ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Flow through 0.E. C U N N I N G H A M , D O L L I N G E R C O R P . . ROCHESTER, 0.B R O U G H T O N A N D R . R. KWAYBILL
N. Y .
U N I V E R S I T Y O F R O C H E S T E R . R O C H E S T E R . N. Y .
O v e r a period of years d a t a on resistance t o f l u i d flow of a variety of fabrics a n d filter media have been accumulated using a modified f o r m of t h e N a t i o n a l Bureau of Standards apparatus f o r measuring resistance t h r o u g h fabrics. These data are presented, a t e n t a t i v e correlation is suggested, a n d several anomalies are pointed out. For felted materials a n d a i r flows in t h e range of 0 t o 125 feet per m i n u t e t h e pressure drop, -A/', in inches of water, can be represented b y t h e viscous flow equation -A/' = k p ~ where k is a constant dependent u p o n t h e fabric, fi is t h e viscosity of t h e f l u i d in centipoises, a n d v is t h e superficial velocity in ft. per min. F o r felted materials of wool, rayon, and c o t t o n k is approximately O.O3W, w h e r e w is t h e c l o t h w e i g h t in ounces per square yard. Woven fabrics obey t h e viscous flow equation a t low velocities, but t h e onset of t u r b u l e n c e causes deviation f o r increased rates of flow. Approximate values of k are presented f o r a n u m b e r of t y p i c a l media. For a l i m i t e d n u m b e r of materials flow data o n water a n d oils of varying viscosity were obtained. Flow was again f o u n d f o r each specific case t o be generally represented b y t h e viscous flow equation, b u t a n a t t e m p t t o correlate t h e data by a p l o t of t h e typeAfIpv2 vs. vpIp, where A/' is t h e pressure drop, v t h e superficial velocity of t h e fluid t h r o u g h t h e porous m e d i u m , p t h e density, a n d p t h e viscosity of t h e fluid, failed. It is suggested t h a t t h i s f a i l u r e is connected w i t h t h e w e t t i n g characteristics of t h e fluid t o w a r d t h e given filter medium.
T
HE growing use of permeable textile media in the filtration of small amounts of contaminant from large quantities of fluid has made knowledge of the flow characteristics through such materials of increasing importance. Essentially, in the operation of such filters the liquid or gas is clarified by the use of felts, woven cloths, battings, or papers; the pressure drop through the filter is relatively low and builds up only slowly through the life of the filter. Unfortunately, in the design of these filters the available theory on flow through porous media is not directly applicable and an experimental approach must usually be taken. This paper attempts to summarize results obtained for a variety of textile filter media over a period of several years. TT'hile correlations of pressure drop, flow rate, and porosity have been made for granular materials (3, 6, 8 ) , consolidated porous media (6),certain plug type flonmeters (7,12), and textile fabrics (IO), the results are difficult to apply practically to porous filter media of the textile type because of the uncertainties with respect to the actual interstitial areas available for flow. This makes application of the Kozeny equation unsatisfactory since no definite value can be given for the porosity or fraction of voids. Attempts have been made t o overcome this; Backer (g) was able t o correlate the air permeability of certain simple woven cotton fabrics with their crimp and minimum pore area. The situation is further obscured by the possibility of either streamline or turbulent flow or a transitional zone between the two existing simultaneously in the different size flow channels and by the difficulty in measuring the kinetic effects. FLOW OF A I R
Apparatus. The apparatus used in the measurement of the resistance of fabrics t o the flow of air is a modification of the apparatus described by Schiefer and Boyland (11). It is shown photographically in Figure 1 and the essential working parts are shown in outline in Figure 2.
