Viscositv of Ethvlene and of Carbon ioxide under Pressure J
J
The viscosity of ethylene vapor was measured at 40' C. and at pressures from 4.40 to 137.1 atmospheres absolute. The vapor was forced through a glass capillary by the weight of a pellet of mercury and the time of fall of the pellet determined. The viscometer was calibrated, independent of the results on any other gas, but the calibration was checked by measurements on carbon dioxide vapor. The values reported are averages of measurements made with several sizes of pellet. The maximum probable error is 2 per cent below and 4 per cent above 89 atmospheres. The viscosities of these gases may be used in the design of equipment for high-pressure processes. By supporting the general correlation of the effect of pressure on the viscosity of gases presented earlier ( I ) , they serve as a basis for predicting the viscosity of other gases at high pressures.
E. W. COMINGS University of Illinois, Urbana, 111.
R. S . EGLY Commercial Solvents Corporation, Terre Haute, Ind.
METHOD of predicting the viscosity of pure gases and vapors a t elevated pressures was described in a previous article ( 1 ) . The data available in the literature were used in developing this method. No measurements of gas viscosity a t high pressures were available in the range of reduced temperatures from 1.03 t o 1.63. Since the effect of pressure on the viscosity varies greatly in this temperature range, viscosity measurements have been made on ethylene in an apparatus of the capillary flow tlype. This apparatus is a modification of the design used by Rank i n e (9) a n d l a t e r e m p l o y e d a t higher pressures by Nasini and Pastonesi (7). The instrument was calibrated without reference to any other gas,
A
Description of Apparatus The viscometer was constructed of Pyrex glass as shown in Figure 1. It consisted of two parallel tubes connected at the ends. The tube on one side was a capillary, 86.3 cm. long; that on the other side had a 5-mm. outside diameter and a 3-mm. bore. During operation the instrument occupied a vertical position, and a m e r c u r y p e l l e t descended in the larger tube, forcing the gas or vapor up through the capillary. Two tungsten wires were carefully placed in the wall of the larger tube near the top in such a way as to cause very little distortion of the tube bore. Two similar wires were placed near
tlhe other end of the tube, and each of these pairs was used t o indicate the passage of the mercury pellet. When the pellet closed the circuit through a pair of these wires, a current of a few milliamperes caused a relay to operate and close a circuit in which the current was interrupted every tenth second by a commutator attached to a synchronous motor. These impulses were counted by a solenoid-operated counter. JT7henthe mercury pellet made contact with the lower pair of wires, a relay stopped the counter. The time of fall of the mercury pellet was then read from the counter in tenth seconds. The glass viscometer was placed in a steel bomb, and an external pressure of nitrogen maintained to balance the pressure of the test sample within the instrument. I n this way the difference between the internal and external pressures was kept below 3.4 atmospheres (50 pounds per square inch), even during periods of pressure adjustment. A side tube a t one end led to a ground-glass head. This head was held against a flat steel surface by an aluminum ring. A thin gasket of gum rubber was placed between the glass and steel surfaces. This connection to the sample line, similar to that used by Cummings (W), is shown in Figure 1. It led to the sample compressor and the pressure gages. A metal guard held the instrument in the bomb and prevented it from jarring against the steel walls. The head of the bomb at one end was provided with one pressure-tight opening for the sample line, four for wires to two thermocouples, and two for electrical connections to the tungsten contact wires. The other head proFIGURE1. GLASS VISCOME- vided for the two wires of a third thermocouple. The three TER, SHOWING CONNECTION TO thermocouples (iron-constantan) were used to measure the SAMPLE LIN~ 1224
October, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
1225
the mercury up the cylinder was indicated with three electrical contacts in its walls and two in the head. I n operation, mercury was forced into this cylinder from a second cylinder by nitrogen under pressure. The nitrogen for the latter cylinder and for the viscometer bomb was compressed by a threestage Rix compressor with provision for returning it to a gas holder and recompressing. The temperature of the viscometer was held constant by an automatic temperature controller to ~ 0 . 5 C., " and this was improved by manual adjustment during the test period so that the variation was seldom more than *0.3' C. The temperature was measured by the calibrated iron-constantan thermocouples with a Leeds & Northrup type-K potentiometer and a type-R galvanometer. A view of the front panel assembly is shown in Figure 6. Lines carrying the test sample were electrically heated to prevent condensation a t the elevated pressures.
