I V.
I
E. SENECAL
Engineering Research Laboratory, E. I. du Pont de Nemours & Co., Inc., Wilmington, Del.
Fluid Distribution in Process Equipment Future process design needs better control of circulating fluids. Solutions are suggested here for several types of nonuniform distribution problems
FLUIDS
have been called the lifeblood of a chemical plant. This is not a bad adage, for economic health, in fact survival, of most modern chemical plants depends upon obtaining proper distribution of fluids throughout the body of the plant. This involves getting the right fluids to the right places, at the right times, in the right amounts, and with the right flow properties. Examples of how uniform fluid distribution relates to successful operation of a process may be found in almost any unit operation where fluids are brought in contact with other fluids, particulate solids, or extended solid surfaces. Successful functioning of equipment where flow from a central feed pipe is subdivided into a number of separate parallel paths-e.g., tubular heat exchangers, tubular reactors in parallel, or gas and liquid spargers-depends upon arrangement of pressure changes to ensure approximately equal flow through each path. Other examples where flow distribution of a fluid is important are in gasliquid or liquid-liquid contactors (packed columns, wetted-wall columns, spray or bubble contactors), gas flow in textilespinning chimneys, pipeline reactors where reaction time is important, and even in pipeline mixers where homogeneity is obtained through controlling flow patterns and mechanisms by which the streams are mixed. General Status of the Field
The problem of fluid distribution is older than the chemical industry, and research into fluid mechanics dates back at least to Bernoulli. Therefore, procedures for solving a number of fluid-distribution problems should be available in the literature. I n fact, much effort has been expended in this direction and a number of excellent papers have been published. The field
of fluid distribution is so broad, however, and the flow mechanisms are so complex, that only a small percentage of the many facets have been covered. Consequently, there is insufficient information available on techniques and design procedures for obtaining proper distribution in many cases encountered in practice. This situation may perhaps be attributed to two main factors: 1. Most investigators have been concerned with particular systems operated within narrow ranges of conditions. Empirical correlations obtained from each experimental program are consequently handicapped by serious limitations in application. Generalization or extrapolation of data is difficult and often results in conclusions conflicting with information provided by other investigators. 2. The chemical industry is becoming increasingly competitive and is demanding refinements in fluid distribution never before required. This demand reflects the recognition that these refinements result in better process economics.
Most fluid-distribution problems may be classified as either one or a combination of two recognizable general types of distribution. The first type involves coarse or gross fluid distribution in macroscopic subdivision, making use of specific recognizable apparatus such as baffles, perforated spargers, overflow weirs, drip points, and sieve plates to obtain uniform distribution of flow. The second type concerns fine distribution in subdivisions of microscopic size, in contrast to gross distribution, depending on the hydrodynamic conditions in the conduit, or on the natural distribution tendency of any packing which may be present to obtain a uniform velocity field. The question arises as to degree of fineness of distribution being sought. This must be answered for particular
cases rather than by a generalized statement. Ideally, a condition of no gradient across a given profile is generally sought, whether it be velocity, concentration, reaction rate, or temperature. Realization of this idealized state is, of course, influenced by mechanical and hydrodynamical limitations. Furthermore, there are differences between ideal macroscopic and ideal microscopic distribution which are more than mere differences of degree or scale. For example, if uniformity is related to the maximum discrepancy between any two points across a given profile, the primary (macroscopic) distributor in a packed tower may be a manifold type which, essentially, may discharge uniformly from each of its outlets, while the velocity profile across the packed bed (microscopic distributor) may vary severalfold because of channeling. Uniformity in the macroscopic case is obtained by comparing discontinuous points, while microscopic uniformity is based on continuous points. Therefore, the two cannot be compared on a basis of uniformity alone. A number of rules of thumb have been developed for distributor designs involving both macroscopic and microscopic distribution. These rules, unfortunately, do not often meet with more rigid requirements imposed by present standards. It is increasingly evident that to obtain an optimum design, engineers must give proper consideration to three conditions: 1. Flow behavior in the distributing unit. Optimum design can be obtained only through full understanding of the flow behavior involved in the distributing unit itself. An undesirable alternate solution is through expensive trial and error design on each piece of equipment. 2. Upstream flow conditions. Many distributor designs have failed because the mechanism of flow upstream of the VOL. 49, NO. 6
JUNE 1957
993
, , ''
Fit
d pip ~ i v &ideal morneniutn and &fie& energy predomhate in E, friction in C, and upheam dmrbance plus tpomentum and kinetic energy in D I .