1196
The essential portion of the apparatus is a vertical tube of 3.028-inch inside diameter (cross-sectional area of 1/20 square foot) across the top of which the material to be tested may be placed. A heavy flange around the top of this tube has an internal circumferential groove which connects several small openings through the tube wall with the manometer connection tube. This flange, which also supports the tube on its stand, is beveled a t an angle of 45' on its outside circumference. A loose ring beveled on its inside circumference to mate the flange may be placed on the flange with the test material in between, for the purpose of applying a light smoothening action to the fabric. In the case of stiff materials, the smoothening ring is not used. Materials which might be opened up by the stretching effect of the differential pressure are backed up with a disk of 40-mesh screen, the resistance of which is negligible at the velocities used (up to 125 feet per minute). I n any case, an edge seal is obtained by means of a brass ring lined on its lower side with a soft rubber gasket, and weighted with a 7-pound steel weight, which has an inside beveled opening of the same diameter as the inside diameter of the tube. The weighted ring is guided into place by means of a slide bar. The lower end of the tube connects through a streamlined elbow t o an orifice meter of 2-inch inside diameter. Orifice plates are made readily interchangeable by two wing nuts on the orifice flange studs. Air is drawn through the apparatus by means of a vacuum pump connected to the flowmeter, but a vacuum cleaner blower is also suitable for the purpose. Actually, two tubes connect the apparatus with the pump with a valve in each tube; this arrangement has been found to permit finer adjustment of the flow. A pad of cotton wool in the bottom of the tube straightens the flow and protects the orifice plates. In order to provide both low and high resistance readings on a single manometer of convenient length, slant gages are not used. Instead, the manometers used are vertical well-type manometers. That is, the U-tube is vertically mounted and the high pressure branch of the U-i.e. , the well-has a cross-sectional area which is very large compared with that of the low pressure branch of the U. The fall in liquid level in the well is therefore negligible compared with the rise in the small tube, and it is only necessary t o measure the rise above the zero setting. Vernier scales permit reading the manometers to 0.01 inch and the results are made readily duplicable by the nonfouling oil that is used as a manom-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 6
FLOW THROUGH POROUS MEDIA eter fluid. This oil is a mixture of white mineral oil and methyl salicylate having a specific gravity of 1.000 so that the readings are taken directly in inchefi of water. Procedure. The cloth or felt to be tested is placed across the mouth of the flow tube. With the apparatus so constructed it is not necessary to cut a piece from the bolt. If the material is not sufficiently rigid to lie smoothly, the stretching ring is fitted into place. Finally the weighted seal ring is lowered into place.
way brass cock provides a means of pumping the liquid either through the test apparatus, or back into the reservoir, or dividing it in any ratio between the two. A radially finned sump filter covered with dense felt serves to remove incidental solid contaminants from the liquid. Pressure taps are brazed to the flow tube sections a t a distance of 1 inch from the faces of the respective flanges. These taps are connected, through three-way stopcocks for drainage, to otherwise unjoined vertical lengths of glass tubing mounted on a scale graduated to inch. A glass overflow reservoir is attached to the top of the downstream pressure metering tube. This reservoir is in turn connected by means of rubber tubing to a small, closed, steel reservoir. The steel reservoir has additional brazed-in taps which are connected, respectively, through rubber tubing with a roughly regulated source of compressed air, a mercury manometer, the atmosphere through a quick-opening clamp, and the atmosphere through a delicately regulated needle valve. (The needle valve is the lower portion of a laboratory gas burner having a fixed needle and threaded port-cap. A brass rod brazed to the cap provides a handle for delicate adjustment.) A set of three ordinary milk bottles of 1/2-pint, 1-pint, and 1quart capacity, respectively, and a stop watch for metering the flow complete the apparatus. Procedure. The sample of material to be tested is clamped between the flanges of the flow tube. Flow is measured by inserting one of the milk bottles beneath the overflow of the flow tube and timing with the stop watch. The sudden spreading of the liquid surface as it passes the ledge inside the bottleneck, molded there for holding the cardboard bottle cap, provides a surprisingly sensitive end point. A bottle size is chosen that will require 10 to 40 seconds for filling, and the time readings are readily checked to 1%.
Figure 1 .
Air Resistance Meter
I
I
The vacuum pump is then started, and the flow is adjusted by means of the needle valves in the two vacuum lines until the flowmeter manometer indicates the desired rate of flow. The resistance is read on the resistance manometer. The flow rate is then adjusted to a new value and the resistance again read; this is repeated until the desired number of readings has been obtained.
