August, 1931

RUN

31

32a 32b 32 av.

33a 33b 33 av.

34a 34b 34 av.

41 42 43 44 45

51 52 53 54 55

61 62 63 64 65

71 72 73 74

RUN.

112 113 114 115

1230 124a 1250 1260

P1 Atm.

1 .0

1 .50 4 .84

2 .07 4 .98

2.96 5.15

1 .0 1 . 0 1 . 0 5 1 .50 1.81

1.0 1 .0 1 .05 1 .50 1 .82

1 .0 1 . 0 1 .26 1 .68 2 .01

1 .0 1 .4 1.81 3 .22

P I Afm.

1 .41 1.82 3 .28 4.98

1 .22 1.67 7 .12 7 .77

P2 . I lm .

1 . 0

1 .0 4 .70

1 .0 4.70

1 . 3 5 4.40

1 .0 1 . 0 1 . 0 1.35 1 . 5 5

1 . 0 1 . 0 1 .0 1 .35 1.54

1 . 0 1 . 0 1 . 0 1 .35 1 . 5 1

1.0 1 . 0 1 . 0 2.51

PZ Atm.

1 . 0 1 . 0 1.14 1 .41

1 . 0 1 .0 7.02 7.45

P ni

.A im .

1.0

1 .25 4.77

1.54 4.84

2 .16 4 .78

1 . 0 1 . 0 1 .03 1 .43 1 .68

1 .0 1 .0 1 .03 1 .43 1.68

1 . 0 1 . 0 1.13 1 .42 1.76

1 . 0 1 .2 1 .41 2.87

P m At?%

1.20 1.41 2.21 3.20

1.11 1.34 7.07 7 .61

INDUSTRIAL A N D ENGINEERING CHEMISTRY

Table 11-Present Data, 3-Inch Tube, L = 3.79 Feet (Conlinued) AP,Pm __ p m A P .-

A P L L T , 2 G In. n?o Lbs./sq. f t . / s e c

Granules, D = 0.125 Inch, A i = 0.86

70 18 .5

184 61.0 51.7 65 .0

63 .0

437 178.0 120 153.0

165.0

655 :374.0 305 :384 0

:379

Porcelain Balls,

1 .10 370 0.0216

3.75 370 0.0216

9 .85 369 0.0216

22 .8 366 0.0215

D = 0.9 Inch, A( = 0.51 3.0 0 . 8 0.046 380 0.0218 9 .55 2 . 5 0.145 380 0.0218

21 .8 5.9 0.344 377 0,0218 45 .5 17 .2 1 .01 375 0.0217 66.6 29.6 1.74 374 0.0217

Zinc Balls. D = 1.0 Inch. A t = 0.50 . . 2 . 1 0 .55 0.032 374 0.0217 7 . 1 1.88 0.11 374 0.0217

17 7 4 82 0.285 373 0.0217 36 .8 13 .9 0.826 370 0.0216 55 24.4 1.46 368 0.0216

Pebbles, D = 0.56 Inch, A/ = 0.59 10.0 2 .6 0.151 378 0.0218 28.6 7 . 6 0.44 378 0.0218 64 19 .1 1.11 378 0.0218

127 47 .5 2.79 375 0.0217 180 83 .5 4.93 373 0.0217 Pellets, D = 13.188 Inch, Af = 0.79 (Apparent Sp. Gr., 1.1)

43.5 1 1 . 5 0.675 375 0,0217 122.5 38 .8 2 .28 375 0.0217 270 100 5.90 374 0.0217 307 232 13.7 372 0.0217

Table IIA--Present Data, ll/r-Inch Tube, L - 4.5 Feet A P . P m p& --

AP L L Tm 2

0.24

0 .46

0 .77

1 .25

0 .24 0.46 0 .76 1 .24 1 .59

0.24 0.46 0 .76 1 .24 1.59

0.24 0 .46 0.76 1.24 1 .59

0.24 0 .46 0 .76 1 .24

G In. H20 Lbs./sq. f f . /sec

Pellets, D = 0.375 Inch, Af = 0.55 147 39 .2 2 .05 420 0.023 1 .10 332 104 5.51 415 0.023 1.8 872 428 23.0 410 0.023 3.9

