PRESSURE DROP ACCOMPANYING TWO-COMPONENT FLOW THROUGH PIPES L. M. K. BOELTER University of California, Berkeley, Calif. Berkeley. The system was operated at approximately room temperature, the oil (or water) and air passing through two sides of an adequate heat exchanger to ensure equality of temperature of the two components. Temperatures of the gaseous component were measured at the beginning and end of the test sections by means of thermocouples. The test lengths included two 50-foot sections in series, each provided with an adequate quieting section; one quieting section was 6.5 and the other was 5 feet in length. The pipe was placed horizontally with a maximum variation of 0.05 inch from levelness. A glass section, 2 feet long, was placed at the end of each test section in order that the flow characteristics could be observed visually. Oils of two different viscosities and water were used as the liquid components and were introduced into the line at the pressure maintained in the system. The earlier tests at Davis were conducted at low temperatures. Cooling, in this installation, was accomplished by means of a brine-filled jacket. The test techniques followed for both series of tests were similar. Liquid rates were determined by weighing the liquid feed. Gaseous (air) rates were evaluated from calibrated orifice measurements. Air rates were held constant for a range of magnitudes of liquid rates at a given liquid viscosity. Similarly, oil rates were held constant for a range of magnitudes of air rates at the fixed liquid viscosity.
ROBERT H. KEPNER Division of Agricultural Engineering, University of California, Davis, Calif.
Data are reported on the pressure gradients and the types of flow occurring when unemulsified mixtures of air and oil or of air and water pass through 1/2- and a/4-inch standard pipes, placed horizontally or at a n inclination of 1:6. The equilibrium quantity of oil standing within the pipe was determined as a function of the air-oil ratio, air velocity, and pipe diameter.
I
N T H E course of a study of a fuel-distributing system for heaters in citrus orchards, pressure drops were measured for the flow of air-oil and air-water mixtures through 1/2-inch standard galvanized pipe, 1/2-inch standard black pipe, and S/4-inch standard black pipe, all placed horizontally. Similar data were collected for 40 feet of l/Z-inch black pipe placed at an inclination of 1:6 (1 vertical, 6 horizontal) as well as for a preceding 47-foot horizontal section. The data on galvanized pipe were obtained a t Berkeley and those on black pipe a t Davis. Although the test conditions were established primarily to simulate those which obtain in the fuel lines on orchard heaters, the results should prove of value in the design of condensate returns and of systems in which condensation or evaporation is occurring, as well as of distributing systems for two-phase mixtures which do not emulsify. The oil rate was varied from 0 to 0.06 pound per second and the air rate from 0.005 to 0.020 pound per second. Runs were also made a t various air pressures ranging from 20 to 50 pounds per square inch gage. The liquids used were oil and water. Viscosity variations from 0.00062 to 0.065 pound/(foot) (second) were included in the test agenda. The maximum pressure gradient for these experiments was fixed near 0.05 pound/(square inch)(foot) so that the gaseous flow may be considered incompressible as a first approximation. All pressure gradients were reduced to a reference pressure of 40 pounds per square inch gage. The air was considered dry, and all air volumes referred to in the text are at standard conditions of 14.73 pounds per square inch and 60’ F. The liquid in the pipe was no doubt saturated with the gas (air) and the air contained vapors of the liquids, but no correction for these admixtures was made. The arithmetic mean of the inlet and outlet temperatures was employed to fix the fluid properties.
FIGURE1. DIAGRAM OF APPARATUSFOR AIR-OIL AND AIR-WATER TESTS The equilibrium volume of liquid in the pipe corresponding to each set of test conditions was determined by “blowing down” the line at the end of each run. Data showing the effect on the ressure dro of wetting the inside of the pipe with oil (no oil OW) were ogserved.
Technique and Apparatus Figure 1 indicates the arrangement of apparatus used to conduct the experiments on the l/z-inch galvanized pipe at 426
APRIL, 1939
INDUSTRIAL AND ENGINEERING CHEMISTRY P
6
TABLEI. TABULAR DATAFOR FIGURE 2
I
Run No.