YlIiirr CLOTH
FLOW O F LIQUIDS
Apparatus. The design of the apparatus used in the measurement of the resistances of fabrics to the flow of liquids is adapted from that of the apparatus used with air. It is represented diagrammatically in Figure 3 and an exploded view of the sample holder is shown in Figure 4. The essential portion of the apparatus is two vertical sections of brass tubing having an inside diameter of 3a/~inches and a cross-sectional area of 1/18 square foot. The sections are held together by bolted flanges arranged in such a manner that a circular sample of the material being tested may be held between them. The flange of the lower section of tubing has a female facing, and the upper flange has a flat facing. The test sample is cut to fit into the depression in the lower flange, and it is backed up on the upper, or downstream side, by a brass ring of 3a/, inch inside diameter which supports an 8-mesh bronze backup screen. Plain brass rings are provided for building up the space in the flange groove underneath the sample so that the top of the screen is flush with the top of the flange. A rubber gasket having the same inside diameter as the flange provides a seal between the two sections of tubing and also seals the sample in the tube. The length of the lower section, which is upstream of the sample is 7.5 times the diameter and that of the upper section is 2.5 times the diameter. These are the minimum lengths recommended by the American Society of Mechanical Engineers ( 1 ) for use with an orifice. Both ends of the tube assembly are connected to brass tubing having a 3/r-inch inside diameter by means of spun brass adapters. The lower tube connects with the pump outlet, and the upper tube is provided with a tee which servee as a thermometer well and an elbow which empties the circulated liquid into a reservoir. The reservoir is a 3-gallon tinned steel can, and the pump is a rotary-type with bronze housing and rubber impeller. A three June 1954
BRK TESTER BELOW
W Figure 2. Air Resistance Meter Sample holder (left) Weighted seal rlng ( r i g h t )
After the flow has become steady a t the approximately desired rate, the differential pressure is read on the pressure tubes. Two procedures are provided depending on the magnitude of the differential pressure: 1. A low differential pressure is read directly by taking the difference between the levels of the liquid in the glass tubes. This reading represents the differential pressure in terms of inches of head of the liquid being used. 2. When the differential pressure is sufficiently great to force the liquid in the downstream pressure metering tube up above the scale, the procedure is modified as follows: Air is admitted to the steel reservoir a t a gage pressure slightly higher than the dserential pressure across the sample. The needle valve is adjusted to allow air to escape to atmosphere a t just the right rate to hold the liquid in the downstream pressure metering tube
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1197
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT at the same level as that in the upstream tube. The differential pressure is then read indirectly on the mercury manometer. A temperature reading is taken with each flow and pressure reading. The temperature usually rises during a series of runs because of the heat produced by the pump. In case the viscosity of the liquid is sufficiently lowered to bring about an appreciable change in the flow characteristics, the flow control valve is set
fi
PRESSURE
HERMOMETER
Figure 3. A. B. C. D.
These deviat,ions are indicated in Table I for those fabrics Eo? which k represents an approximate constant. The materials are divided according to their structure into two major classes: felted materials and woven materials. Felts. The air f l o ~resistance of the felted materials obeyed the viscous flow equation for all air flow velocities up to 125 feet per minute. Figure 5 presents a plot of the resistance constant k = - 4P/fiv versus the cloth weight W in ounces per square yard for the felts. The resistance constants of the felts and battings are correlated by the observed linear equation, k = 0.03 W , Thc cotton and rayon materials are even better correlated by multiplying the felt weight by the ratio of the cotton fiber densit>-divided by the wool fiber density. Dyne1 felt is the exception; its higher resistance, as indicated by the values of k = 0.84 for W = 6.0, may be due to the denser character of the calendered surface of the felt corresponding to a lower porosity. The correlation in Figure 5 is recommended as an approximation of t'hc resistance of T Y O O ~ ,rayon, or cotton felted materials of shructure similar to those tested. Woven Cloths. Table I presents the physical chara2teristics and resistance for air flow velocitsiesup to 125 feet per minute of typical examples of woven fabrics and several nonfelted materials. The woven materials differ from the felts in two major respects: Nearly all exhibit pressure velocity curves that deviate from a straight line at the higher air flow rates. (The air flow rate above R-hich the curve is no longer linear is given in Table I.) The ratio of resistance constant k to cloth weight Tli is not a constant as for the felt$.
Liquid Resistance Meter Compressed air Mercury manometer Opening clamp Needle valve
to give the same resistance as in the initial run, and the f l o rate ~ is measured. The temperature coefficient of flow rate at constant pressure is calculated from the equation
SCREEN C -LOTH
-
Coefficient = Rz - Ri RI(T2 - T I ) where R2and R1,respectively, are the final and initial flow rates in gallons per minute square feet, and 7'2 and T I are the final and initial temperatures in O F. The same coefficient applies to temperatures intermediate between T1 and 2'2, and all flow rates are corrected to T I ,at which temperature the viscosity is also taken.