1453 1035 56 .3 405 0.023 6 . 1 Pellets, D - 0.188 Inch, A/ = 0.66 (Apparent Sp. Gr., 1.1)

88 .5 21 .8 1.60 300 0.019 0.403 272 81 5.94 300 0.019 0 .84

55 86 .5 6 . 3 5 300 0.019 0.83 108 183 13 .4 300 0.019 1 .24

f . .-lt

16.6

15.5

14 .5

12 .7

5.05 4 . 3 3 .74 4 . 1 4 . 3

3 . 9 3 . 6 5 3.44 3 .74 4.02

10 .2 8 . 2 7 . 5 7 .1 7 .6

15 .3 14 .1 13 .4 11 .7

f . A t

4.44 4 .45 3.96 3.95

1 3 . 5 11.0 12.0 11 .4

f

19 .3

18 .0

16.9

14 .8

9 . 9 8 . 4 7 .4 8.1 8 .4

7 . 8 7 . 3 6 . 9 7 . 5 8 . 0 5

17 .3 13 .9 12.7 12 .0 12.9

19 .4 17 .9 16 .9 14 .8

f

8.1 8.1 7 .2 7 .2

20 .5 16.7 18.0 17 .3

919

dG - (r

17’7

330

552

900

1230 2360 3900 6380 8180

1370 2630 4340 7100 9120

765 1470 2420 3960 5080

258 485 820

1330

5 P

2220 3640 7900

12350

49 5 1030 1020 1520

111-Relationship between Heat Transfer and Pressure Drop’ Allan P. Colburn and W. Julian King

E. 1. DU POST D E h-EMOURS A N D COMPANY, EXPERIMENT4L STATION, WILMINGTON, DEL., AND ENGINEERING GENERAL DEPARTMENT, GENERAL ELECTRIC COMPANY, SCHENECTADY, N. Y.

For turbulent flow of gases in empty tubes, heat- pressure drop, but in a regular manner as shown by Figure 5. From the curves given it seems possible that the heat-transfer coefficients for almost any type of baffle or packing can be estimated if the pressure drop is deter-

transfer coefficients vary with the 0.44th power of pressure drop as the velocity is increased. The introduction of baffles or packing into a tube increases the heat transfer to a somewhat less extent than the 0.44th power of mined.

..............

M ‘ANY cases arise where it is desirable to increase the heat-transfer rate to or from a gas passing through a tube and the method used has often been the intro-

duction of baffles or “turbulence promoters.” Such a means increases the pressure drop and the question has been raised as to whether this method of increasing the heat-transfer co- efficient is as efficient with respect to the pressure drop as by increasing the mass velocity through the tube.

Apparently the only data in the literature where heat-trans- fer coefficients and pressure drops were measured for different

1 Contribution No. 62 from the Experimental Station of E. I. du Pont de Nemours and Co.

types of turbulence promoters are those of Royds (2), who investigated the effect of turbulence promoters, which he called “retarders,” in a 2 5/s2-in~h tube 7 feet long. Twisted spiral retarders of a different number of twists were used. Royds found that the effect of the number of twists was small, up to one in 20 inches, and that more turns resulted in in- creases in both heat transfer and pressure drop. While his heat-transfer coefficients seem of the accepted order of magni- tude, his pressure drops are much lower than would be calcu- lated for the frictional resistance. As will be shown later, this is doubtless due to the decrease in kinetic energy of the gas as it is cooled, since the gas entered the tube a t temperatures

Vol. 23, No. 8

order to minimize heat transfer between the water coil and the air in the room. Surface temperatures were measured on the outside of the tube a t five positions along its length by copper-constantan thermocouples. These were imbedded in

920 INDUSTRIAL A N D ENGINEERING CHEMISTRY

from 250' to 500" C. and the tube was maintained cold by water cooling. Since sufficient data are not available in Royds' book to make this correction, it is not possible to make a quantitative comparison of results.