Calibration of Viscometer
,
FIGURE 2. BOMBASSEMBLED WITH GLASSVISCOMETER INSIDE, SHOWING METHODOF INVERTING ABOUT THE] MID-POINT The flexible ooila of tubing for the sample and nitrogen are in the insulated enclosure baok of the bomb.
temperature of the nitrogen surrounding the viscometer a t points near each end and the middle of the viscometer. The nitrogen was introduced through a connection in the side of the bomb. The temperature of the bomb was controlled by wrapping it with a single main resistance wire augmented by three control coils equally spaced over each third of the length. Each head was also insulated by a hood provided with a main and a control heater winding. The entire bomb was pivoted about its mid-point to permit its rotation through 180'. This allowed the viscometer to be repeatedly inverted for check runs in each direction. The sample line and the nitrogen line were joined to the rest of the system through coils of smalldiameter flexible tubing; thus it was unnecessary to break any connections when the bomb was rotated. The bomb assembly is shown in Figures 2 and 3. A flow diagram of the complete apparatus is shown in Figure 4. The pressure in the viscometer was measured by two 12-inch-diameter, Bourdon-type pressure gages, one of which covered the range from 0 to 1200 pounds per square inch and the other from 1200 t o 3000 pounds. These gages were filled with oil and connected to the sample line through a mercury U-tube. The oil line to the gages was also connected to a dead-weight gage of the type described by Keyes (6). The gages were checked for practically every series of readings a t each pressure. The pressure deviation from a selected value was not more than 1 pound per square inch at pressures below 1000 pounds and generally less than 2, with a maximum of 5 pounds per square inch in the range 1000 t o 2000 pounds. The test sample was compressed to the desired pressure over mercury in a special cylinder designated as the sample compressor. The construction of the head of this cylinder is shown in Figure 5. This head provided for a small clearance volume above the mercury. The progress of
The dimensions of the capillary tube used in the viscometer were determined to .ensure viscous flow and at the same time give a convenient time of fall of the mercury pellet. A selection was made from twenty-five 0.2-mm.-diameter capillaries. Short end sections of the six best tubes were magnified to either 500 or 1000 diameters in a mineralogical microscope and examined to eliminate those with a bore of elliptical cross section. The end sections of the capillary selected had average diameters of 0.230 and 0.241 mm. with a minimum degree of ellipticity. Since the viscosity is nearly proportional to the fourth power of the capillary radius, it waa
FIGURE, 3. BOMBASSEMBLY essential to measure this dimension accurately along the length of the capillary. A small globule of mercury was introduced into the capillary and assumed a length of about 1.5 cm. The tube was mounted in a horizontal cathetometer (see page 1229), and the length of this mercury thread was measured within 0.01 mm. a t numerous positions along the length. The average of the radius raised to the fourth power
1226
INDUSTRIAL AND ENGINEERING CHEMISTRY
pheres) as determined nith five sizes of mercury pellet, is given in Table I.
TABLE I. SUMMARY OF VISCOSITY DATAFOR CARBON DIOXIDEAT 40" C. A.,~,
Pressure, Atm. 1.00 4.40 28.2 48.6 55.5 67.4 79.3 89.5 103.1 137.1 a
Visoosity in Micropoises for Mercury Pellets of Following Weight, in Grams: 2.466 3.857 4.156 4.515 Mean 159' I6i:i 16i:iJ 161 156:i 160.4 174.2 17413 174 172:4 180.4 187.7 183:i 1SQ:i 182 194.9 193.6 . .. 194 ... 212.5 210.3 208:s ... 210 248.1 240.4 249.2 ... 245 . 376.7 . .. 375 867:s 379.5 ... 524.9 507.7 516 .. 672.3 672.7 .. 672
1.614
...