distributor was cither not tlken into account or else not fully understowl. 3. Downatram flow wnditions. A unit giving excellent distribution of a fluid may actually be detrimental to the pmccas because intolerable downstreah flow phenomena are created. For each condition, potential and kinetic energy changes should be bald with due consideration to n m mentum and friction. For convemience, ea& factor can be expressed as a function of the local velocity head modified by l l ~ m ecc&cicnt, which in turn is a function of geometry of the system, Reynolds number, and ITow pattepn. This coefficient is not, however, readily obtabed in many instantes, from either theoretical wneidetations or existing cxpmimental data. Its value beconra evmmorruncatarn when non-Newmnian m two-phape Bow wndiiions exisr Since design piwedurea are not available for m m distribution problems, the designrr should properly use the wealth of fundamantal data aeailable in the l i t e r a m . Selected references are listed at the end ofthis article.
.
Mocroswpis Fluid Distributors
p;laOnaa ~ i p e~ pThe . per f o r d pipe ck spa%& is a eonnnon type d distributor used in a wide variety of piping wmigurations such as ion achange bcds, absorption towem, and packed towm, as wcH as furnaccs and reactors. It may tither disgibute or
collect fluids in towers ranging from 1 to 30 or more feet in diameter. Figure l,A shows a single manifold, ' which is generally one lateral of a manybranched feed system. Hcre, the arrows depict ideal distribution over the length of the unit-that is, +e discharge arrows, b 5 i of equal height, indicate that the same amount of fluid comes out of each hole in the manifold. Thia ideal distribution is realized when a proper balance edsts between kinetic energy and momentum of the inlet stream, Ection losses along the length of the pipe, p r m e dmp across the outlet holes, and various interactions between these factors. For simplicity, the pubIan is commonly reduced to two important ratios: the ratio of the kinetic energy of the inlet stream to the praaure dropthe outlet; and the ratio of the friction losr in the pipe to the prdrop acrogl the outlet. H rule of thumb ia that each of theac-ratios should equal one tenth or lm. Designing a perforated pipe dstributor on this basis douc may
qearl im-
operatiop
Thwmtically,prrasun cEange over the 1of a manifold having a uniform crw Bection may be represented as
.