COOLING TEMPERATURE

TO DRAFT G U E

- LORIFICE PLATE 1 "OLES FOR %85&%" MEASURING AIR TEMP.

Figure 1-Apparatus Used to Investigate Heat Transfer and Pressure Drop in Baffled Tube

To determine the relationship between heat transfer and pressure drop for various kinds of turbulence promoters, the General Electric Company has carried out an extensive set of experiments. At the same time, the du Pont Company has investigated heat transfer and pressure drop in packed tubes. It was thought by the authors that a general correlation of these two sets of data would do much toward developing a general relationship between heat transfer and pressure drop for any type of tube filling.

Experimental Study of Turbulence Promoters

The experimental apparatus used in this investigation con- sisted of a %foot length of 2 6/s-inch steel tube cooled by water in a '/d-inch copper coil soldered around the tube. Air was supplied from a blower, metered by a sharp edge orifice, heated by electric coils in a furnace, well mixed in a special chamber, passed through the tube, and again mixed as shown by Figure 1. The auxiliary coils shown were used to maintain the outer shell of the mixing chamber connections (insulated from an inner guide tube by an air space) a t the same temperature as the cooling tube to minimize the conduction of heat along the metal. The external heating coils on the mixing cham- bers were used to compensate for radiation losses.

Temperatures of the cooling water were measured with mercury thermometers, and the inlet temperature kept as much below room temperature as the outlet was above, in

f

2

3

9

Figure I-Spiral Barnes for Promoting Heat Transfer i n Tubes 1-1-foot steel spiral 7-inch pitch 2-3-foot steel spiral 8-inch pitch 3-%foot steel spiral 7-inch pitch 4-Small steel spiral 4-inch pitch 5-Small steel spiral 3-inch pitch 6-Small steel spiral Z'/r-inch pitch 7-Copper spiral IVe-inch pitch 8-Copper spiral 3-inch pitch 9-Propeller-shaped brass baffles

IO-Copper wire spirals

the solder between coils a t equally spaced points along the the tube. The leads were bared and shellacked to the solder for several inches around the tube to prevent loss of heat from the junction by conduction through the wires.

MASS M L O C I W

Figure 3-Heat-Transfer C,oefficients for Turbulence Pro- moters at Different Mass Velocities

(Numbers on lines refer t o types of promoter shown by Figure 2)

The temperature of the air a t the entrance to the experi- mental tube was measured by a high velocity thermocouple of the type recommended by Haslam and Chappell (1). This was used to indicate the temperature a t regularly spaced points across a diameter from which an average was computed. It was assumed that an arithmetic average of these values would be satisfactory a t the entrance position since there was not a very great temperature difference a t different points. The necessity of using a high-velocity thermocouple was indicated by preliminary tests during which, under the same conditions, the high velocity thermocouple read 412" C., a plain bare thermocouple read 397" C., and an uncovered mercury thermometer registered 366" C. At the outlet the average gas temperature in the mixing chamber was used.

Heat-transfer coefficients were calculated from the heat lost by the air, the surface area of the pipe, and the logarithmic mean temperature difference between the air and the tube wall.

The pressure drop through the tube wa8 measured a t the points shown in Figure 1 by means of an inclined draft gage.

Various types of baffles were used in the study, as shown by Figure 2.

In checking the observed values of pressure drop through

August, 1931 I N D U S T R I A L AND ENGINEERING CHEMISTRY 921

Table I--Data on Turbulence Promoters

h APobsd. APoor. L RUN DEVICE m tin tout Atin Atout QI twin twout 111 Q2 G c. c. c. c. c. c. In. HzO

Empty 3 3 3 ?