4-
-
2.5 N
P x
n
z
-
1.5
2m -I
1.0-
8
0.8-
I
e
-
w
0.6-
O
E
3
-
VI
0.4a
-
2 5
c
.I51
0.1
/
L-6
3
.
5
'
7
*
"
15 25 1.5 2.5 AIR RATE-LBS./SEC.X 10' 9
4
6
8
1 0
Constant weight ratio of air to oil, 0.315. Oil S o . 3: 31.4' A. P. I., 6 0 / 6 0 ; 40 pounds per square inch gage reference pressure. Half-inch, level, wrought-iron pipe Constant weight ratios of air to oil of 0.315, slope = 1.96; viscosity: A = 0.00804 pound/(foot)(seoond) at 29' F.; E = 0.00540at 44" F. Air alone; C, pipe previously wetted with oil, slope = 1.87; D , pipe dry, slooe = 1.84. Gage Pressure, Lb./Sq. In. 40 20 50 0 30
a
$
Discussion of Results Curve A , Figure 2, is constructed from data obtained a t different line pressures and corrected to a line pressure of 40 pounds per square inch gage upon the basis that the pressure drop varies inversely as the air density for a given air rate. These corrected data coincide with those obtained a t 40 pounds per square inch, which illustrates the fact that, within the pressure range studied, the pressure drop a t any line pressure for a given air-oil ratio and a fixed air rate varies inversely as the air density. This result may be anticipated because the momentum that may be transferred by the gas to the liquid depends upon the product of the density and the velocity which, in turn, is proportional to the gaseous flow rate. The Weisbach expression (4 states that
then
t
'F.
Wsir
Woil
Lb./sec.
Lb./sec.
AP* AL
Lb./(sq. i n . ) ( f t . )
7 8 10 11 1 2 3 4 150 151 152 153 154 155 156 157 72 73 74
19.8 19.5 20.1 19.8 30.0 29.4 29.2 30.3 39.8 40.1 39.8 39.8 40.0 39.2 40.4 40.0 49.7 50.6 50.7
30 31 33 34 13 14 35 36 38 39 16 20 24 29 83 91 40 41 42
20.1 20.1 20.1 19.7 30.0 31.0 29.7 29.4 30.2 29.9 40.4 39.8 40.3 40.9 39.7 40.1 50.8 50.7 49.9
0.029 0.0175 0.011 0.0065 0.0305 0.019 0.0135 0.008 0.039 0.0255 0.0175 0.013 0.009 0.0275 0.0465 0.034 0.0265 0.0135 0.010
Viscosity = 0.00540 Lb./(Ft.)(Sec.) a t 44' F .
FIGURE2. FRICTION LOSSESFOR AIR-OILMIXTURESAND AIR ALONE
Let
P Lb./sq. in.
Viscosity = 0.00804 Lb./(Ft.)(Sec.) a t 29' F.
-
LL F
427
G
=
0.032 0.0175 0.012 0.0075 0.0285 0.0195 0.0075 0.0115 0.0295 0.019 0.0255 0.0215 0.013 0.0075 0.028 0.034 0.0235 0.0225 0.014
Air Alone, */*-In. Level Wrought-Iron Dry Pipe
301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318
11.75 10,05 9.80 9.80 10.15 9.85 9.90 10.05 19.10 20.2 19.8 20.0 19.9 24.95 25.3 25.3 24.95 25.05
.... .... .... .... .... 65 66 66.5 66.5 67 67 67.5 67
Rerun Air Alone,
319 320 321 322 324 325 326 327 328 329 330 331
14.8 12.04 31.9 34.4 36.7 37.75 18.56 6.36 7.90 15.65 21.30 29.65
.... .... .. .. .. .. .... .... f
.
.
.
.... .... .... .... .... .... '/t
In. Level Wrought-Iron Dry Pipe
.... .... .... .... ....