SBcIM RlffiS
BOTTOM
Figure 4.
Liquid Resistance Meter Sample Holder
AIR FLOW RESISTANCE
The physical characteristics of the samples of filter media are presented in Table I with the resistance to the flow of air. The air flow resistance is given by the constant k in the following form of the Darcy equation
-4P
kfitv
(2)
in which - A P is the pressure drop across the filter element in inches of water; p is the fluid viscosity in centipoises; u is the superficial velocityin feet per minute based upon the cross sectional flow area of the sample holder, and k is a proportionality constant peculiar to each material. Equation 2 is a simplification of the Kozeny equation for florv through porous media in viscous motion for which the ratio of inertial forces to viscous forces is small corresponding to a low Reynolds number. The constant k is a function of the geometrical configuration of the cloth including the important variables of length and shape of flow channels and porosity. At higher air velocities the increase in fluid turbulence and inertial forces causeb deviations from the simple linearity of pressure drop and velocity expressed by Equation 2. 1198
For design purposes an average resistance constant is presented in Table I which with Equation 2 will give a straight line approximating the experimental nonlinear pressure drop versus velocity curve to the tabulated maximum air velocity. The wide variation in t,he resist'ance constants for the woven cloths indicates that the complex geometry of the weaves is evidently the governing factor in determining their resistance. Because of the limited number of samples and lack of weave data it was impossible to determine the individual effects of such factors as n-eight,,count, number of plies, type of n-eave, amount of twist and crimp applied to the individual t.hreads, the number of threads per inch. Some of these factors, however, are known to be significant ( 2 , I O ) . The effect of weaving is that the resistance constant of the woven woo1 felt is several times as great as predicted from the correlation of Figure 5 for the ordinary wool felts. LIQUID FLOW RESISTANCE
The resistances to the flow of water and several oils were measured for a number of the fabrics listed in Table I. Oil
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 6
FLOW THROUGH POROUS MEDIA Table I.
Filter hIedium Cotton materialb Cotton flannel Cotton sheeting Cotton duck Terry cloth Wool woven felt Spun Saran cloth A Spun Saran cloth B Spun Saran cloth C Vinyon A Vinyon B Vinyon C Vinyon D Vinvnn E N ion- GEss cloth A Glass cloth rilter paper
Weight, (Oz./Sq. Yd.) 3.0 10.0 4.1 14.0 8.25 14.0 20.8 16.9
e
-AP Inches
Count
Plies
... ...
110 X '56 56 X 60 30 X 48 36 X 36
...
...
... 2 'X' 3 2 x 2
60 X 28 60 X 22 60 X 24 65 X 49 26 X 24 48 X 42 38 x 31 38 X 46.5 34 x 28 26 X 20 48 X 28
16.8 14.8 18.0 10.3 7.5 8.25 8.1 22.2
9
d
Physical Characteristics and Resistance t o Air Flow of Filter Media
2 3 10 3 3 3 2 2
x 2 x 3 x 10 x 3 x 2 x 2 x 2 x1
2x2
21.4 ... 50 lb./ 1000 sq. it. Approximate value since curve not straight line. Fibers oarallel. resin bonded. Resin ikpregnated. 0.020-inch thick. Velocity above which curve is not straight line Velocity for which approximate value of K is valid.
...
properties are given in Table 11. Table I11 presents a comparison of k calculated for air, water, and oils. A rather large increase in k , the resistance constant, is observed for water flow through most of the media, apparently the result of wetting effects although degree of aeration of the water used may also be a factor. Thus, deaeration of water flowing through borosilicate fritted glass disks reduces water flow resistance 50% in the range of nominal maximum pore size of 5 to 14 microns (4). Coarse sizes, 40- and 160-micron pore size, and the ultrafine size, 1.2 microns and below, showed negligible effects. Similarly, deviations in the flow resistance of a brass screen disk were observed for boiled and nondeaerated water ( l a ) . A hysteresis loop has been observed for water flow through porous Kel-F in which decreased flow resistance was obtained after greatly increased pressure differentials had apparently forced water through the pores that were not wetted at low flow rates (9). Similar phenomena are believed to be responsible for the relatively low recovery of oil displacement from porous media. Since the liquids used in the tests in Table I11 were not deaerated,
( ~ 2 0 1 , !OO
Weave
F t /.&fin. 0.10
Chain k l l Plain Plain
2.95
Plain' ' ' Regular twill Plain Chain twill Chain twill Chain twill Chain twill Plain Plain Plain Regular twill Chain twill
=
22
wu 0.056
Air Velocity, Ft./Min.d
1.59
0.32 15.2 0.43 2.03
0.17a 8.3
0.62
1.7 0.14 6.1
3.5a 1.4= 0 , 4Iia
3.65 1 .o 0.75 12.0 1.12 0.78 5.7 0.83
...