55.5 56.0 82.2

319 317 315

224 174 192 145 188 191 203 157 37 66 77 78

114 79

128 198 211 124 77

108 158 141 111 64

190 61

172 78

241 224 134

211 163 181 134 176 178 190 145 26 56 66 66

102 68

112 187 199 109 65

194 143 122 QQ

1305 1975 2500 1370 1670 1630 2120 1150

9 . 5 9 . 3

10.2 10.0 10.6 10.1 10.1 10.0 10.8 9 . 5 9 . 5 9 .5

11.0 10.5 10 10 10 10.8 10.8 10.0

29.9 29.7 30.5 31.1 30 30.4 30.7 31.3 31.2 30.0 30.0 51.0

6 6 . 3 96.5

125.5 70.8 82.8 84.8

107.0 54.7 85.6

181.5 173.0 97.5 83.5 4 4 . 3

111.0 53.4 68.5

116.2 55.1 81.7

120.4 77 .7 46 .0 26 .9

126.5 33.3

185.8 20.0

107.0 70.7

127.0

0.418 0.415 0.609 0.255 0.404 0.41 0.62 0.236 0.199 0.443 0.436 0.502 0.399 0.192 0.587 0.409 0.597 0.592 0.210 0.403 0.601 0.410 0.198 0.601 0.598 0.601 0.601 0.601 0.601 0.611 0.637

2 . 6 4 .42 5.36 3.53 3.52 3.71 4.68 2.81 7.56

12.60 11.34 14.11 7.73 5.18

10.39 3.50 4.4s

10.42 5.82 8.1 8.1 6 . 2 5 4 .05 6.55 8 . 9 7 8.79

11.50 4.26 4.77 4 . 4 3

10.63

0.004 0,028 0.046 0.013 0.017 0.018 0,032 0,008 0.45 2 .00 2 .20 2.35 0.21 0.058 0.438 0 .02 0.05 0.52 0,084 0.272 0,392 0.190 0.05 0 .28 0 . 4 4 5 0.34 0 .52 0 .025 0.031 0,009 0 ,442

0.0085 0.116 0.035 0.495 0.058 0.807 0.016 0.237 0.0225 0.314 0.0234 0.328 0.0426 0.595 0.0102 0.148 0.453 7.45 2.00 35.5 2 .20 38.4 2 .35 40.8 0.219 3.31 0,059 0.925 0.456 6 .72 0.025 0.347 0.060 0.82 0 .54 8.12 0.087 1.61 0.281 4 . 2 5 0.481 5 . 8 0.198 2 . 9 0.052 0.79 0.31 6.15 0 .464 6.05 0.345 7 . 0 0.546 6 . 9 5 0.028 0.56 0.046 0.57 0.0177 0.24 0 . 4 6 2 6 . 8

34.5 54.5 55,5 84.0 32.0 2 6 . 8 59.8 58.8 68 .0 5 4 . 0 26.0 79.5 55.5 81.0 81.2 28.5

312 310 305 302 311 316 319 317 317 315 321 314 317 308 312 315 318 318 307 107 390 117 438 108 392

8 9

10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

4060 2600 44

45.7 45.0 40.5 41.5 43.0 42

9 10 10 10 10 10 8 8 3

5 4 . 6 44 39 43 .2 41.8 41.0 43.8 42.5 4 2 . 5 41.6

e;.; J J . J 26.8 81.5 8 1 . 4 81.5 81.5 81.5 81,5 8 2 . 5 82.2

11 11 11.5 10.5 9 .2

10 10 12.3 9 . 3

2430 1300 865

4000 1180 5350 615

3040 1790 3740

._ 53

177 48

157 62

227 208 113

41.0 39.0 42 .8

312 318

11 11

the empty tube against predicted values from the Fanning equation, it was found that the observed values were quite low and that the discrepancy could be quantitatively ex- plained by the difference in kinetic energy of the gas entering and leaving the tube. Since the heat-transfer coefficient should properly be correlated against the frictional resistance, the observed values of pressure drop have therefore been corrected for the kinetic energy change of the gas by Equation 2, below.