...
...
.
..... __.
... .
Esperimental Procedure
Probable Error, % (10)
Mercury pellets of 1.5 to 5.0 grams were used in the experiments. The mercury was carefully cleaned by distihtion, by washing with nitric acid and water, and then by drying at 120' C. The pellet was first introduccd into the viscometer through the glass head, and the viscometer and bomb were then asscrnbled. The vapor to be tested was admitted to the instrument. The carbon dioxide was a commercial product with a purity of 99.5 per cent; the ethylene was of anesthetic quality, 99.5 per cent pure. They were used as received. The viscometer was evacuated with a pump, and the test gas was forced in from the mercury compressor to a pressure of 4.4 atmospheres. After 20 minutes the instrument was evacuated; this procedure was repeated three times to ensure that the air was thoroughly flushed out. During this time and for the final introduction of the sample, as well as during subsequent adjustments in ressure, the mercury pellet was held in an enrargement a t one end of the viscometer where it did not interfcrc with the flow of the vapor. The temperature and pressure were maintained conqtant for 30 minutes before each series of readings. A series consisted of two to seven mcasurernents of the time of fall of the mercury pdlet in each direction. The maximum deviation from the average of the time of fall measurements was less than 0.5 per cent. All the measurements rcported here were made at 40' C. Sevcral series of measurements were taken at different pressures with one size of mercury pellet. In several cases the series carried out whi!e the pressure was being increased were again checkcd while it was being decreased. After a number of series had been made, the viscometer was removed from the bomb and cleaned thor-
0.5 0.1 0.2 0.6 0.8 2.2 2.6 7.3 0.2
Extrapolated.
DIAGRAM OF APPARATUS FIGURE4. FLOW
was obtained from these measurements by graphical integration similar to the method described by Fisher (4). The ratio L / r 4so determined was 4.540 X I O 9 The volume of the pellet tube between the tungsten contact wires was determined for each direction of fall by filling the tube with mercury and weighing the amount displaced as the mercury was drawn off between the two contacts. These volumes were 3.852 and 3.872 cc. The corresponding distances between the contacts as measured by the horizontal cathetometer were 52.93 and 53.21 em. The viscometer used here is subject to errors at low pressures due to lack of symmetry of the gas volume. Rankine points out that, when the volume swept out by one end of the mercury pellet is symmetrically placed with respect to the remaining volume of the viscometer, the errors involved from this source are negligible at atmospheric pressure. With air in the viscometer containing a 4.5-gram pellet and the side arm open to the atmosphere (giving a n infinite volume on this side of the pellet), calculations indicated that the pellet would fall toward the infinite volume 6.5 per cent more sloivly than toward the other end. The measured time for this case was 6.1 per cent slower. The most unfavorable conditions encountered in the tests may lead t o errors of 0.4 per cent in individual readings. However, the error from this source drops to a negligible 0.01 per cent when the mean fall time, averaged from a reading in each direction, is used. This procedure was followed in interpreting the results. As a check on the calibration the instrument was used to determine the viscosity of carbon dioxide since this has also been determined by Phillips (8) and by Stakelbeck (11). The viscosity of carbon dioxide at 40" C. at pressures from 65 to 2000 pounds per square inch absolute (4.40 to 137.1 atmos-