and the p...entapC of maldistribution bethe first and last outlee may be represented a0
yo maldiaaibution
*
Thus, maldistribution in manifolds can show up (Figun 1, B, C, and D) as excau flow near the dosed end, the feed end, or both ends of the manifold. When effects associated with momentum and kinetic en= predominate, higher flows occur from holes near the dosed end of the distributor. When the friction term dominates, the first hole d i e charge more than their proper share. A wmbination of the first case (Figure 1,B) and advene upstream ilow eonditions result in flow r a t a fromholes at both ends hizher - than in the middle (Figure 1,D). These equations pronde the "infinite resuvoir" solution ' which will guarantee gocd distribution. Simply, a pipe of sufficient diameter should be used to ensure reducing the velocity in the pipe to a negligible value. However, large diameter pipa are often impractical because of spacc. -In the chemical industry, fluids frequently required special materials of conshuction and economic considerations are incompatible with the u9e of ovusized p i p . Many chemical streams demand minimum retention time, which again requires the piping size to bc held to a minimum, Another simple solution is making the outlet holes small enough M that a pipe of reasonable diameter a p proaches the4nfinite requirement on a comparative basis. In the c h d plant, the usc of small holes as outlets has w e r a l - d r a w b a M a n g e x of plug&, higher power requirements, and detrimental high-velocity jets. The &orated pipe is perhap the simplest t y p of distributor deaign commonly used in the chemicabindustry (7F-9F). Obtaining an optimum design from theoretical considerations is seriouely hampered by t h r a principal factors. Fht, actnal change in veloeity profile at each outlet is not considered. Second, the momentum transfer from fluid drawn off to fluid remain&g in the pipe is assumed to be perfect, which is not m e . Third, general practice assumes an orifice cdEcieni of 0.63 (2.5wlodty heada loss) which is the weakest point in the design. Ragure drop aaayl the orifice is gcacrdly one or two ordua of magnitude greater than the kinetic energy, momwltnm, or friction term of the manibld pipe and therefore, a d aror in the orifice &ient is of major importance. The &ient is a function of hole size relative to pipe diameter and wall thickness, upstram pressure, inedium which the fluid diachargea, llow rate fmm the hole, and flow rate in the pipe acro~ul the hole. More experimental data are nMaary totheaaet value of this codfrcient aa a tinction of t k variablea
.
portiUY a liqk- -.-...g to a base material pa$ed under the air jet. A number of applications in the paper, printing, and bhemical industries invoke the use of such an air jet, commonly called an air knife, to obtain ? unifmmthickness of liquid over the width and length of the base material. With the air knife, the designer must give proper consideration to upsbnd downstream flow conditions M o r e the dcnign c+ be considered acceptable. The d t a of an experimental program on the w of an air knife in the printing industry (7E-7E)can be explained and expanded through fluid-flow considerations. For example, Bggume that the air knife has b&n designed and that a uniform jet has been obtained over the length of the slot. Even with uniform distribution, an improperly operated air knife will reault in q air jet which is unstable in the point of impingement, causing uneven thicknew of the liquid layer. Upstream flow conditions must be for pulsations in the feed syatem caused by the blower or by Bow through piping codigbations. Oscillations in Bow am p m t i d a r l y common in distributors fed from both eads when flow corned from a COU IIM I source and is split through a tee upsof the distributor. In other casea, the unsteady flow may be traced to operation in the transition zone (on a Reynolds number criterion) either in the fecd -s or +tiibu&. Similarlv, dormstream flow conditions may cauW uneven thicknesses of the liquid layer. The jet may operate in the transition zone of flow. The jet should impinge on the surface M o r e ita center-@e velocity dmps below the exit valye from the l i p of the slot. This ia becauw a rectaogular-dot jet with a high aspcct ratio (width-heiiht) is inhermtly unstable byond this point. This htability mum at a distance equivalent to about five to eight times the slot opening fmm the lip ofthe air knife. The q l e of impingement of the air jet on the surface, split of the jet,
I
all or a
is commonly used in extruding films such as allophane, or in coating procagc~lwhere a layer of material is evenly deposited on a moving base. Another example of this category is the air kniie used as a “doctor blade” to control thicknes of material deposited on a wntinuous moving surface. The slottype may ala0 be used in packed towers, serving a function W a r to the pede rated pipe,dthough this is not a common application. The prosedurcfor obtaining apropedy deaigned slot-type diwibutor is OM p e p rnorc somp!icated than that for a perforated pipe. In the pedorated pipe, the h i d discharges through a number of hole and thickness of the pipe wall generally dicta to provide acntially right-angle dseharge. Thh is not true of the slot-type distributor and, M e s s proper care is taka, a distribution such as in P i 2, may re&. Again the dmigner must make a proper balance of kinetic and momentum &&ga and
friction and diesharge lases as well aa upsweam and downs-
flow conditiooll(7.444, 7Z-7E). ) Many materialnd e d through slota require rainhum retention time and them&, a small diameter distributor is d a M . Scnral technique may be be uaed to reduce the diameter of the &tributor:
1. Feed fmmboth ends, thus reducing the ,kinetic enagy tgm by a factor of 4 for a given diametes and Bow rate. 2. Theamuweetl‘ohal d & n may be altcrcd (Fgun 3). Tho slot is moved away from the intlnmce of velociiy of themainteedsPatm. 3: The prrrnnur dro acmgl theslot c a n b e i m r c M d by 74lgtheninS the tipsofthe slot ( P i3). 4 sorcnS~ybeinscrtedbehiod the dot (Figure 3) to increase the presmaterial &e dmpltnd to screen f-
frmthcprocessilhram.