An approximate integration of Bernoulli's theorem gives the following expression for the pressure drop due to difference in kinetic energies a t positions 1 and 2:

results showed that small cores were of little help in increasing the heat-transfer rates, but the data were too inaccurate to enable exact general conclusions to be drawn. It should be possible, however, to evaluate the relationships theoretically by assuming that the heat transfer and pressure drop in a cored tube would be the same as in an empty tube of the same hydraulic radius, and this procedure is carried out below.

Experimental Study of Packed Tubes

An investigation of the heat transfer between a tube filled with various types of packing and a gas flowing through, and of the concurrent pressure drop, was described in the previous sections. To relate values of heat-transfer coefficient to pressure drops under comparable conditions, results have been taken from Figure 2 of Part I and Figure 3 of Part I1 at mass velocities of 0.5, 1.0, and 2 pounds per square foot per second; these data are given in Table I1 and are plotted on Figure 5 .

Table 11-Data on Packed Tubes - (pm AP/L)--? ---- h/Cp----

where AP = pressure drop, pa". = average density of the fluid, u = linear velocity of the fluid, and g = acceleration of gravity. This equation for air at atmospheric pressure becomes:

= 0.00027G2(Tz - Ti) (2) 0.000135 Gz (T22 - Tis) T8".

AP =

where AP = inches of water, G = mass velocity in pounds per second per square foot, and T = temperature in OK. Since the gas is cooled in the tube, the kinetic energy is greater at entrance than exit, so that the observed pressure drop is the difference between frictional resistance and kinetic energy change. Values of the kinetic energy correction were cal- culated by the above equation for all of the results and added to the observed pressure drops to obtain the correct values of frictional resistance. The original and corrected data are given in Table I.

Plots have been made of h/cp vs. G and of pAP/L vs. G as shown by Figures 3 and 4 where AP represents the corrected frictional resistance. Straight lines have been drawn through the points for each type of baffle; values have been taken from these lines for G = 0.5 and G = 1, and plotted on Figure 5. To keep the results general, in order to apply to any gas, heat-transfer rates have been reported as values of h/c, and pressure drops as p AP/L . CORED TUBES-A type of promoter, not investigated with

the other turbulence promoters, is simply a centrally located cylindrical core in the tube. Following the investigation of packed tubes referred to below, some data were taken of heat transfer and pressure drop for cases of cored tubes. The

PACKING l/a-inch broken solids '/la-inch pellets 0.9-inch balls 1.0-inch balls Z/le-inch pellets l/r-inch broken solids a/a-inch pellets @/is-inch pebbles

G = 0.5 1.0 2 .0 G = 0.5 1.0 2 . 0 4 . 3 2 . 6 0.18 0.15 3.1 2 . 2 5 1.0 0.52

15.5 9 . 5 0.65 0.54

11.3 8.1 3 .6 1.87

57 34

42.0 29.5 13.0 6.7

2.35 1.93

45.5 80.5 5 4 . 4 97.0 59.0 104 59.0 104 59.5 105 63.5 112 69.0 123 71.0 127

143.0 171.0 185 185 187 198 217 226

Discussion

EMPTY TuBEs-The relation between heat transfer and pressure drop for empty tubes can be determined from the following general equations (under conditions of turbulent flow) :

For heat transfer, the Reynolds equation gives:

1 h = - f c p G 2

For pressure drop, the Fanning equation is

(3)

2fLGz a d

AP = - (4)

(in consistent units) where h = heat-transfer coefficient, f = friction factor, G = mass velocity, AP = pressure drop in

922 INDUSTRIAL ,4ND ENGINEERING CHEMISTRY Vol. 23, So. 8

Figure &Pressure Drop for Turbulence Promoters at Different Mass Velocities

(Numbers on lines refer to types of promoter shown by Figure 2)

I.

weight u n i t s per u n i t a r ea , L = length of tube, p = density, g = accel- eration of gravity, and d = inside di- a m e t e r of t ube . The friction factor m a y be approxi - m a t e d over t h e usual range by the equation

f = 0.06

wherep = absolute viscosity (in consist- ent units).