64 64 64.5 64 64.5 65 64.5 65 64 64.5 65.5 65
....
--
.... .... .... .... .... ....
Air Alone, 1/*-In. Wrought-Iron Pipe Previously Wetted with Oil
unit weight rate = pV (3)
Run
No.
which indicates that the pressure gradient for a single component varies inversely as the density at a given mass flow rate. The friction factor f is nearly independent of density for a given flow rate. Curve B, Figure 2, corresponds to a lower viscosity than curve A . Curves A and B also offer evidence of the fact that, within the range of air rates studied (at a constant air-oil ratio), the pressure gradient varies as a power of the air flow-in this
First test Second teat section section Lb./sq. in.
351 352 353 354 355 356 357 358
* Corrected t o 40 lb./ss.
in.
AP* r-
tsv. F. 62 63 63 65 64 64 64 64
gage.
Wair
Lb./sec.
,
AL First test Second test aection section L b . / ( s g . in.)(ft.) 0.00235 0.00273 0.00360 0.00646 0.0115 0.0145 0.0213 0.0333
INDUSTRIAL AND ENGINEERING CHEMISTRY
428
7.0
TABLE 11. TABULAR DATAFOR FIGURE 3, CURVE11"
.
75 76 77 78 79 80 81 82 83 84 85 86 87 ..
3.0. I
*
2.0-
t: *z ';s
3I %
E w
K
88
1.0-
70. -
7 30W In
P
.30. ' 1.5
'
' 3.0
'
P
t
Weir
L b . / s q . in. 40.3 40.0 40.2 39.7 39.8 39.8 39.7 39.7 39.7 39.6 39.9 39.6 40.0 39.9
F. 41.0 41.5 41.0 41.0 41 .O 41.5 41.5 41.5 41.5 41.5 41.5 41.0 41.0 41 . O
Lb./sec.
a
AL L b . / s e c . L b . / ( s q . in.)(ft.) 0.00446 0.00669 0.00932 0.02024 0.0168 0.01418 0.02575 0.0229 0.0286 0.0324 0.0405 0.0503 0,0385 0.0476 Woil
0.00958
39.8 40.2 39.9 39.8 40.1 39.7 39.9 40.0 40.0 39.9 40.0 40.0 40.0 40.3
:
20
AP* -
Run No.
5.0.
0
VOL. 31, NO. 4
'
I
5.0
"
70
.
IO
20
30
50
70
OIL RATE-LLBS./SEC.~ IO'
5 D a t a for eurves I and I11 Figure 3 are tabulated as runs 95 t o 104 and Cbrrected t'o 40 Ib./sq. in. gage. 159 t o 167 i n Table 111.
*
LOSSESFOR AIR-OIL MIXTURES FIGURE 3. FRICTION Oil No 3 31 4O A. P. I. 60/60. viacosity = 0.00573 pound/(foot)(second) ad 4 i 0 F. and O.OOf40 at $2O F.; '/*-inch level wrought-iron pipe Curve Air R a t e Oil Viacoaity Lb./eec. Lb./(ft.)(sec.) ' F. 0.00958 0,00740 32 I I1 0.00958 0,00573 42 I11 0.00634 0,00740 32 IVa 0.01272 0.00573 42 Line A B C D E a
Wt. Ratio, Air t o Oil 2.0 1.5 1.0 0.8 0.6
Slope 1.70 1.70 1.70 1.70 1.70
Line
F
0 H I
Wt. Ratio, Air t o Oil 0.5 0.4 0.3 0.2
4 AND 9 TABLE 111. DATAFOR FIGURES Run No.
L b . / s q . in.
