR, the coefficients for flow perpendicularly between the tubes, were assumed to be unaffected by the rate of flow. Since the passage between the tubes was more of a nozzle than was the passage through the restrictions at the baffle, it was considered that the friction loss for flow between the tubes would be less than for flow through the baffle restrictions. In the computation procedure, 2g6.Ht curves were plotted of versus Gb for the half-moon baffles and similarly NVb2 2g6.Ht ---versus GH for the disk-and-doughnut baffles. The vertical difference NH vH2 between points on the curves for different numbers of baffles, for a particular value of Gb (or GH for the disk-and-doughnut baffles), was the means for evaluating CP (or CR). Eq. 8 (or Eq. 9) was then used (using 6 Ht, the total head loss for the exchanger) in order to determine Cb (or CA and CH). CP and CR were found to vary with tube size and tube spacing. It was also indicated fairly definitely that the pressure loss was affected by the total deviation from the central flow path and since the total head loss for each repeating section has been considered as being made by restrictions in series, the turning effect has been made a part of CP. For the half-moon and disk-and­ doughnut baffles, CP and CR are given graphically by Fig. 14. The variation of Cb, CA and CH, and C0 with Reynolds number indicates that the loss is more of a frictional effect than a contraction and sudden expansion effect so that the resultant relations between Cb, CA and CH, and Co and Reynolds number are more nearly parallel in shape to the friction curves than to the Heat Transfer and Pressure Drop in Heat Exchangers 4 (~) 0./ o,z 0,4 ~ +I c I I I, (, y ~+ 1~1/' a v: a. 0 I II Q./ __ ..,6 ~"''-" -_.,, o. -~ - z,o 1.5 1.0 CR 0.6 o.~ 0;03 . 0.1 0 . .3 /.0 (~J(q} FIG. 14. Plot of cp and CR for Pressure Drop for Half-Moon and Disk-and-Doughnut Baffles. curves for orifice coefficients with Reynolds number. This is again indicated by the effect of cooling on the coefficients since, as is shown by Fig. 15, the coefficients are dependent upon the Prandtl number for a particular Reynolds number. For the half-moon baffles the Prandtl number function as used is Cp.)o.5 ( Cp.)o. (k ,for the disk-and-doughnut baffles it is k 11 ,and for the orifice baf­ fles it is (:)°·2 • The variation of Cb, CA, CH, and C0 with Reynold's and Prandtl's numbers is shown, respectively, by Fig. 16, 17, and 18. In Fig. 18, a is given by the expression The University of Texas Publication 0001 001 01 ·( c 0' ~-+++-t-++-+-+--+~~-H-1-H Heat Transfer and Pressure Drop in Heat Exchangers ,,, p Fluid Symbol I ,, H Waf,r ~N "" N " • 151 'II ... "' + • • "' + t • .-­ c • ~ • I c . <\o,! . N c ...,.~ • •~ • " ...,,~... . .... .~-~ .,.,, • "1 I l0 111til 4x/0 3 10 4 4 x /0 4 10 5 (-;?)(~:9 o. 6 Fm. 16. Plot of c. for Half-Moon Baffies. GENERAL COMPARISON Colburn's equation,1* using the maximum velocity for flow across the tube bank, does not make sufficient allowance for the variation in baffle spacing. The results from the Colburn equation for a particular half-moon baffled tube bundle (~" o.d. tube, 1 3/ 32" pitch) as compared with the results from Eq. 5 are as follows: Baffi e Spacing Colburn's Equation 2.33" 33% high 3.01" 29% high 4.24" 13% high 7.11" 6%low For the disk-and-doughnut baffles, Colburn's equation gives lower results than the writer's Equation 6. For the baffle spacing of 2.33", the results are about 5% lower for the same tube size and spacing given above and for a baffle spacing of 4.24", the results are 29% lower. With lower Reynold's numbers I" ~ " " " " ,S N 8 ,, ,, " ,, 16 ,, !1_,, " 16 N " -H­ # ;" " r: . " ,, a 0 1/ "B" " I" Wafer Oi I 'CJ" /~ " *Number refers to reference. I'he University of Texas Publication _.;!l_,, // N x-:!fr 4-.,..,,,. P-4.5 n.