Substituting for f and solving Equa- tions 3 and 4 for h i n t e rms of A P gives (in consistent units) :

h - = 0,077 pO.11 d0.33

F o r gases po.l1 is essentially a con- stant so that Equa- tion 6 can be sim- plified. Using cus- t o m a r y u n i t s , E q u a t i o n 6 be- comes:

h - = 341 DO.33

CV

( ! ? y ) 0 . 4 4 (7)

where h = P. c. u. per square foot per hour per O C. (equivalent to B. t. u. per square foot per hour per O F.), D = inches, p = pounds per cubic foot, AP = inches of water, and L = feet.

Plots of Equation 7 for diameters of 1 and 3 inches are given by Figure 5. This equation and the plot show that, for a given size of pipe, as the mass velocity is increased the heat-transfer rate goes up with 0.44th power of the pressure drop.

For conditions of a constant rate of mass flow per tube, the velocity may also be increased by decreasing the tube size. Under these circumstances the relationship between heat transfer and pressure drop becomes:

where m = total mass flow per tube in pounds per hour. Thus, an increase of pressure drop due to the use of a smaller pipe does not cause so great an increase in heat transfer as th2; same pressure drop increase due to a higher rate of flow in the original tube.

CORED TUBES-FOr tubes containing centrally located cylindrical cores, Equation 7 applies if D is defined as the equivalent diameter or clearance. For a given mass rate through an empty tube or annulus, an increase in velocity caused by inserting a core in the pipe gives results represented by the following equation:

.

where m = total mass flow per tube in pounds per hour, d, = diameter of pipe, and d, = diameter of core. Thus the heat-transfer coefficient increases even less rapidly with pressure drop, where the velocity is increased by coring the tube, than by decreasing the tube size, which indicates that this procedure is therefore less desirable.

PACKED AND BAFFLED TuBE&The data on heat transfer and pressure drop in packed and in baffled tubes are shown plotted on Figure 5. Two important conclusions may be drawn: first, that heat-transfer coefficients can be materially increased by use of baffles, etc., and second, that values for almost m y type of packing or baffling lies on the same curve of heat transfer us. pressure drop, so that if the pressure

G.05 I 2 - - - MTA mR PICKED TUBES e I A

EAT& FOR EAUFFLLD TUBES 0 0

om1 001 01 I 10 I PRESSURE DROP.

Figure 5-Relationship between Heat-Transfer Coefficient and Pressure Drop i n Empty, Baffled, and Packed 'Pubes

August, 1931 INDUSTRIAL A N D ENGINEERING CHEMISTRY 923

drop for a new type of baffle is known the heat-transfer coeffi- cient can be estimated. It is interesting to notice that the baffles causing only slight increases in pressure drop give al- most ?s high heat-transfer coefficients as would be obtained for the same pressure drop through the empty tube. While these curves are drawn for a 3-inch pipe only, curves for other sizes may be estimated parallel to these and at distances apart determined by lines for the empty tubes constructed from Equation 7. From inspection of the curves it seems that the maximum increase in heat-transfer coefficient ‘that can be obtained without too great a rise in pressure drop is about sixfold, under which conditions the pressure drop is 200 times as great. The same increase in heat transfer might be ob- tained by raising the velocity in the empty tube, in which case the pressure drop would be 60 times the original.

Nomenclature

m = air rate, pounds per hour t l , = temperature of gas a t inlet

= temperature of gas a t outlet t.d in = temperature of water a t inlet tw = temperature of water a t outlet & = temperature difference between gas and tube

surface at gas inlet

Atout = temperature difference between gas and tube

Q1 = heat given up by air, P. c. u. per hour -w = water rate, pounds per hour

= heat gained by water, P. c. u. per hour = mass velocity, pounds per square foot per second = heat-transfer coeofficient, P. c. u. per square foot h

APobad. = observed pressure drop, inches of water 4PCor. = pressure drop due to frictional resistance, obtained

= average gas density, pounds per cubic foot P = tube length, feet 1P = pressure drop, inches of water CP = specific heat of gas

surface a t gas outlet

P per hour per C.

from IPobad. by correcting for kinetic energy

Acknowledgment

The writers wish to acknowledge the suggestions and assistance of T. H. Chilton and W. H. McAdams, and the assistance of R. S. Thurston and A. T. Sinks, who carried out the experimental work on turbulence promoters.