Extrapolated from dotted constant weight-ratio lines.
f
=
0.079
(4)
t
F. 3/4-I~.
Slope 1.74 1.79 1.87 2.02
case 1.96. This conclusion will be employed to extrapolate data to air rates other than those studied experimentally. Curve C presents the pressure gradient for a 1/2-inch galvanized pipe previously wetted with oil and then thoroughly blown down, and curve D the same pipe clean and dry. The slope of the curve increases slightly with wetting. The increase of the pressure gradient, due to wetting and to the transport of liquid compared with a dry pipe, may be observed by noting the relative positions of curves C, A , and D. Table I gives the supporting data for Figure 2. The data on pressure drop per unit length for 1/2-inchblack pipe are shown in Figure 3 as a function of oil flow rate for three different air rates. The system pressure was maintained a t 40 pounds per square inch gage. Table I1 gives the supporting data for Figure 3. From Figure 2 for an air-oil ratio of 0.315 and for an air rate of 0.01 pound per second the pressure drop is 5.3 times that for the same rate of flow of air in a dry pipe. Points of equal air-oil ratios were located on curves I and 111, Figure 3, corresponding to equal oil viscosities (that is, approximately a t the same temperature) for the two constant air rates. These points were connected by straight lines as noted in connection with Figure 2, curve A . For high airoil weight ratios (little or no oil) the slope of these lines was found to be 1.70; for lower ratios the slope reached 2.00 and slightly higher. For smooth pipes an approximate expression (1) for the friction factor f in the turbulent region is given by Blasius as:
P
95 96 97 98 99 100 101 102 103 104
*
Wair
Woil
Lb./sec.
Lb./sec.
Ap* AL
Vol. Oil Vol. Pipe
Lb./ (sq. in.)(ft.)
LEVELWROUQHT-IRON PIPE
0.01523 Lb. Air/Sec., 40 Lb./Sq. In., 42.5" F. 0,01523 0.0200 40.3 42.6 0.01517 0.0154 39.7 42.0 0.01517 0.0625 40.2 42.5 0.01517 0.0625 39.7 42.5 0.01523 0.0334 39.8 42.5 0.01523 0.0238 39.7 42.0 0,01523 0.0400 40.2 42.5 0,01523 0.0465 39.8 42.5 0,01523 0.0588 40.2 42.5 0.01523 0.0525 40.0 42.5 0.0255 0.01523 0.0688 40.0 42.5 0.0300 0.01523 0.0801 40.1 42.5 0.0280 0.01523 0.0783 39.8 42.5 0.0260 0.01517 0.0724 39.6 42.5
0.14 0.13 0.26 0.25 0.20 0.18 0.21 0.22 0.24 0.24 0.27 0.34 0.36 0.34
0.02107 Lb. Air/Sec., 40 Lb./Sq. In., 42' F. 0,02122 0.6526 40.1 42.5 0,02100 0.0425 40.2 42.0 0.02100 0.0500 40.2 42.0 0.02107 0.0416 39.3 42.0 0.02107 0.0344 40.5 42.0 0.02107 0.0293 40.6 42.0 0,02100 0.0243 39.6 42.0 0.02100 0.0111 40.1 42.5 0.02107 0.0312 40.5 42.0 0,02100 0.0239 40.0 42.0 0,02107 0.0664 39.9 42.0 0.02100 0.0556 40.3 42.5 0.02100 0.0771 39.9 42.5 0.02100 0.0802 40.2 42.5 0.02100 0.0668 40.3 42.5
0.19 0.15 0.17 0.15 0.15 0.13 0.12 0.08 0.14 0.11 0.21 0.22 0.23 0.25 0.23
I/P-IN. LEVELWROUGHT-IRON PIPE 0.00958 Lb. Air/Sec., 40 Lb./Sq. In., 32' 31.0 39.8 31.5 39.8 31.5 39.7 31.5 39.7 31.5 39.7 32.0 39.8 0.00866 32.0 39.7 0.00866 32.5 39.5 0.00958 32.5 39.9 0.00958 32.5 40.1
0.11 0.11 0.15 0.17 0.19 0.20 0.20 0.21 0.22 0.23
F. 0.0150 0.0160 0.0185 0.0215 0.250 0,0320 0.0285 0.0360 0.0410 0.0475
0.00634 Lb. Air/Sec., 40 Lb./Sq. In., 32.5' F. 32.5 40.2 32.5 40.1 33.0 40.3 32.5 40.3 32.5 40.2 32.5 39.8 32.0 40.0 32.0 39.9 32.0 39.9 Corrected t o 40 lb./ss. in. gage.