An example of a dot-type diiaibutor i s l h o r m i n F i ~ e 4 . Thisfigurrrep ramb an ad view of a prows which immhrra the w of an air jet to Temoye
surface, and smbility of the liquid laye must also be taken into Consideration. AU the above conditiona must be taken into account before a uniform thicknew can be asaured. The diiu cnce ktween proper and improper de sign can mean the difference between a salable and unacceptable prcduct; or the dSercnce in production rate of a
factor of two or more. Annular or Volute Type. Annular or volute-type distributors are used where two or more streams are brought in contact or mixed with one another, yith each stream concentric about a u5mmon axis. Jet educators, concentric reactors, spray dryers, and spray con denser8 are examplea. The annular or volute-type distribu tor may be treated as a slot-typ wid the additional factor of swirbg Bow. Distributors of this type may have
+
Figure 4. An air iet remaves all OT a portion of liquid adhering to the base material as it passes under the oir
straom VOL49,NO.b
JWRl97I
995
Figure 5.
Upper section of a two-fluid spray dryer
Feed slurry 6. Spray chamber 2. Primary air 7. Excess secondary air 3. Bustle 8. Deposit of wet feed 4. Secondary air 9 . Recirculating wet feed 5. Restricting orifice This is the ideal flow pattern usually envisioned by the designer. 6. This is probably the realistie flow pattern 1.
A.
the tangential or radial types. The swirling flow alters friction factor coefficients and introduces the need for new momentum considerations. Insufficient experimental data are available to take these factors accurately into account. Downstream from the distributor, interactions of the different feed streams generally have important effects upon the process operation. Eccentric flow will set up undesirable flow patterns that, depending on the process involved, may cause uneven reaction rates, nonuniform retention times, wall depositions, or low carrying capacity. Literature on interactions created by various jet systems (7B-7ZB, 70-80) can sometimes be used in designing the system to provide desired downstream operating conditions. In Figure 5,A, showing a typical spray dryer design, the arrows depict flow patterns as visualized by the designer. In this example, a two-fluid atomizer is used. The following analysis, however, will apply to any other type of atomization used in spray dryers. Feed material to be spray-dried passes down through the central feed tube and is atomized and partially dried by the primary air. Drying is completed by hot secondary air which is fed into the bustle through a horizontal radial feed line. The secondary air then passes from the bustle through a restricting orifice into the spray chamber where a portion recircul a t a to form a protective blanket over the walls and ceiling of the dryer. This prevents deposition of the wet feed during the drying process. The dried product falls ta the bottom of the tower, where it
996
is either continuously or periodically removed and packaged. The more realistic flow pattern for this particular design is shown in Figure 5,B. High velocity of the secondary air stream in the horizontal feed line produces a jet action which causes a pressure rise on the opposite wall of the bustle. Since flow through the restricting orifice does not cause a pressure drop much greater than pressure rise, more air comes out of one quadrant than the others. This unbalance causes the primary ai1 and feed to veer to one side in the spray chamber. With this flow pattern, the recirculating wet feed can come in