Literature Cited

(1) Haslam and Chappell, IND. ENG. CHEM., 17, 402 (1925). (2) Royds, “Heat Transmission by Radiation, Conduction and Convection,”

p 190, Constable, 1921.

Dependence of Reaction Velocity upon Surface and Agitation

I-Theoretical Consideration’ A. VI‘. Hixsonl a n d J. H. Crowel13

DEP 4 R T M E U T OF CHEMICAL EXGINEERING, COLUMBIA UNIVERSITY, NEW YORK, N. Y.

HE problems of agita- tion have long been a

This research had for i t s purposes a general in- moved with a violent irregu- vestigation of t h e subject of agi ta t ion a n d t h e estab- lar action, a stirring up, dis- T source of much trouble l ishment of a basis which might serve for a quant i ta - turbance of tranquility, or a

for the chemist and chemical tive comparison of different agitations. Since t h e commotion. The important engineer on accoun t of the velocity of a heterogeneous reaction is generally qui te features in this definition are great lack of knowledge con- sensitive to the effect of agitation, its use was con- violence and irregularity. cern ing both their qualita- sidered in this connection. However, in t h e use of a Since the mind cannot con- tive and q u a n t i t a t i v e as- heterogeneous reaction for such a purpose, t h e surface ceive of agitation without the pects. In fact, agitation is effects are equally impor tan t and had, therefore, to be presence of matter, it may be even a difficult s u b j ec t to studied as a part of the original problem. thought of as one of the at- talk about spec i f ica l ly be- A detailed analysis of t h e vague idea of agitation tributes of matter. There- cause the terms that are used has been m a d e wi th an a t t e m p t towards breaking fore, when the three states to describe it are so general it down into its final fundamenta l elements. of matter are considered, six and indefinite in their appli- A new law ( the cube root law) has been derived f r o m possible binary combinations cation. In this research an theoretical considerations in which t h e velocity of are obtained-that is, solid- effort i s made t o l ay t h e solution of a solid in a liquid is expressed as a funct ion solid, liquid-liquid, gas-gas, foundation for a more logi- of the surface a n d the concentration. solid-liquid, liquid-gas, and cal and practical method of solid-gas. In addition, the attack. The problem whose investigation is here proposed more complex solid-liquid-gas system could be considered, but is, “HOW is it possible to introduce a practical and numeri- in general, it is found that a great many agitations are of the cal evaluation of the phenomena that are produced in a binary kind. This division is based upon a consideration system undergoing agitation?” of the uses of agitation in the industry, where the purposes

Due to the extreme indefiniteness of the entire subject, for which it is applied may be placed in the following classi- it was found that the adoption of a very generalized view- fication: point gave many advantages in correlating the widely diverse a uniform distribution situations where agitation occurs. or mixing of the materials used, or to increase the rate at which

Webster defines agitation as a state of being agitated or this distribution is taking place. To keep the distribution of chemicals undergoing a reac-

From a dissertation presented by Mr. tion, or obtained in one, in a satisfactory condition so that Crowell to the Faculty of Pure Science, Columbia University, in partial undesirable side reactions are avoided while the main reaction fulfilment of the requirements for the degree of doctor of philosophy, proceeds in the direction desired. June, 1930. To maintain a uniform distribution or elimination of

heat, thereby preventing local overheating or overcooling. To increase the specific surfsce by separating the phases

(1) .To procure and

(2) I Received February 21, 1931.

(3)

(4) 2 Professor of chemical engineering. 8 Present address, The Selden Company, Pittsburgh, Pa.