0.23 0.25 0.24 0.28 0.27 0.31 0.32 0.32 0.34
APRIL, 1939
INDUSTRIAL AND ENGINEERING CHEMISTRY
h
TABLEIV. Run No.
DATAFOR FIGURE 5
AL AP*
P
t
Wair
Woil
L b . / s e c . L b . / ( s q . in.)(jt.) Lb./sec. L b . / s q . in. O F. 0.0175 0.0304 41.0 0.00633 40.1 0,0135 0.00516 0.0304 41.0 41.0 0.0308 0.0480 0.01283 43.5 40.1 0.0304 0.0385 0.01159 43.5 39.7 0.0304 0.0340 0.0105 43.5 39.7 0.0300 0.0230 0.00783 43.5 40.3 0.0156 0.0110 0.00659 41.0 40.5 0.0152 0.0135 0.00766 41.0 41.5 0.0075 0.00491 0.0148 40.9 43.5 0.0285 0.0125 0.0150 40.3 43.0 0.0235 0.01131 0.0152 40.1 43.0 0.0205 0,00991 0,0152 40.2 43.5 0.0150 0.0165 43.5 0.00875 39.9 0.0150 0.0095 38.0 0.00541 40.1 0.0154 0.0075 0.00466 40.0 39.0 0.0152 0.0050 0.00350 40.0 39.5 33.0 0.0128 0.0272 0.0495 39.7 0.01132 0.0286 0.0375 40.2 33.5 106 0.0310 0.01025 0.0278 40.3 33.5 107 0.0200 0.0075 0,0278 40.3 33.5 108 0.0255 0.00875 0,0272 39.7 33.5 109 0.0264 0.0165 40.0 34.0 0.00625 110 0.0278 0.0175 34.0 0.00625 39.9 111 0.0150 34.5 0.00525 0.0278 39.8 112 0.0204 0.0210 22 40.3 42.5 0.00933 0.0192 0.017 40.3 43.0 0.00708 23 0.0204 0.013 24 40.3 43.0 0.00632 0.0200 0.0105 40.0 43.5 0.00500 25 0.01281 0,0198 0.0355 39.8 42.5 129 0.028 42.5 0.01140 0,0202 39.9 130 42.5 0.01059 0,0198 0,023 40.5 131 0,00825 0.0206 0.018 39.8 42.5 132 0.0135 143 40.1 44.5 0.00508 0.0307 0.0185 40.0 44.5 0.00650 0.0299 144 41.0 0.0115 0.0313 0.0405 89 39.6 0.0296 0.050 90 39.9 41.0 0.0130 0.0304 0.034 91 40.1 41.0 0.00941 0,025 92 40.0 41.0 0,00800 :-. 0.0314 0,022 40.2 41.5 0.00691 0.0314 93 * Corrected to 40 lb./sq. in. gage.