-40 ,q,-Wa1'er /N ~'' ...... .,._ T ,, -~ P-II " (f/f -p ; -# "' -H n -'1 -4.95 n-3,!J " ­ I N 0 -11 ,, -II I( -.5,5 "' 111-.2~..5A'1 -'1 e-" " -/,ffe. ".v -4.5''.,-4,0 H" -0// ~1 1 --II '' -N .H -,n " -" " -0// E ,11-" ,, -,., "' -,, ,, -,, ,. -Oil<::'"' o -" " -" " -·• " -" •• -Wa/lf'r _L,., I,, A -T ,, -/1ifi'" "' -,, ,,. -,, ,, ­ I A -,, "" -,,, II -•• ,, -,, ,, ­ 0/1 13"" FIG. 17. Plot of CA or CH for Disk-and-Doughnut Baftles. such as encountered with medium viscosity oils, the deviation in the two schemes are about the same. If Colburn's equation is applied to the orifice type baffles, even though it is not strictly applicable to such a case, the results are, for a particular example, 48% lower when based on the velocity of flow parallel to the tubes in the region between the orifices and 190% higher when based on the velocity through the orifice. Grimison's method2 for determining the heat transfer rate gives results that are 17% lower than those given by Eq. 5 for a tube bundle with half-moon baffles and with a tube diameter of ¥2" and an equilateral pitch of 1 3/32". Quoting McAdams3 for average values for flow across single tubes, the results given by Eq. 5 for half-moon baffled tube bundles are about 40 to 45% higher than for flow across single tubes. In the case of the drop in pressure across the exchanger, only the portion dealing with the flow across the tube bank can be satisfactorily considered. Heat Transfer and Pressure Drop in Heat Exchangers 36 The University of Texas Publication For this particular portion of the exchanger, if the same half-moon baffled tube bundle is used as an example as was used in the case of the heat transfer coefficients, the writer's results are about 64% greater than those given by Grimison's work. That is, by the writer's Eq. 8 v 2 ci.203) 2 /':::,. H = n Cp -= 2 X 0.92 = 0.0412 ft. lb./lb. fluid 2g 64.4 and by McAdams' transformation4 of Grimison's work (1.203) 2 /':::,. H = 4 X 0.0816 X 2 = 0.0147 ft. lb./lb., 64.4 0.11 ] as f"' = 0.23 + (9320) -0 · 15 = 0.0816 1.094 )l.OS [ ( ---1 0.5 When Eq. 8 was applied to the writer's data, the head loss resulting from the angular displacement of the fluid after passing through the baffle, as well as that before entering the baffle, was considered a part of the coefficient, CP. Hence, the values given by the second part of Eq. 8 for the loss of head in flowing across the tube bank should be higher than Grimison's values by the amount produced by 2 elbows, each equal to approximately 90°. When this same method of approach is applied to the data from the work of Stack,6 in which a 4" inside diameter shell was used with half-moon baffles with tube bundles of various tube sizes and spacings, good agreement is ob­tained. The average values of CP for several different baffle spacings for each of two different tube bundles which were compared falls within 17 and 30% of the values shown by Fig. 14, while the average value of Cb falls toward the bottom of the field of points of Fig. 16. Data for eccentric orifices and for annular orifices that would apply to the complex orifices involved in these exchangers have not been found in the lit­erature. The values generally cited are for those cases where the stream is reasonably straight in its flow with respect to the axis of the passage and where disturbances are at appreciable distances ahead of the orifice. In these cases, the disturbances are close to the orifices and the stream, in the case of the half-moon and disk-and-doughnut baffles, is turned as it enters the orifice. BIBLIOGRAPHY 1. "A Method of Correlating Forced Convection Heat Transfer Data and a Comparison with Fluid Friction," by A. P. Colburn, Trans. A.I.Ch.E., vol. 29, 1933, pp. 174-209. 