contact with and deposit on the wall and ceiling of the drying chamber, then fall off periodically and contaminate the product collected a t the bottom of the tower. A more serious consequence may result if the deposited material becomes overheated and a fire or explosion ensues. T o ensure the desired flow pattern and safe operating conditions, adverse effects of the secondary air stream must be eliminated. This may be accomplished through a compatible arrangement of increasing the diameter of the horizontal feed line and reducing the diameter of the restricting orifice. Turning vanes may also be used. Miscellaneous. A number of distributor designs fall directly into none of the categories previously mentioned. These include weirs, perforated plates, screens, turning and straightening vanes, grids, packings, and baffles. Various combinations of the many types of distributing devices may be encountered.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Generally these types are usedin'systems where a fine degree of distribution is not being sought. Information on the distributing characteristics of most of the listed miscellaneous types is available in the literature. Conclusions
Most distributing systems can".be designed with a reasonable degree of accuracy where maldistribution of about i 5 % can be tolerated. The trend in the chemical industry, however, is to recognize desirability of designs which provide essentially uniform distribution. Uniform distribution should be obtained on an optimum design basis, keeping the original investment such as equipment size and operating expense such as power requiremenu to a minimum. Effects of upstream flow conditions on distribution and effects of downstream flow conditions on products of the process must be incorporated in distributor design considerations. -4 prerequisite for optimum geometric configuration of many fluid distributors is additional information on the complex flow phenomena involved. Refined experimental data are needed on discharge coefficients as a function of the many variables involved, interaction of combining streams, effect of chemical reactions of flow patterns, and behavior of non-Newtonian and two-phase flow. Nomenclature = diameter, feet = Fanning friction factor, dimensionless
D f
FLUID MECHANICS =EC
= conversion factor, 32.17 (lb.) (ft.)/
h = Ah = L = V =
(Ib. force) (sec.z) fluid head. feet difference in head, feet length. feet linear velocity, feet per second
(6C) Torda, T. P., Ackermann, W. O., Burnett, H. R., J. Appl. Mechanics 20, 63 (1953).
Jets-Penetration and Mixing (1D) Baron,
Subscripts L = lateral 01 = first outlet in lateral
L.
G.,
Natl. Advisory Comm. Aeronaut., Tech. Note 1615. 1948. Calla han, E. E.,’Ruggeri, R. S., I b i f , 2466, 1951. Ehrich, F. F., J . Aeronaut. Sci. 20, 99 (1953). Fenn. D. B., Natl. Advisory Comm. Aeronaut., Repts. and Mem. E53JOS, 1954. Folsom, R. G., Ferguson, C. K., Trans. Am. SOC.Mech. Engrs. 71, 73 ( 1 949). Fossett, H., Prosser, L. E., Inst.
(1A) Albertson, M. L., Dai, Y. B., Jensen, R. A.. Rouse., H.., Proc. Am. SOC. Civil ‘Engrs. 74, 1571 (1948); 75,901, 1019,1541 (1949). Andrade, E. N. da C., Proc. Phys. Soc. (London) 51, 784 (1939). Andrade, E. N. da C., Tsien, L. C., Ibid., 49. 381 (1937). Baron,. T:, Chem. Eng. Progr. 50, 73 11954). ,@A) Corrsin, S.; Uberoi, S., Natl. Advisory Comm. Aeronaut., Tech. Note 2124, 1950. (6A) Forstall, W., Gaylord, E. W., J . Appl. Mechanics 22, 161 (1955). (7A) Krzywoblocki, M. Z., J. Am. Rocket SOC.26, 760 (1956). (8A) Pai, S. I., “Fluid Dynamics of Jets,” Van Nostrand, New York, 1954.