16 17 18 138 139 140 141 28 29 134 135 136 137 181 182 183 105
429
Curves for a 3/d-inch diameter black DiDe are included in Figure 4, and the-data are given in Tagle 111. These data were also extrapolated to a 0.01272 pound per second air rate for oil with a viscosity of 0.00573 pound/(foot) (second) in order to allow direct comDarison with the 1/2-inch h e data. ADparatus limitations precluded the determination bf overlapping data. The curves of Figure 5 illustrate the increase in pressure gradient as a function of air flow for several different oil rates over that which would obtain if oil only were forced through the line; Table IV gives the supporting data. The pressure gradient is increased approximately seven times for an air-oil weight ratio of 0.315 and for an oil flow of 0.0304 pound per second (15 gallons per hour) as contrasted with the gradient a t zero air-oil ratio. The absolute viscosity of the oil was 0.00540 pound/(foot)(second) a t 44' F. I n order that a comparison between the various data obtained on a 1/2-inch line may be made, the results are plotted in Figure 6; the supporting data are given in Table V. The effect of slope is particularly notable. The pressure gradient in an upwardly sloped line is increased because the air must do work to lift the oil. As will be shown later, the oil level in the sloped pipe will increase; this in turn affects the oil level and the pressure drop in the preceding horizontal section. The pressure drop is almost doubled a t high oil rates for 0.01273 pound per second (10 cubic feet per minute) air rate if the pipe is inclined upward a t a slope of 1:6, as contrasted with the horizontal pipe. The pressure drop in the preceding horizontal section is increased approximately 25 per cent.
In more accurate expressions ( I ) the exponent is reduced slightly and a constant term added. Substitution of Equation 4 in Equation 3 yields:
Thus for single-component flow (for air-oil ratios near infinity) the pressure gradient varies with the 1.75 power of mass flow G. Within the narrow range of air flows presented in Figure 3, the results appear to indicate that the exponent of the pressure gradient variation with air flow is only slightly affected by the oil flow at low oil rates but increases with high oil rates. The air-oil ratio is constant along the straight lines drawn. Along one of these straight lines the pressure drop is a power function of the air flow, the exponent being the slope of the line. The slope of the straight lines in Figure 3 would also be the same if plotted against air rates as the abscissa. Thus curve A , Figure 2, is one of the constant airoil ratio family of curves of Figure 3 shown as a function of the air rate. The slope of curve A in Figure 2 does not quite correspond to those in Figure 3 because of the deviation of data. In order to compare data for a l/Z-inch with that for a 3/4-inch pipe, extrapolations were made from Figures 3 and 4 to obtain data for the same oil viscosity and air flow rate. The dotted lines were drawn parallel to the full lines and used to extrapolate the experimental data to an air rate of 0.01272 pound per second (10 cubic feet per minute) for oil with an absolute viscosity of 0.00573 pound/ (foot)(second) (oil No. 3 a t 4 2 O F.).
Courtesy, Olive7 United Filters, Inc.
ACIDPUMPS OPERATINGIN
A
SEWAGE DISPOSAL PLANT
INDUSTRIAL AND ENGINEERING CHEMISTRY
430 I
VOL. 31, NO. 4
Y
.os -
.07
-
.OS
-
t:
Y .
5
.05-
? P
0
.04w
.30L '
45
0.7
' ' ' LO
E
2.0
OIL RATE-LBS./SEC.~
FIGURE4.
5.0
3.0
%O
IO'
-
u u) )
.03-
PRESSURE GRADIENTFOR AIR-OIL MIXTURES
-
Oil No. 3 31.4' A. P.I 6 0 / 6 0 t = 43' F.; viscosity 0.00557 pokd/(foot)(seod&d)at 4& F.;pressure 40 pounds per square inch gage a/,-inoh level wrought-iron pipe. Air rate, i n pounds per skcond: curve I, 0.01523; 11,.0.0210?; 111, 0.01272 (extrapolated from the constant weight-ratio lines) Wt. Ratio, Wt. Ratio, Line Air t o Oil Elope Line Air t o O i l Slope E 0.6 1.97 1.77 A 1.5 F 0.4 1.98 1.82 B 1.0 G 0.3 2.03 1.90 C 0.8 H 0.25 2.09 1.95 D 0.6
.02
-
.01
-
0 0
.o I
.O2
.03
.I
OIL RATE-LBS./SEC
FIGURE 6. FRICTION LOSSESFOR AIR-OIL MIXTURES IN HALF-INCH PIPEAT DIFFERENTSLOPES Oil No. 3 31.4O A. P. I., 60/60, t 37O F.; viscosity,
-
0.00640pdund/(foot) (second) a t 37O F.; pressure, 40 pounds per square inch gage Curve Air R a t e Slope Lb./sec. A 1:6 B Level section preceding 1:6 seotion Level" D 1:6 C F Level section preoeding I :6 section Level" G E 1:6 H Level section preoeding 1 :6 section Level" I Values from re-run with all pipe level e after slope runs G3 Extrapolated from previously presented data.