2. "Correlation and Utilization of New Data on Flow Resistance and Heat Transfer for Cross-flow of Gases over Tube Banks," by E. D. Grimison, Trans. A.S.M.E., vol. 59, 1937, pp. 583-594. 3. "Heat Transmission," by W. H. McAdams, McGraw-Hill Book Co., Inc., New York, N.Y., 2d Ed. p. 229. 3a. Ibid., pp. 389, 390, and 407. 4. Ibid., p. 126. 5. "Heat Transfer and Pressure Drop in Exchangers," by Byron E. Short, The University of Texas Bulletin No. 3819, May, 1938. 6. "Effect of Diameter Spacing, etc., on Pressure Drop Around Tubes of Shell Type Heat Exchangers," by B. E. Short and T . F. Stack, Oil and Gas Journal, vol. 32, May 10, 1934 pp. 115-116, 118. 7. "Heat Transfer in a Commercial Exchanger," by B. E. Short and M . M. Heller, Bulletin No. 3128, The University of Texas, 1931. 8. "Heat Transfer Coefficients and Friction Factors for Heat Exchangers," by B. E. Short, Thesis, Cornell University, September, 1939; abstract published by Cornell University Press, 1939. 9. "Fluid Friction at Parallel and Right Angles to Tubes and Tube Bundles," by E. N. Sieder and N. A. Scott, Jr., A.S.M.E. unpublished papers, No. 83, 1932. 10. "Investigation of Heat Transfer Rates on the External Surface of Baffled Tube Banks," by R. A. Bowman, in "Heat Transfer," A.S.M.E. unpublished papers, No. 28, 1936, pp. 75-81. APPENDIX Additional Symbols tt = initial temp. of tube fluid, deg. F. 1 tt = final temp. of tube fluid, deg. F. 2 ts = initial temp. of shell fluid, deg. F 1 ts = final tanp. of shell fluid, deg. F. 2 ~p = pressure drop across shell, in. of hg. Wt =weight of tube fluid, lb. per hr. W9 =weight of shell fluid, lb. per hr. Qt =heat absorbed by tube fluid, B.t.u. per hr. =heat given up by shell fluid, B.t.u. per hr. Q9 em =log mean temp. diff., deg. F. U =overall transfer coefficient. B.t.u. per hr.­sq. ft.-deg. F. Heat Transfer and Pressure Drop in Heat Exchangers 39 DATA BAFFLES• HALF-MOO!t TUBE DIA.-3/1" TRANSFER AREA-48. la SIZE-3.92• HIGH TUBE PITCH· 1/2" SHELL FLUID· WATER * Stt first page of Appendix HO.OF TUBES-98 TUBE· FLUID-WATER for Syllbols. I RUN NUMBER * t;. \ \. t'2 b. p wt w. Qt Q. a,. u 19 BAFFLES 51 58.3 77.3 140.6 74.8 0.37 18,540 5,365 352.8 353.0 34.76 211 .0 52 58.2 85.3 140.7 86.0 0.88 18,380 9,220 498. 2 503.8 40.10 258.3 53 58.l 88.8 140,4 92.l 1.39 18,520 11,900 569.0 574.8 42.14 280.8 54 58.l 91.6 139.6 97.6 2,?2 18,?30 15,040 628.0 631.0 43.60 299.5 55 58.0 95,0 139.5 102.7 3.24 18,220 18,360 673.5 676.5 44.59 314.1 56 58.1 99.2 140.1 lOe.2 5.19 18,330 23,630 752.5 756.0 45.34 345.2 67 58.1 99.6 141.2 109.l 5.19 18,300 23,730 759.0 760,5 46.08 342.6 58 57.9 100.3 139.a 110.8 6.86 18,370 27,430 778.0 781.0 45.50 355.4 59 58.0 101.5 140.l 112.6 7.78 18,370 29 ,150 800.0 802.5 46.18 360.2 60 58.0 103.l 140.2 114.3 9.63 18,420 32,430 830,5 838 .0 46.00 375.4 61 58.0 104.5 140.6 117.0 11.67 18,540 36, 730 862.0 867.0 46.63 384.4 62 57.8 104.9 140,0 117.3 13.52 18,460 38,530 870,0 873.0 46.25 391.l 63 57.5 94.6 139.0 101.7 3.33 18,550 18,420 688.0 687 .5 44.31 322.8 219 60.l 96.4 139.6 102.4 3.06 18,530 18,280 673.5 680.0 42.73 327.8 220 60,l 101.., 139.4. 110.5 5.98 17,950 26,090 750.5 753.5 43.75 356.7 15 BAFFLES 228 58,9 80.9 138.8 80.3 0.28 15,720 5,900 345.2 345.0 36.70 195.6 229 58.8 78.5 139.0 77.9 0.28 18,540 5,970 365.0 364.6 35.90 211.4 230 58.9 81.0 138.7 81.7 0.'