Vol. 33, No. 10
TABLE 11. EXPERIMENTAL DATAFOR ETHYLEKE AT 40"C. WITH MERCUEY PELLETWEIGHING 2.466 GRAMS End of
Run No. 71
Ahs. Viaoometer Pressure, toward Which Atm. Pellet Fell 4.40 B 4.40 A B 4.40 4.40 4.40 .4 4.40
B"
72
76
75
74
73
28.2 28.2 28.2 28.2 28.2 28.2
B
48.6 48.6 48.6 48.6 48.6 48.6
B
55.5 55.6 55.5 55.5 55.5 55.5 55.5 55.5
B
79.2 79.2 79.3 79.3 79.3 79.3
B
102.9 103.0 103.0 103.1 103.1 103.1
B A
A €3
i:A
: A B
A 4 B A
B A B A
A
B A
B 4
B
A B A
VisoomeJer Temp., C 40.0 40.0 40.0 40.0 40.0 39.9
Falling Time, Sec. 156.2 157.2 157.3 156.8 157.2 156.1
Adjusted Falling Time. Sea. 156.2 157.9 157.3 157.5 157.2 157.1
40.2 40.2 40.1 40.1 40.1 40.1
170.4 169.9 171.5 170.0 170.6 169.9
170.4 170.7 171.5 170.8 170.6 170.7
170.8
40.1 40.1 40.0 40.0 39.9 39.9
188.7 187.2 188.5 186.9 189.3 187.4
188.7 188.1 188.5 187.8 189.3 188.3
188.5
40.2 40.2 40.2 40.1 40.1 40.1 40.1 40.1
200.1 199.0 200.4 198.4 200.0 198.2 199.8 198.2
200.1 199.0 200.4 199.3 200.0 199.1 199.8 199.1
199.6
40.0 40.1 40.2 40.2 40.2 40.1
287.1 285.9 287.5 285.0 288.5 284.4
287.1 287.2 287.5 286.3 288.5 285.7
287.0
89.8 39.9 40.0 40.0 40.0 40 0
484.6 433.5 435.5 435.2 432.4 435.7
434.6 435.5 435.5 437.2 432.4 437.7
435.5
Mean Time, Sec.
167.2
October, 1941
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
oughly with acetone, 95 per cent ethyl alcohol, water, hot sodium dichromate cleaning solution, and finally distilled water until it no longer gave an acid test with litmus. It was dried by warming and evacuatin . Another pelfet of a different weight was introduced and the measurements were repeated at the same pressures. In all, five pellets were used for each vapor.
1227
of the mercury (corrected for gas buoyancy) which is needed to overcome the capillary effects, then the mass which is useful through the action of gravity for overcoming viscou~ drag and end effects is m
(
y
)
--a
From Poiseuille’s equation the mass which will be needed to overcome the viscous drag is
The energy loss due to end effects per unit mass of vapor flowing through the capillary is proportional to the square of the velocity in the capillary. It follows that the effective mass of mercury required to overcome this loss is (3)
FIGURE5. HEADOF SAMPLE COMPRESSOR Combining Equations 1,2,and 3, A representative set of data for ethylene with a single pellet is given in Table 11. The volume of gas displaced by the ellet between the contacts moving toward the end designated was less than that displaced in moving toward end B . The readings of fall time were therefore put on the same basis by multiplying those taken in the A direction by the ratio of the displacements, 3.870/3.852.
2
(4)
Discussion of Results The force of gravity on the mercury pellet serves to overcome the viscous drag of the gas flowing through the capillary in laminar motion. It must also overcome the capillary force between the mercury pellet and the pellet tube since the curvature is distinctly different a t the two ends of the pellet as it moves down the tube. It must also supply the small amount of energy lost in end effects at the capillary and in setting up a parabolic velocity gradient in the capillary. If a is the mass 0
I
I
I
I
I
2
4
0 XI03
8
IO
I/t
I
I
I 2 1 4
VSEC.
FIGURE 7. EXPERIMENTAL DATAFOR ETHYLENE TO DETERMINE CAPILLARITY CONSTANT a
FIGURE 6. FRONT OF PANEL The dead-weight gage is in the foreground with the two 12-inch pressure ga e6 nearT%e bomb by. T h e timer unit is on the table and the Rix compressor t o the ri ht assembly is behind the pane1,on the left I t s shrhft extends througt the panel but is hidden behind the dead-weight gage and allows the bomb to be rotated from the front of t h e panel.