K
.. .. 50 ..
Max. Air Velocity; Ft./Min.
... ... 100 ...
25
100
0.33=
40
0.78' 0.0sa
25 50
100 100 100 20 30 60 70 80 100 80 70 70
0.22a 1.11
10
0.28a
20 40 50
5.75 0.bga 0.4Za 2.80 0.436
10 20 50 30 40
it is probable that entrained or dissolved air caused some increased resistance in certain pore size ranges of the materials. Structural changes, such as swelling of the fabric or electrical effects, may also be responsible for some of the large increases in resistance noted. EFFECT O F W E T T I N G AGENT
Inasmuch as the liquid test indicated the possible importance of wetting effects, the influence of a surface active wetting agent was studied by measuring the flow resistance of terry cloth and Vinyon E for an aqueous solution of 0.01 wt. % Sterox CD, a polyoxyethylene ester, having a surface tension of 44.5 dynes per em. as measured by a du Nouy ring-type tensiometer. The viscosity, as measured with an Ostwald-Cannon-Fenske viscosity pipet, was found to be 0.94 cp.
Table I I. Properties of Oils Oil
Specific Gravity, 60e/600
Viscosity, Saybolt Universal Seconds -70° F. looo F. 130' F. 220 565
0.875 0.88
A B C
100 232 400 t o 420
...
0.88
62 119
(Viscositv index = 90)
Table 111.
Summary of Resistance of Filter Media t o Flow of Fluids
Filter Medium Wool felt A Wool felt B Wool-cotton felt Cotton flannel Terry cloth Vinyon A Vinyon B Vinyon C Vinyon D Vinyon E Glass cloth B Fritted glassb Filter paper
Resistance Constant, '
Air
0.139 0.162
0.243 1 .59 0.225
3.47" 1 .40Q 0 . 46Q 0.28" 5.7a 2.7ga
... 0.43=
Water
0:393a 0.712
...
0.46" 3.125 2.385 0.76" 0.25a
48 6.34
...
...
Oil A
0.23 0.33 0.31 3.66
... ...
0:57 0.16
... ... 33 ...
Approximate value since curve not straight line. Resin bonded, 0.020-inch thick, 50 lb./sq. f t .
June 1954
K
=
* NU
Oil B
Oil C
0.23 0.28 0.24
0.18 0.34 0.32
... ... ... ...
0.44 0.12
...
2.77
...
...
... ...
0.36
.. .. ..
0.28
...
... ...
0.52
Weight, os./sq. yd.
Figure 5.
Effect of Weight on Flow Resistance of Felted Materials Wool felt A Wool felt B S Wool felt C a Wool-cotton felt Z Wool-rayon-cotton felt A Cotton battlng A # Cotton battlng B K 0.84; W 6.0 Dyne1 felt
R
Table IV presents the comparison with water flow, The flow resistance constant k is increased several-fold, an unexpected result. The hydrophobic portion of the Sterox C-D molecule may have an affinity for and be absorbed to the fabric while the more polar head is oriented to the water. This would increase the resistance to water flow either t,hrough molecular attraction forces or by changes in the geometrical shape of the flow passages. The results of these tests indicate that wetting effects are of sub-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1199
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT errors. The curves labeled 11 are for fiox of the same fluicis through Vinyon D, a woven fahric. The initiation of a transition from viscous to hrbulent flow n-it,h increase in u p / p or Reynolds number for the air and ivater curves is Been as a change in the slope. Further research is necessary to arrive at, a general correlation of the resistance of filter media to the flow of fluids inasmuch as the resistance seems to be a function of several complex and litt,le understood factors. To accomplish this satisfact,orily, careful control of surface energy relationehips, aeration of the liquids used and their time of contact with the fabric will be necessary. SUMMARY
Figure 6.