AIR RATE-LBS./SEC.
io'
FIGURE5. FRICTION LOSSESFOR AIR-OIL MIXTURESAT CONSTANT OIL RATES Half-inoh level wrought-iron pipe, oil No. 3, 31.4" A. P. I., 60/60; system pressure, 40 pounds per square inch gage Curve A C
D B
Oil R a t e Lb./seo. 0.0304 0.0202 0.0152 0.0278
-ViscosityLb./(ft.)(sec.) 0.00540 0.00540 0.00540 0.00706
F. 44 44 44 33
Calod. Zero Air Flow Points Lb./(ep. in.)(ft.) 0.00419 0.00279 0.00209 0.00497
J To present more clearly the importance of viscosity, a set
of runs a t an air rate of 0.00634 pound per second was completed for water and three different oils as liquids. The data are shown in Figures 7 and 8 and in Table VI. The results between a viscosity of 0.01 and 0.1 pound/(foot) (second) indicate that the pressure gradient varies with the 0.60 power of the liquid viscosity. At lower liquid rates the exponent
is reduced slightly. The data for water [p = 0.000715 pound/(foot) (second) ] indicate that the effect of viscosity decreases a t lower viscosities. Data presented by O'Bannon (2) and observations of the flow pattern in the glass pipe section indicate that for low viscosities the liquid tends to flow in slugs. I n two-component flow, waves are generated on the surface of the liquid, much of which flows in the bottom of the pipe. If the amplitude of the waves reaches the mean depth of the liquid in the pipe, the %ow will tend to be discontinuous.
Flow Characteristics A system which will serve as the first idealization for twocomponent flow in the region studied may be visualized as a liquid flowing in the bottom of the pipe and the gas above it. The traction of the gas on the liquid surface will cause the liquid to flow. The equilibrium volume of oil in the line should vary with the gas-liquid ratio, gas flow, liquid viscosity, pipe diameter, and inclination of the pipe line. Figures 9, 10, and 11 illustrate this statement. The curves in Figure 9 reveal the effect of oil rate and air rate for two
APRIL, 1939
j
INDUSTRIAL AND ENGINEERING CHEMISTRY
I /A
431
; 2 5
2.
a.I 0
K a W
5
07
u)
pa
a5
OJL
.o&
' '.&I
'
' .005 ' ' ' '
.01
"
ABSOLUTE VISCOSITY-LBS./FT
OIL RATE-LBS/SEC
FIGURE '7. VARIATIONOF PRESSURE GRADIENT WITH LIQUID RATEFOR FOURLIQGIDS AT A COXSTANT AIR RATEOF 5 CUBIC FEETPER MINUTE (0.00634 POUSDPER SECOND) IN A HALFINCHHORIZONTAL PIPE Pressure drop at zero oil flow was taken from curve D Figure 2,for dry pipe as 0.00266 pound/(square inch) (foot\ Surface Tension Curve Liquid -Viseosit y(67' F.) Lb./(ft.) (sec.) O F. Dynes/cm. 65.5 31.1 0.0615 A Oil 1 0.032 68 30.8 B Oil 2 0.00715 31.5 28.8 C Oil 3 0.000715 62 76.0 D Water
different pipe diameters. I n Figure 10 the apparent effects of viscosity and slope are shown; the data are given in Table VII. The increase of equilibrium volume for a 1:6 slope over that of the horizontal pipe was found to vary linearly with oil rate for a given air rate. Figure 11 indicates that the effect of viscosity on the equilibrium volume is not great except for liquids with a viscosity below 0.01 pound/(foot) (second). All of the equilibrium volume curves reveal trends which may be anticipated from a consideration of the traction exerted by the liquid on the gas a t the interface; the volume ratio (which is also the ratio for the cross