$7 19,130 7,410 423.5 423.0 37.60 234.2 231 59.0 86.7 139.7 89.9 0.70 18,850 10,420 522.8 519.0 41.00 265.1 232 59.0 86.8 139.8 90.0 0,70 18,620 10,480 518.5 522.0 41.06 262.7 233 59.2 91.2 139.4 96.9 1.20 18,150 13,610 581.0 579.0 42.80 282.3 234 59.4 95.3 140.8 102.9 1.90 18,240 17,320 655 .0 656.0 44.48 306.2 235 59,5 98.6 139.9 108.4 3.15 18,540 23, 120 725.0 727.6 45.00 335.0 236 59.5 101.5 139.5 112,8 4.91 18,370 28,950 771.5 774.0 45.22 354,8 237 59,5 103.4 139,6 115.5 6.51 18,330 33,520 804.0 809.0 45.46 367.8 238 59.5 104.9 140.2 117.8 7.92 18,370 37,350 834.5 838.5 45.80 378.8 239 59.5 100.2 140.4 119.7 9,63 18,330 41,460 856.5 860.0 46.00 387.1 11 BAFFLES 247 59.2 77.2 141.5 76.5 0.14 18,380 5,080 330.3 330.2 35.84 191.6 248 59,2 86.5 J.40,l 91.4 0,42 18,420 10,390 601.5 606.0 42.00 248.2 249 59.5 93.1 139.5 101,6 0,88 18,400 16,260 619.0 616.0 44.20 291.2 250 59.5 97,2 139.7 108.1 1.67 18,210 21,780 686.0 687.0 45.46 313.8 251 59.6 99.4 140.5 111.3 2.18 18,470 25,360 737.0 739.0 46.15 332,0 252 69.5 102.4 141.3 115.9 3.33 18,330 3l,CX30 787.0 788.0 47.20 346.8 253 59.3 105,2 141.8 119.8 4.91 18,390 38,370 844.0 845.0 47.58 368.8 254 59.0 105.4 140.4 120.9 6.39 18,520 44,090 859.0 858.0 47.17 378.8 7 BAFFLES 285 61,3 81.0 139.3 86.7 0.14 18,120 6,850 357.5 360.5 39,54 188.0 286 61.5 89.1 140.4 99,l 0.32 18,100 12,120 499.5 501.0 44.06 236.8 287 61.6 92.l 140.2 104.0 0.51 18,170 15,320 554,0 655,5 45.18 255.0 288 61.6 95.9 140.4 109.4 0.74 18,230 ro ,reo 625.0 620.0 46.10 282,0 289 61.5 98.0 140.8 112,3 1.11 18,340 23,610 670.0 674.0 46.70 298,3 290 61.5 99,7 140.5 115.0 1.48 18,160 27 ,330 004.0 697.0 46,90 307,7 291 61.5 102.1 141.0 118.4 2 .04 18,100 32,550 734.0 737.0 47.32 322.4 292 61.5 104.2 141.5 121.4 2.59 17,390 37,000 742.0 745.0 47.65 323. 8 293 61,5 105.0 140.5 122.3 3.33 17,670 42,280 769,0 770.5 47.06 339.8 3 BAFFLES 301 so.a 77.0 138.5 93.2 0.07 17,870 6,450 289.0 292.0 45.40 132.3 302 61.0 81.8 139.7 100.4 0.12 17,910 9,550 373.0 375.0 48.12 161.l 303 61.1 87.7 139.6 109,5 0.20 17,290 15,320 459.0 461.0 50,15 190,4 304 61.2 92.l 140.0 114.2 0.39 18,250 21,800 563,0 563,5 50.40 232.2 305 61.4 96.0 140.8 119.2 0.64 16,620 26,800 576.0 578.0 50.~ 235.0 306 61.2 95,3 141.0 118.7 0.54 17,360 26,680 an.a 593.0 51.42 239,0 307 61.l 95.3 138.9 118.9 o • .,6 18,720 32,230 641.0 643.5 50.35 264.8 308 61.2 96 .2 139.2 119,6 0.76 17,940 32,150 627.0 628,0 50.30 259.2 309 61,2 97.2 138.4 310 61,2 98.4 138.2 120.7 122.2 1.07 18,410 1.34 18,430 37,620 663.0 42,800 685.0 665.0 49.80 276.8 689,0 49.70 286,6 311 61.2 97.,4. 139.l 121.4 1.00 18,380 37,620 664.5 666.0 50.35 274.S 40 The University of Texas Publication DATA BAFFLES-HALF-MOOH SIZE-3.92• HIGH TUBE DIA.-3/8" TUBE PITCH-11/16" TRANSFER AREA-25.510 , SHELL FLUID-WATER • S•• first page of Appendix NO.OF TUBES-52 TUBE FLUID-WATER tor Sy•bol1 • Heat Transfer and Pressure Drop in Heat Exchangers DATA BAFFLES-HALF-MOON TUBE DIA.-1/ Z" TRANSFER AREA-43.1e0 , SIZE-3.92• HIGH TUBE PITCH-19/32" SHELL FLUID-WATER * S•• first page or Appendix NO. OF TUBES-66 TUBE FLUID-WATER for Sy11bols. The University of Texas Publication DATA BAFFLES-HA~F-MOON TUBE DIA.-1/2" TRANSFER AREA· 31.40 , SIZE-3.92 HIGH TUBE PITCH-11/16" SHELL FLUID-WATER *See first page of Appendix for Symbols. NO OF TUBES-48 TUBE FLUID-WATER t * RUN tt2 t,2 w, e. ttl b. p '1 u I\ ~~ NUl1BER 19 BAFFLES 156 58.9 73.6 138.4 79.3 0.28 38.45 231.l 18,990 4,765 279.0 280.8 156 59.0 78.9 138.3 90.5 0.70 274.8 19 070 8,000 380.0 382.2 44.05 157 59.l 84.4 140.l 100,8 317.5 1.48 482.0 488.0 48.35 19:100 12,440158 Ee.2 139,4 86.l 106.l 49.46 331.3 3.15 19 130 15,060 514.5 517.0 159 Ee.3 89 .9 139.8 589,5111.2 4.17 50.90 367.3 587.0 19:180 160 59.3 92.5 140.5 115.5 5.74 374.8 18,460 ~·~8 612.0 612.0 52.00 161 59.2 92.6 5,74 142.4 116.0 383.2 19,160 640.0 642.8 63.20 24:400162 59.l 93.2 139.9 117.6 400.8 8.36 19,370 660.0 52.45 661.5 163 59.1 140,794.8 119.7 9.81 ~·~8 402.6 18,760 670.0 670.0 63.00 164 59.1 $,5 139.9 121.3 410,812.50 18,680 52,80681.0 677.0 36~370 165 59.0 95.4 15,65138.7 121.6 19 120 40 ffiO 52,35 423.8 696.5 698.5 11 BAFFLES 470 61.5 140,373.0 80.2 0.05 18,980 218,3 183.7 3,620 217.5 37 .ffi 471 61.5 78,073.4 140.3 0.05 18,850 3,610 224.8 225.0 36.05 198.6 472 61,6 78.2 138.9 91.5 0.19 18,760 6,610 312.0 313.2 43.58 228.0 473 83,1 140.3 101.0 61.8 0.37 18 ffiO 10 33:> 401.0 268.2 405.3 47.60 474 62.0 87.5 109.3 0.83 18:950 483,0 140.