The constant K1 (SV1A/m4g) was evaluated from the measurements described under “Calibration of Viscometer”, and found to be 3.318 x 106. Constants a and IC2 remained to be evaluated from the experimental results. The data were first plotted as m(p, - p ) / p , against l / t a t constant temperature and pressure. Since the term K2p/t2is small a t most and decreases rapidly a t large values of t , these graphs were straight lines with the intercept a a t l / t equal to zero. The data for ethylene plotted in this way are shown in Figure 7. The lines for the several pressures passed practically through a common intercept and indicated that pressure had no consistent effect on the capillary constant a in the pressure range involved in the tests. The data for carbon dioxide produced a similar family of lines intersecting in a single intercept. The value of a for ethylene was 0.13 and that for carbon dioxide 0.09 gram. The data were next plotted with the term [ m ( p , - p/p,) - a]t as ordinate and l / t as abscissa a t constant pressure. This should give
I N D U S T R I A L A N D E N G I N E E R I N G CHEMIST R Y
1228
RESULTSFOR ETHYLENE AT 40" C. TABLE111. EXPERIMENTAL t,
Wt. of Pellet, Grams 1.614
2.466
8.312
4.156
4.780
Abs. Pressure. Atm. 4.40 28.2 48.6 55.5 67.4 79.3 89.5 103.1 137.1 4.40 28.2 48.6 55.5 79.3 103.1 4.40 28.2 48.6 55.5 67.4 4.40 28.2 48.6 55.5 67.4 79.3 89.5 103.1 137.1 4.40 28.2 48.6 55.5 79.3 103.1
No. of Trials
6 6 6 6 6 6 5 6 4 6 6 6
a
6 6 8 7 6 6 4
8
7 6 6 10 6 5
8
6 10 12 6 6 7 6
Mean Falling Time, Sec.
248.1 26.5 0 297 1 313 9 363 0 449.8 548.5 657 842 157.2 170 8 188.5 199.7 287 0 435.5 114.3 122.8 137.8 146.2 167.7 90 6 100.0 114 4 122.2 140.4 177.7 218 261 332 78.3 85.1 96.6 102.6 146.9 215
P,
Density
Grama/
Liter 3.75 23.0 73.5 91 0 128.8 184.0 229.5 207 5 318.0 3.75 23.0 73.5 91.0 184.0 267.5 3.75 23.0 73.5 91.0 128.8 3.75 23.0 73.5 91 .o 128.8 184,O 229.6 267.5 318.0 3.75 23.0 73.5 91.0 128.8 184.0
Vis&aity,
Poises X 106 110.8 118.3 132.0 130.3 160.6 198.1 240.8 287.4 366.8 110.6 120.0 131.9 139.5 199.1 300.1 109.5 117.5 131.4 139.2 159.2 109.8 121.1 138.0 147.2 168.6 212.6 259.8 310.1 392.9 109.6 119.0 134.6 142.7 203.0 295.0
Reynolds Number 28.6 154 393 437 464 433 364 297 216 45.2 235 620 685 676 429 62.9 334 852 938 1012 79.2 398 977 IO61 1141 1022 850 693 511 91.7 476 1186 1304 906 608
mean value a t any pressure (all pellet sizes) was less than 2 per cent, except for ethylene a t 89.5 and 137.1 atmospheres, where the average deviations were 3.8 and 3.4 per cent, respectively. Only two pellet sizes were used a t the latter pressures. Values of the probable error are shown in Table IV. Table I11 includes the Reynolds numbers for the runs on ethylene. These reached a maximum of 1300. I n Figure 8 each of the lines is for a single temperature and pressure. For each line, then, the abscissa. is directly proportional to the Reynolds number. The ordinate is proportional to the viscosity when there are no end effects. The curves therefore indicate the constancy of viscosity over a range of Reynolds numbers.