In general the flow resistance of felted materials may he cspressed by a modification of Darcy's law or Equation 2, the proportionality constant k of which is presented and correlated with fabric weight for the flow of air, water, and oils through several typical felts. Similar constants represent approximate viscous flow resistances for woven fabrics; however, the onset of fluid t,urbulenceoccurs a t lower fluid velocities than for t,he felted materials and consequently the resistance to fiow deviatep from the viscous flow equation. 1Iuch of the water data exhibit markedly increased v a l u e of k conipared to the air data, and the oil data exhibit' somewhat increased .i-alues of k . The deviations appear to be due to wetting phenomena and also to aerat,ion effects in the liquids. Tests with a met,ting agent added to water exhibit a several fold in."', Ft. - I crease in resist'ance to f l o ~for bot'h a Tiriyon cloth and t.erry Modified Type of Friction Factor vs. Reynolds cloth. The transition from laminar t,o turbulent flow is presented by Number a modified plot of friction factor versus Reynolds number for a Oil typical Vinyon \\-oven cloth. S o transition M-as found for felts Air Water A B C E. Wool felt m A r + in the range of fluid velocities investigated. D. Vinyon + . t + * ACKNOWLEDGMENT
stantial influence in determining the flow resistance of liquids and cannot be neglected. Further analysis requires more fundamental research on this interesting phenomenon.
The authors gratefully aclinoxledgr the courtesy of the Dollinger Corp. in allowing the releaPe of these data. NOMENCLATURE
Table I V .
Effect of Wetting Agent
Resistance Constant Water 0.01 "& Filter Kater Sterox CDa hIedium 0.46 0.96b Terry cloth 122 48 Vinyon E Surface tenaion = 44.5 dynedoin a t 20' C . Approximate value since curve not a straight line
+
(1
b
pressure drop across filter media irichPb of water in Equation 2 LJ = superficial linear fluid velocity, ft.,'min based on area of sample tube in Equation 2 9 = fluid viscosity, cp., in Equation 2 k = proportionality or resifitance constant in Equation 2 p = fluid density -SP
=
~
LITERATURE CITED
(1) -4ni, SOC. 5Iech. Engrs., 29 15'.
CORRELATION OF FLUID PROPERTIES
While Equation 2 should correlate the effect of fluid viscosity and velocity for fluid motion in viscous flow which is independent of density, it gradually becomes invalid for increasing turbulence of inertial effeck The fluid flow data for a typical felt and woven cloth have ~ ~ 1 p t ' p . This is esbeen plot,ted in Figure 6 as - ~ P / p u versus sentially a friction factor versus Reynolds number plot in 7r.hich the geometry characterizing the filt,er media has been omitted bccause the geometrical factors are not clearly understood for the filter media. Consequently each mat,erial should exhibit a separat,e curve for all fluids. The curves labeled B for the flow of air, water, and three oils through wool felt B have slopes of -1 and therefore obey the viscous flow equation. Deviations from a single line are believed due to wetting effects and experimental
1200
39th St.. Xew-York. Special Research Comm. on Fluid Meters, "Fluid Meters, Their Selection and Installation," 1933. ( 2 ) Backer, S.,Teztile Research J . , 21, 703 (1951). (3) Brownell, L. E., and Katz, D. L . , Ciitm. E n y . Proyr., 43, 537 (1947). (4) Cenco A'ews Chats, 78, 25 (1953). (5) Cornell, D., and Kata, D. L., IND. EXG.C H m f . , 45, 2145 (1953). (6) Ergun, S., Chem. Eng. Prog~.,48y89 (1952). (7) Iberall, -k. S.,J . Research n'atl. Bur. Standards, 45, 398 (1950). (8) Morcom, A. R., T r a n s . Inst. Chem. Enyrs. ( L o n d o n ) , 24, 30 (1946). (9) Porous Plastic Filter Co., Glen Cove, N. Y., Release S o . T-103. (10) Rainard, L. W., Teslile Research J . , 17, 167 (1947). (11) Schiefer, H. F., and Boyland, P. A I . , J . Research N a t l . Bwr. Standards, 28, 637 (1942). (12) Souers, R. C., and Binder, R. C., Trans. Am. SOC.Mech. En,g., 74, 837 (1952). RECEIVED for review November 33, 1953.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ACCEPTEDApril 12, 1954.
Vol. 46, No. 6