~ 15;668 5g.oo ~.7 475 62.0 90.5 139. 114.4 1.53 18,390 21 3 524.0 t~:8 5 .45 .8 476 62.1 92.6 139 .8 118.l 18,680 2.27 51.50 25:320 570.5 572.2 ~.o 477 62.0 93,7 140.2 120.l .53.10 614.5 615.5 52.15 i§;~8 478 95,962.1 141.2 123.l 4.17 ~·M8 642.0 644.0 52.92 386.5 479 62.0 140.7 124.4 40'45096.8 5.33 18 850 656.0 659.0 52.65 397.8 3 BAFF ''° 518 62,0 73.4 140.8 94.9 18 720 212,84 640 212.8 48.13 140.8 519 62.0 73,l 140.6 94.6 48,04­19:020 4:700 212.2 216.2 140.7 0,()4. 520 62.2 78.0 140.6 105.3 19,130 301.7 303.0 52.25 183.9 521 0,17 J·i~ 353,662.5 81.5 139.2 112.0 18,620 353.7 53.50 210.6 522 62.5 B 3,640 7,750 10,600 10,825 15,360 18,070 21,240 24,900 24,930 29,500 201.0 196.5 311.0 358,0 353.6 411,8 438,5 462,0 484.0 493.0 501,0 200,0 200.4 310,8 358,6 357,0 410.0 438.0 451,5 482.0 492.0 502,5 35,70 35.97 43.26 44.44 45.23 47,30 47.40 47.48 48,07 49,10 48.82 215.2 208,9 275.0 308.0 299.0 332.B 363.7 364.0 385.0 384.0 392.3 659 660 661 662 663 664 665 666 66.0 66.3 66,5 66.5 66.7 66.7 66.7 66.7 75,6 es.5 89.B 91.B 94.2 95.B 97.0 97.9 139.6 138.3 138.6 138.5 139.l 139,5 139.6 139.B 83.4 ).03.4 111.l 114.B 118.7 121.2 123.0 124.3 0.23 1.25 2.87 4.40 7.13 10.00 13.33 16.48 15,650 15,650 15,630 15,620 15,700 15,700 15,710 15,690 2,675 8,680 13,450 16,650 21,280 25,030 28,750 31,820 149.9 301,0 364.3 395.2 431.7 456,0 475.5 490,0 150.5 303,0 369.5 395.0 432.6 457.5 478,0 492.5 35,74 44.SO 46.66 47.48 48.35 48.82 49.15 49,26 160,4 258.7 298.6 318.4 341,3 357 , 0 370.0 380.3 11 BAFFLES 3 BAFFLES 667 668 669 670 671 672 673 674 66.2 66.5 66.7 66.B 66.B 66.B 66,8 66.B 75.2 82.l 86.9 89.7 91.l 93.2 94.5 95.5 137.5 137.7 138.6 139.7 138.9 139.7 l39 .6 139.7 95.4 110.4 118.3 122,5 124.0 126.l 127,6 128.6 0,09 0.46 l.20 2.13 3.15 4.54 6.67 B.52 15,690 15,696 15,700 15,710 15,650 15,675 15,690 15,710 3,370 9,000 15,600 21,000 25,390 30,420 36,360 41,100 141.2 244.B 316,5 360,3 380.6 413,B 434.6 451.0 141.7 246.2 316.0 360.0 379.0 413.6 436,4 453.7 43.72 49,62 51.63 52.78 52.40 52.70 52,58 52.50 123.4 188.6 234.3 261.0 277.7 300.2 316.0 328.4 DATA BAFFLES-ORIFICE TUBE DIA.-1/2" TRANSFER AREA-26.1'c• TUBE PITCH-25/32" SHELL FLUID· WATER SI ZE-5/8 • DI.A. HOLE HO.OF TUBES-40 TUBE FLUID-WATER RUN NUl'IBER tti t t2 t •1 t •2 "'p wt w. ~ Q. e• u 19 BAFFLES 686 687 688 689 690 691 692 003 004 695 69,0 69.5 6'9 ,5 00.7 69.9 70.2 70.2 70.2 70.3 70,4 81.3 87.4 87.7 90,B 93,9 97.4 98.0 99.l 99.6 101.l 138.2 140.B 140.l 138.0 138.0 141.3 138.4 137.9 138.5 138.2 90.B 102 .3 102.7 108.5 114.0 119.5 120.9 122.7 123.4 125.4 0.17 0.46 0,46 l.02 l.Efi 2,87 4.54 6.75 6,76 10.32 15,605 16,180 15,620 15,640 15,740 15,910 15,800 16,280 15,800 15,780 4,165 7,500 7,Bf.5 11,170 15,770 19,890 25,070 30,700 30,730 37,950 192.0 290.0 283.0 330.0 377.6 433.5 440,0 470.5 463.4 484.5 197.4 289.0 293.3 329.5 378.5 434.3 438.6 466.6 464.0 485.6 36,53 42.30 42.0B 42,BB 44,07 46.53 45.34 45.33 45,60 45.62 201.0 257,l 294,2 327.8 356,2 371.l 388,7 407.0 Heat Transfer and Pressure Drop in Heat Exchangers NO.OF TUBES-•O TUBE FLUID-WATER t •2 t t t tl t2 "i b. p wt w• "' Q. e• u 92.0 106.3 70,l 80,9 138.0 70.4 88.l 138.0 0.14 0.42 15,495 15,720 3,775 8,950 167.8 278.3 173.7 283.4 36.80 42.60 174.4 250.0 113.870.6 92.5 140.6 0.79 15,750 13,020 345.4 348.0 45.62 289.6 118.0 122.l 124.2 126.7 70.7 95,3 139.2 70.8 97.8 139.6 70.8 99.2 138.7 71.0 100.8 139.3 BAFFLES 1.58 2.59 4.17 6.11 15,690 