.
1200
uw
v)
s
w
1000
c,
csI
-
800
E
?IS
e 00
& 28.23
400
4.40
0
straight lines with slopes of K2p and intercepts of KIP. The graph for the ethylene data is shown in Figure 8. The points a t the loner pressures fall on horizontal straight lines which indicate that K 1was zero and the end effects were negligible. The points a t higher pressures do not warrant any other conclusion. This same conclusion could be drawn from the dimensions of the capillary which had a ratio of length to diameter of 3670. The density of carbon dioxide was obtained from the data of Michels and Michels (6). The density of ethylene was taken from the work of Danned and Stoltzenberg ( 3 ) . With K 2 equal to zero, the viscosity becomes (5)
This relation was used to calculate the viscosity a t a definite pressure frotn the average time of fall of all the runs a t each pellet size. These values for ethylene are shown in Table 111. The mean viscosity for all pellet sizes a t each pressure are given in Table IV. These are the final results for the viscosity of ethylene a t 40" C. from 65 to 2000 pounds per square inch absolute (4.40 to 137.1 atmospheres). The average deviation of the viscosity measured a t one pellet size from the
...
0
0
Extrapolated.
...
4
6
x
10s
8 I/SEC.
IO
12
14
FIGURE 8. EXPERIMENTAL DATAFOR ETHYLENE TO DETERMINE END-EFFECT CONSTANT Ke
o,06
CARBON DIOXIDE
A T 40'C.
PHILLIPS STAKELBECK
L__
---0.05
In
ETHYLENE A T 40'C.
0,04
E 0,OJ ).
5 0.02
sL? '
0.01
0
20
40
PRESSURE
60
80
100
120
140
ATMOSPHERES
FIGURE9. EFFECTOF PRESSURE ON VISCOSITY OF ETHYLENE AND CARBON DIOXIDE 1
... ... ... ...
2
I/t
OF VISCOSITY DATAFOR ETHYLENE AT 40' C. TABLE IV. SUMMARY
in Micropcisen for Merrury Pellets of Following ~ b ~ Visoosity . Pressure. Weight, in Granis: Atrn. 1.614 2.466 3 . 3 1 2 7 1 5 6 4.780 Mean 109.3" 1.00 4.40 lib's lib's ib$:5 ib$:s lb$:6 110.1 28.2 118.3 120 0 117.5 121.1 119.0 119.2 48.6 152.0 131.9 131.4 138.0 134.6 133 55.5 139.3 139.5 139.2 147.2 142.7 141 162 67.4 160.6 159.2 168.6 79.3 198.1 199:l 212.6 20310 203 259.8 250 89.5 240.8 103.1 287.4 300:l 310.1 296:O 298 137.1 366.8 392.9 379
Vol. 33, No. 10
Probable Error, % ( 1 0 ) 0.2 0.5 0.9 21..41 2.3 8.0 3.4 11.6
The experimental results for carbon dioxide a t 40" C. are shown graphically in Figure 9, where they may be compared with the measurernents Of and Of The three determinations agree within 1 or 2 per cent for pressures up to 50 atmospheres. Between 60 and 80 atmospheres the data of the present investigation are 'about 1 or 2 per cent higher than those of Stakelbeck, which are, in turn, approximately 10 per cent higher than those of Phillips. At about 85 atmospheres the curve of Phillips' data crosses that of Stakelbeck's, and from this point to around
October, 1941
INDUSTRIAL A N D ENGINEERING CHEMISTRY
110 atmospheres the present data are from 3 t o 6 per cent higher than Phillips'. At higher pressures our data are slightly lower than those of the other two investigators. The curve for the viscosity of ethylene at 40" C. against pressure is also shown on Figure 9. No other data are available for comparison.