Mech. En
(12D) (13D)
Jet s 4 a x i a f (1B) Alexander, L. G., Kivnick, A., Comings, E. W., Henze, E. D., A.Z.CI2.E. Journal 1, 55 (1955). (2B) Charyk, J. V., Glassman, I., John, R. R., “Fourth International Symposium on Combustion,” Williams & Wikins, Baltimore, Md., 1953. (3B) Crosby, R. S., S.M. thesis, Dept. of Mech. Eng., Mass. Inst. of Tech., 1949. (4B) Forstall, W., Jr., Shapiro, A. H., J . Appl. Mechanics 17, 399 (1950). (5B) Friedrich, C. M., Forstall, W., Jr., Proc. Third Midwestern Conference on Fluid Mechanics, Univ. of Minnesota. 1953. (6B) Gaylord, E. W:, Ph.D. thesis, Dept. of Mech. Engr., Carnegie Inst. of Tech., 1953. (7B) Howarth, L., Proc. Cambridge Phil. SOC.34,185 (1938). (8B) Koucky, R. W., S.M. thesis, Dept. of Chem. Ene.. Mass. Inst. of Tech., 1956. ‘ (9B) Landis, F., Shapiro, A. H., Proc. of Heat Transfer and Fluid Mech. Inst., Stanford Univ. Press, 1951. (10B) Nickerson, R. J., S. M. thesis, Dept. Mech. Eng., Mass. Inst. of Tech., 1950. (11B) Tuve, G. L., Heating, Piping, Air Conditioning 25, 181 (1953). (12B) Von Rosenberg, D. O., Mass. Inst. of Tech. Rept. 53-118, Dept. of Chem. Eng., 1953.
Jets-Parallel J. G., von, Zng.-Arch.
Alexander,
.
Bibliography Jets-General
(1C) Bohl,
T.,
Chem. Eng. Progr. 47, 181 (1951). (2D) Callaghan, E. E., Ruggeri, R. S.,
11,
(1940). (2C) Corrsin, S., Natl. Advisory Comm. Aeronaut., ACR 4H24,1944. (3C) Ferguson, C. K., Proc. Heat Transfer and Fluid Mech. Inst., Am. SOC.Mech. Engrs., 1949. (4C) Lock, R. C., Proc. Cambridge Phil. SOC.50,105 (1954). (5C) Sears, W. R., J. Appl. Mechanics 20, 445 (1953).
(14D) (15D) (16D)
YS.
(London) J. G3 Proc.
160,224 91949). Keagy, W. R., Weller, A. E., Proc. Heat Transfer and Fluid Mech. Inst., Am. SOC. Mech. Engrs., 1949. Kuethe, A. M., J . Appl. Mechanics 2,87 (1935). Laurence, J C., Natl. Advisory Comm. Aeronaut., Tech. Note 3561, 1955 Nottage, H. B., Slaby, J. G., Gojsza, W. P., Heating, Pz ing, Air Conditionine 24. 165 11952t . , Zbid., p. 117. ‘ Pai, S. I., J. AppZ. Mechanics 22, 41 (1955). Ruggeri, R. S., Natl. Advisory Comm. Aeronaut., Tech. Note 2855, 1952. Ruggeri, R. S., Callaghan, E. E., Bowden, D. T., Ibid., 2019, 1950. Weatherston, R., J. Aeronaut. Sei. 16,697 (1948).
Je ts-Slot (1E) Elrod, H. G., Jr., Heating, Piping, Air Conditioning 26, 149 (1954). (2E) Koestel, A,, Hermann, P., Tuve, G. L., Ibid., 22, 113 (1950). (3E) Krzywoblocki, M. Z . , Quart. Appl. Math. 7.313 (1949). Madison.‘ R. ‘L..Elliott. W. R..
Forstall; W., J. Appl. Mechanics 23,437 (1956).
Manifolds (1F) Acrivos, A., Babcock, B. D., Pigford, R. L., Annual Meeting Am. Inst. Chem. Engrs., Detroit, Mich., December 1955. (2F) Berman, A. S., J. Appl. Phys. 24, 1232 (1953). (3F) Cichelli, M. T., Boucher, D. F., Chem. Eng. Progr. 52, 213 (1956). (4F) Codegone, C., Appl. Sci. Research A4,76 (1953). (5F) Dow, W. M., J . Appl. Mechanics 17, 431 (1950); 18, 221 (1951). (6F) Keller, J. D., Zbid., 16, 77, 320 (1949). (7F) McNown, J. S., Proc. Am. SOC.Civil Engrs. 79,l (1953). (8F) Van der Hegge Zijnen, B. G., Appl. Sei. Research A3, 144 (1951). (9F) Yuan, S. W., J. AppZ Phys. 27, 267 (1956).