15,650 15,650 15,560 18,300 24,130 301.UO 36,840 386.0 423.0 444.0 464.6 388.0 421.6 442.7 463.0 45.62 46.56 46.15 46.60 323.4 347.4 368.0 381.0 102,8 111.0 117.4 121.6 123.7 126,0 128.3 130.0 70.l 80.9 137.7 70,5 8L8 137.8 70.8 88.4 139.3 71.0 91.6 138.5 71.l 93.8 137.9 71.2 95.9 138.l 71.3 97.5 138.9 71.3 99.0 139.7 0.06 0.10 0.28 0.48 0.79 1.34 1.95 2.64 15,840 15,94,0 15,910 15,650 15,590 15,710 15,810 15,710 4 ,9ffi 8,615 12,760 19,200 24,980 32,430 38,830 45,150 171.l 228.0 279.6 322.0 353.8 388.0 413.8 435.3 :).73.8230.8 280.0 324.0 355.2 390.5 414.0 438.0 43.65 46.57 48.75 48,73 48.25 48.26 48.82 49.10 149.8 187.3 219.2 252.7 280.3 307.4 324.0 339.0 BAFFLES-ORIFICE s1ze-s/a• DIA.HOLE RUN NUMBER 11 BAFFLES 696 007 698 699 700 701 702 3 7Cl3 '104 705 706 707 708 709 710 BAFFLES-ORIFICE SIZE-9116" DIA HOLE * S•• first page of Appendix DATA TUBE DIA.-1/2" TUBE PITCH-25/32" DATA TUBE DIA.-1 / 2" TUBE PITCH-1 3/32" TRANSFER AREA-26, 16tJ• SHELL FLUID-WATER TRANSFER AREA-13.080 , SHELL FLUID-WATER TUBE FLU ID-WATER I'he University of Texas Publication \ t t t RUN w• wt t2 6 p •1 •2 ~ NUMBER 19 BAFFLES 718 72 . 8 80.6 138.l 86 .7 0.42 101,.213 , 350 2,130 109.4 72 . 8 86 .7 102.3 719 138.3 2 .18 13 ,630 5,380 189 .2 193 .7 720 72.8 89 .7 138.l 109.8 4.82 13 , 760 236 .7 8,380 232.5 721 72.8 114.9 92.0 138.1 8 . 85 13,540 11 ,260 260 .3 261.0 722 72 .8 94.2 138.5 119 .5 13 ,360 15 .28 15 ,040 285.8 285.8 723 72.8 95.3 138 .2 121.4 21.fJ.'3 13,470 18,020 304.0302. 3 724 72.9 96 .0 137 .6 122. 6 30.57 13,620 21 , 150 316.0315.2 11 BAFFLES DATA BAFFLES-ORIFICE TUBE DI A.-5/8" TRANSFER AREA-16 •. 360 • TUBE PITCH-1 1/ 16" SHELL FLUID-WATERSIZE-11/16" DIA.HOLE NO.OF TUBES-20 TUBE FLUID-WATER u em ~ 30 .77 39 .56 207.0 292 .3 42 .52 334 .3 44 .06 361.1 384 .0 45 .47 45 .70 404 .5 423. 245. 53 731 732 733 734 735 736 72 .0 72.0 72 .0 72.l 72 .1 72 .1 78 ,9 00 .6 90 .6 92 .7 9L5 95.7 137.8 137 .2 1.'38 .4 139 . 2 138.4 139.2 88,9 109.1 117.7 122.0 124.9 127 .0 0.19 2 .04 5 .70 10.28 18.46 27.04 13 ,350 13 , 300 13,440 13 ,525 13 ,195 13 ,575 1,950 7,110 12 ,040 16,210 21,900 26,240 91.7 194. 2 249 . 8 279 .5 295 . 2 319 .5 95 .4 199.8 249 .2 278.9 295.7 318.6 33.62 43.60 46.72 48.20 48 .23 49 .00 166 . 8 272.2 326. 8 354 .4 374 .0 398.6 3 BAFFLES 159,3 745 48 .07 125.3 129.0 744 72.0 80.9 139 .6 110.8 0.27 13,980 4,475 160.0 746 47.00 123.0 124.2 72 .0 81.0 137.9 110.2 0.27 13 ,685 4,490 195.6 747 49 .30 161.3 137. 9 116.9 0.65 7,680 157 .8 72.2 83 .8 13,680 50.80 240 .3 748 138,5 200 .0 201.8 72 .3 86 .7 1.76 13,860 12,460 122.3 290.8 749 51.5321,550 245.0 245.8 90.4 4.91 72 .5 138.7 127.3 13 ,685 321.7 52 .009,54 274.029,380 273.3 72.6 92.5 139.4 130.l 13,760 DATA BAFFLES-DISK-ANO-DOUGHNUT TUBE DIA.-3/8• TRANSFER AREA-25.510• SIZE-4,s• DISK,4 o• HOLE TUBE PITCH-11/16" SHELL FLUID-WATER * S•• first page o# Appendix HD.OF TUBES-52 TUBE FLUID-WATERfor SY•bo Is, Heat Transfer and Pressure Drop in Heat Exchangers DATA BAFFLES-DISK-AND-DOUGHNUT TUBE DIA,-1/2" TRANSFER AREA-26.160' TUBE PITCH-25/32• SHELL FLUID-WATER SIZE-.t.5• DISK,4.0" HOLE NO ~ TUBES-40 TUBE FLUID-WATER t t RUN ttl tt2 w e 82 wt Qt Q. A p "i. u s m NUl'IBER 19 BAFFLES 770 74.6 82.7 139.2 87.2 0 .01 15,660 2,470 165.6 126.8 128.3 29.30 771 74.7 88.7 137.3 99.6 0.11 15,470 216.2 219.6 35.48 233.0 5,825 772 75.0 94.8 139,9 111.l 0.34 15,610 10,860 309.6 312.8 40.50 292.3 773 75.0 99,7 139.4 375,0 33!).4 119.3 1.06 15,075 18,700 372.2 41.94 774 75.0 102.3 140,7 123,9 1.90 15,650 426.0 426.0 43.47 374.8 25,430 775 75.0 103.2 139.2 125.1 3.02 15,630 31,450 441.3 441.6 42.73 395.0 776 75.0 101,0 138,3 126.1 4.26 15 ,675 456.0 42.04 413.5 37,430 454.5 777 74.5 89.7 139.8 0.14 15,300 37.73 235.0 102.l 6,295 232.0 236.8 778 74.9 90.1 138,2 