1229
the measured values increase more rapidly from a value that is about 19 per cent low t o one that is about 11 per cent high. The viscosities reported here are probably accurate within 2 per cent at pressures up to 89 atmospheres and within 4 per cent in the range 89 t o 137 atmospheres.
Nomenclature 8
A a
6
4
T3 2
I ,5 Ito
FIGURE10. COMPARISON OF EXPERIDATA WITH VISCOSITY RATIO CURVES
MEKTAL
when acted upon by gravity will overcome capillary effects a t end of ellet, grams E = energy lost by e n 8 effects per unit mass of gas flowing through capillary, sq. cm./sec.Z = acceleration of gravity crnJsec.2 = constant equal to ~ l A / r r 4 g cm. , x sec.2 = constant equal to aV2A/?rZr4 = length of capillary, cm. ?n = mass of mercury pellet, grams P R = reduced pressure, ratio of pressure to critical pressure 1F = radius of capillary, cm. TR = reduced temperature, ratio of temperature to critical temperature in degrees absolute t = time for pellet to descend from upper to lower set of contaets, sec. U = velocity of gas in capillary, cm./sec. = volume displaced by pellet between two sets of contacts,
v
CC.
a
These data on ethylene may be compared with the viscosity predicted by a correlation presented earlier (1). There i t was suggested that the viscosity ratio, p / p 1 , is a unique function of reduced pressure P R at any value of reduced temperature TK,independent of the gas or vapor being considered. p / p ~is the ratio of the viscosity at an elevated pressure to that at atmospheric pressure both at the same temperature. The curves of viscosity ratio for several values of TR are shown in Figure 10 over a limited range of PR; the experimental values of p / p l are also given. The results for carbon dioxide would be expected to be in good agreement, as they are, since the correlation was itself based partly on the carbon dioxide data of Phillips and Stakelbeck. The viscosities of ethylene and of carbon dioxide were not measured at atmospheric pressure in this investigation, but this value was obtained by extrapolating the data at the higher pressures. The value so obtained was used in calculating the viscosity ratio. The experimental viscosities agree with the correlation curves within the accuracy claimed for the correlation. At pressures below the critical, the measured viscosity of ethylene increases less rapidly with pressure than the predicted values. At pressures above the critical,
= cross-sectional area of pellet tube, sq. cm. = mass of mercury (corrected for gas buoyancy), which
p p pl pm
priDortionaIity constant in relation E = au2 (no units) = density of vapor, grams/cc. = viscosity of vapor, grams/cm. X sec. (poises) = viscosity of vapor a t 1 atm. = density of mercury, grams/cc. =
Literature Cited Comings, E. W., and Egly, R. S., IND.ENQ.CHEM.,32, 714 (1940).
Cummings, L. W. T., Stones, F. W., and Volante, M. A., Ibid., 25, 728 (1933).
Danned, H., and Stoltzenberg, H.,
2. angew. Chem., 42, 1121
(1929).
Fisher, W. J., Phys. Rev., 28, 73 (1909). Keyes, F. G., IND.ENQ.CHEM.,23, 1375 (1931). Michels, A.. and Michels, C., Proc. Roy. SOC.(London), A153, 201-24 (1935).
Nasini, A. G., and Pastonesi, 0.. Gazz. chim. ital., 63, 821 (1933). Phillips, P., Proc. Roy. SOC.(London), A83, 265 (1910). Rankine. A. 0..Ibid., A87. 48 (1912).
(IO) Sherwood, T. K., and Reed, C. E.,'"Applied Mathematics in Chemical Engineering", p. 359, New York, McGraw-Hill Book Co., 1930. (11) Stakelbeck, H., 2. ges. KaEte-Ind., 40, 33 (1933). PRESBINTED before the Division of Petroleum Chemistry at the lOlst Meeting of the American Chemical Society, St. Louis, Mo.
HORIZONTAL CATHETOMETER (see text page 1225)