‘Packed Beds (ZE) Baker, T., Chilton, T. H., Vernon, H. C., Trans. Am. Inst. Chem. Engrs. 31, 296 (1935). (2E) Chatenever, A,, Calhoun, J. C., Jr., Trans. Am. SOC.Mech. Engrs. Petroleum Diu. 195. 149 (1952). . , (3E) Dankwerts, P. V., ‘Chem. Eng. Sci. 2, l(1953). 4E) Zbid., 3, 26 (1954). 5E) Er un S., Chem. Eng. Progr. 48, 89 f19;2) (6E) Gilliland; E. R., Mason, E. A., Oliver, R. C., IND.END. CHEM. 45, 1177 (1953). (7E) Hill, S., Chem. Eng. Sei. 1, 247 (1952). (8E) Hirai, E . , Chem. Eng. (Japan) ¶ 8 , 528 (1954). (9E) Kramers, H., Alberon, C., Chem. Eng. Sei. 2, 173 (1953). (10E) Leva, M., “Tower Packing and Packed Tower Desirrn,” U. S. Stoneware, 1953. (11E) Morris, G. A., Jackson, J. A., “Absorption Towers,” Imperial Chemical Industries, Ltd., 1953 (12E) Norman, W. S., Trans. Znst. Chem. Engrs. (London) 29, 226 (1951). (13E) Ryan, J. F., Ph.D. thesis, Pennsylvania State College, 1953. (14E) Sherwood, T. K., Chem. Eng. Progr. 51, 303 (1955). (15E) Wilson, D. A,, Geffen, T. M., Holmgren, C. R., motion picture, Stanolind Oil and Gas Co., 1953.
Screens and Grids (1G) Baines, W. D., Peterson, Trans. Am. SOC.Mech. Engrs. 73,467 (1951). (2G) Collar, A. R., Aeronaut. Research Council, Great Britain, Repts. and Memo. 1867,1939. (3G) Schubauer, G. B., Spangenberg, W. G., Klebanoff, Natl. Advisory Comm. Aeronaut., Tech. Note 2001. 1950. (4G) Taylor,’ G. I., Batchelor, G. K., Quart. J. of Mech. and Appl. Math. 2 , l (1949). (5G) Towle, W. L., Sherwood, T. K., Seder, L. A., IND. END. CHEM. 31,462 (1939).
Turning and Straightening Vanes (1H) Anderson, A. G., Straub, L. G., “Hydraulics of Conduit Bends,” Bull. 1, St. Anthony Falls Hydraulic Lab., Univ. of Minnesota, 1939. Harper, J. J., J. Aeronaut. Sci. 13, 587 (1946). Madison, R. D., “Fan Engineering,” Buffalo Forge, New York, 1948. Madison, R. D., Heating, Piping, Air Conditioning 9, 152 (1937). Madison, R. D., Parker, J., Trans. Am. SOC. Mech. Engrs. 58, 167 (1936). (6H’I Patterson, G. N., Aeronaut. Re~, search Comm., Repts. and Memo. 1773,1937. (7H) Silberman, E., Tech. Paper 14, Series P, Univ. of Minnesota, St. Anthony Falls Hydraulic Lab., 1953.
(8H) Szczeniowski, B., J. Aeronaut. Sei. 11, 73 (1944). (9H) Weske, J. R., Natl. Advisory Comm. Aeronaut. Tech. Note 1471, 1948. RECEIVED for review January 2, 1957 ACCEPTED March 13, 1957 Division of Industrial and Engineering Chemistry, ACS, Symposium o n , Fluid Mechanics in Chemical Engineering, Lafayette, Ind., Dec. 27 and 28, 1956. .
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