37,05 239.0 102.7 15,300 6,590 231.6 234.0 0.13 779 'i5 .1 89.9 15,700 234.7 36.83 240.8 138.2 102.4 0.13 6,560 232.0 780 75.9 102.4 Zl 360 416.5 416.2 42.33 376.2 139.3 124.0 2.26 15,760 11 BAFFLES 001 169.0 35.77 175.l 75.5 86.0 139.0 15,600 4,140 163.7 98.2 o.os 40.23 220.8 802 7 ,120 232.2 233.6 75.8 90.7 140.5 107.7 0.10 15 ,610 263.5 11,480 283.7 287.0 41.18 803 76,l 113.9 0.19 15,650 94.2 138.9 352.2 314.5 19,530 42.48 804 76.3 138.9 0.51 15,800 349.3 98.4 120.9 42.92 352.0 395.6 15,780 28,520 395.0 805 76.4 101.4 139.0 125.1 1.11 377.4 421.0 42.63 15 815 37 050 420.8 806 127.0 76.3 102.9 138.3 1.89 1 BAFFL~S 831 832 833 834 835 76.2 76.4 76.5 76,8 76.8 84.0 91.9 95.1 100,l 102.4 140.4 140.4 139.6 139.5 138,9 96.5 113.2 118.6 125.5 128.3 0.03 0.13 0.21 0.56 1.20 15,680 15, 800 15 ,980 15,675 15.640 2,880 9,070 14,220 28, 130 37 500 121.8 245.3 296.8 365.8 401.0 126.4 246.5 298.2 365.2 3W.7 35.33 42.42 43.27 43.83 43.58 131.8 221.1 262.2 319.0 351.9 3 BAFFLES 106.8 38.68 2,980 108.0 111.0 15,710 0.03 848 76.2 138 .9 101.7 83.1 169 .3 43.63 193.2 194.5 7,230 15,875 0.05 139.9 113.0 76.3 88.5 849 210.9 45.'78 252.7 13, 160 252.5 0,09 15,815 139;9 120.7 76.6 92.5 850 248.4 45.62 296.4 298.0 20,720 15,740 0.20 139.0 124.6 76.8 95.6 851 285.8 343.8 46.36 346.4 29,900 15,915 0.37 128.5 98,7 140.0 76.9 852 45.02 302.2 350.0 07 ,800 356.0 15,680 0.58 129.0 99.7 138.2 76.0 853 DATA JAFFLES-DISK-AND-DOUGHNUT TUBE DIA.-1/2" TRANSFER AREA-26, 160 , SIZE-4,95" DISK-3.5• HOLE TUBE PI TCH-25/32" SHELL FLUID-WATER* see first page of Appendix for Sy11bol1. NO.OF TUBES-40 TUBE FLUID-WATER The University of Texas Publication DATA BAFFLES-DISK-AND-DOUGHNUT TUBE DIA.-1/2• TRANSFER AREA-26.16tJo $1ZE-s.s• DISK,2.s• HOLE TUBE PITCH-2s/32• SHELL FLUID-MATER NO.OF TUBES-40 TUBE FLUi D-MATER DATA BAFFLES-DISK-AND-DOUGHNUT TUBE DIA .-1/2• TRANSFER AREA-13.°'a• SIZE-4.s• DISK, 4.0" HOLE TUBE PITCH-1 3/32• SHELL FLUID-MATER * see first page of Appendix for Symbo Is. NO.OF TUBES-20 TUBE FLUID-WATER Heat Transfer and Pressure Drop in Heat E xchangers DATA BAFFLES-DISK-AND-DOUGHNUT SIZE-4.5" DISK,4,0" HOLE TUBE DIA.-5/8" TUBE PITCH-1 1116" NO Of TUBES-20 BAFFLES-HALF-MOO~~AHD ORIFICE TUBE DIA.-5/9• HO. OF BAFFU:S-19 TUBE PITCH-($EE BELOW) *See first page of Appendix TRAH$FER AREA· 16,3'o• SHELL FLUID-WATER TUBE FLUID-WATER TRANSFER AREA-($EE BELOW) SHELL FLUID-(SEE BELOW) The University of Texas Publication DATA BAFFLES-DISK-AHO-DOUGHNUT TUBE DIA. (SEE BELOW) TRANSFER AREA-(SEE BELOW) SIZE-•.s• DISK,•.o• HOLE * See first page of Appendix TUBE PITCH-(SEE BELOW) SHELL FLUID-(SEE BELOW) for Syllbols, HO.OF TUBES-20 TUBE FLUID-WATER Heat Transfer and Pressure Drop in Heat Exchangers DATA ZERO BAFFLES TUBE DIA,-(SEE BELOW) TRANSFER AREA-(SEE BELOW) * S•• first page of Appendix TUBE PITCH-(SEE BELOW) SHELL FLUID-WATER for Syiboh. NO.Of TUBES-(SEE BELO!il) TUBE FLUID-WATER PUBLICATIONS OF THE BUREAU OF ENGINEERING RESEARCHt •1. Bulletin No. -z. Bulletin No. •a. Bulletin No. .,. Bulletin No• 6. Bulletin No. • 6. Bulletin No. • 7. Bulletin No. • s. Bulletin No. ... Bulletin No. 1725. u. Bulletin No. 4238. 36. Bulletin No. '240. as. Bulletin No. 4808. 37. Bulletin No. 4324. •out of print. 16. 164. 189. 362. 1. 26. 62. 66. Rice I~ation In Texas, by T. U. Taylor. 1902. The Austin Dam, by T. U. Ta:vlor. 1910. The Composition of Coal and Lignite and the Use of Producer Gu In Texas, by W. B. Phillips, S. H. Worrell, and D. M. Phillipa. 1911. Methods of Sewage Disposal for Texas Cities, by R. M. Jameson. 1914. Annual Flow and Run-Off of Some Texas Streams, by T. U. Ta:vlor. 1916. Street Paving In Texas, by E. T. Paxton. 1916. Road Materials of Texas, by J. P. Nash. 1916. Run-Off and Mean Flow of Some Texas Streams, by T. U. Taylor. 1916 • Texu Granites, by J. P. Nash. 19}7. Papers on Water Supply and Sanitation, by R. G. Taylor, Editor. 1917. Papers on Roads and Pavements, by R. G. Tyler, Editor. 1917. Boiler Waters: Their Chemical Composition, Use and Treatment, by W. T. Read. 1917. The Friction of Water In Pipes and Fittings, by F. E. Giesecke. 1917. Testa of Concrete Aggre;iates Used In Texas, by J.P. NB8h. 1917. Chemical Analyees of Texas Rocks and Minerals, by E. P. Schoch. 1918. Physical Properties of Denae Concrete as Determined by the Relative Quantity of Cement, by F. E. Glesecke and S. P. Finch. 1918. Road Building Materials In Texas, by J. P. Nash, c:OOperatlon with C. L. Baker, E. L. Porch, and R. G. Tyler. 1918. The Strength of Flne-Aggreirate Concrete, by F. E. Giesecke, H . R. Thomu, and G. A. Parkinson. 1918. Papers on Pavements Presented at Engineering Short Course, by R. G. Tyler. 1919. ProirreBS Report of the Engineering Research Division of the Bureau of Economic Geology ""nd Technolo1r:v, by F . E. Giesecke, H. R. Thomas, and G. A. Parkin· son. 1922. Silting of the Lake at Austin, Texas, by T. U. Taylor. 1924. The Friction of Water In Elbows, by F. E. Glesecke, C. P. Remlng, and J, W, Knudson. 1927. Effect of Various Salts in the Mixing Water on the Compressive Strength of Mortars, by F. E. Giesecke, H. R. ThomBS, and G. A. Parkinson. 1927. Testing of Motor V chicle Headllghtlng Devices and Investigation of Certain Phaaea of the Headlight Glare Problem, by C. R. Granberry. 1928. Effect of Phyelcal Properties of Stone Used as Coarse Agirregate on the Wear and Compressive Strength of Concrete, by H. R. Thomas and G. A. Parkinson. 1928. Preliminary Report on Relation between Strength of Portland Cement Mortar and Its Temperature at Time of Test, by G. A. Parkinson, S. P. Finch, and J. E. Huff. 1928. A Study of Test Cylinders and Cores Taken from Concrete Roads In Texu During 1928, by J. A. Focht. 1929. A Method of Calculating the Performance of Vacuum Tube Circuits Used for the Plate Detection of Radio Signals, by J. P. Woods. 1981. Heat Transfer in a Commercial Heat Exchanger, by B. E. Short and M. M. Heller. 1981. Heat Transfer and Pressure Drop In Heat Exchangers, by Byron E. Short. 1988. Air Conditioning for the Relief of Cedar-Pollen Hayfever, by Alvin B. Willis and Howard E. Degler. 1939. Wavelength of Oscillations Along Transmission Lines and Antennu, by Dr. Ernest 114. Siegel. 1940. A Method for Measuring Hydration-Pressure Relationships In Bentonltlc Materials and Heaving Shale, by H . H. Power, Barnaby L. Towle, and Joseph B. Plaza. 1942. The City, the Housing and the Community Plan. Some Basic and Historical Con­siderations, by Hugo Leipziger. 1942. The Inftuence of Storage Conditions Upon the Phyelcal Properties of Lignite, by Carl J. Eckhardt, Jr., and Chapin Winston Yates. 1942. Cathodic Protection of Metals In Ice Plants, by Robert W. Warner and A. J . :Mc­Crocklin, Jr. 1943. Heat Transfer and Pressure Drop In Heat Exchan;iers, b:v Byron E. Short. 1943. (Revision of Bulletin No. 3819.) 10. • 11. • 12. 18. 14. • 111. • J6. • 11. 18. •1e. zo. •21. 22. 28. i24. 25. 26. 27. 28. 29. •so. 81. 82. aa. Bulletin No. 1733. Bulletin No. 17311. Bulletin No. 1752. Bulletin No. 1769. Bulletin No. 1771. Bulletin No. 1814. Bulletin No. 1816. BnDetln No. 1839. BnDetln No. 1856. Bulletin No. 1922. Bulletin No. 2216. Bulletin No. 2489. Bulletin No. 2712. Bulletin No. 2780. Bulletin No. 2813. Bulletin No. 2814. Bulletin No. 2826. Bulletin No. 2922. Bulletin No. 8114. Bulletin No. 3128. Bulletin No. 8819. Bulletin No. 8932. Bulletin No. 4031. Bulletin No. 4206. tA limited number of copies of the bulletins not starred are available for free distribution. iBy error printed 1111 Bulletin No. 2831.