section of the pipe area filled with liquid to the total cross-sectional area of the pipe) increases with increased liquid rates, increases with viscosity (in regions in which an increase occurs), increases with pipe size, and increases with decreasing air rates. The first idealization of the flow system noted above must be modified based upon the data presented so far. Waves are generated a t the interface, and a t higher velocities the high-viscosity liquids will tend to spray and the low-viscosity liquids will tend to flow in slugs. Observation of the flow through the glass sections revealed that for a liquid of a given viscosity and a t a constant air rate, the liquid splashes more and the surface waves increase in amplitude and frequency as the liquid rate is increased. For a fixed liquid rate and a fixed air rate, more splashing occurs and the surface waves increase in amplitude as the liquid viscosity is decreased. For water the waves reach amplitudes such that the crests almost reach the top of the pipe and give the appearance of slugs of liquid passing a t high velocity with very little motion of the liquid between slugs. The portion of the liquid which flows along the bottom of the pipe would appear to move a t high velocity (turbulently) near the interface. Splashing as used above implies that oil appears to adhere to the upper surface and sides of the pipe in bands of varying thickness, the oil being supplied from the sides of the oil-air interface.
.OZ SEC.
.05
FIGURE 8. VARIATIONOF PRESSURE GRADIENTWITH LIQUIDVISCOSITY AT A CONSTANT AIR RATEOF 5 CUBIC FEETPER MINUTE(0.00634 POUNDPER SECOND) IN A
HALF-INCH PIPE
Slope of lines is
0.60 for the viscosity 2 0.01 pound/(foot)(seoond) 0.045 Eb. Ziquid/scc. 0 0.035 0.025 0 0.015 0 0.010
f
+
..
OIL RATE-LLBS/SEC
FIGURE 9. FRACTION OF PIPE VOLUMEWHICHIs FILLED WITH LIQUID AS A FUNCTIOK OF OIL RATEFOR Two PIPE SIZES, PLACED HORIZONTaLLY Oil 3,31.4' A. P. I., 6 0 / 6 0 ; pressure. 40 pounds per square inah gage */,-in pipe. viscosity 0 00573 lb./(ft.)(sec.); 42' F . : A . ' 0.01b23 lb. airjseb. B. 0.0210 lb. air/sec. '/An. pipe; viscosity, 0.00740 lb./(ft.) (sec.) ; 32' F.: C. 0.00634 Ib. air/sec. D . 0.00958 lb. air/sec.
For each pipe size, a minimum air flow rate existed below which the horizontal pipe filled and the oil was moved in large slugs by large air bubbles. The air rates were 1.2 and 2 cubic feet per minute for the 1/2-inch and S/rinch pipes, respectively. The minimum air rates were practically independent of the oil rate for the oil of 0.00740 pound/(foot) (second) viscosity. The minimum rates were increased about 10 per cent for the pipe sloped 1:6.
INDUSTRIAL AND ENGINEERING CHEMISTRY
432
-
6 TABLEV. DATAFOR FIGURE
AP* AL Level section preceding the t Weir urd 1:6 slope 1:6 slope O F . Lb./sec. Lb./sec. Lb./(sq. in.)(ft.) Part of Pipe on 1:6 Slope 7--
Run No.
185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 209 210 2ii 212 213 214 215 202 203 204 205
P L b . / s q . in.
40.1 39.8 40.0 40.2 40.4 40.0 40.2 40.2 39.7 40.0 40.0 40.3 40.4 40.2 39.9 40.0 39.9 39.7 39.9 40.0 39.9 39.9 39.8 40.1 40.3 40.0
37.0 37.5 37.5 37.5 37.5 37.0 37.0 37.0 37.0 37.0 37.0 37.0 37.0 37.0 37.5 36.5 36.0 36.0 36.5 36.5 36.5 36.5 37.0 37.0 37.0 37.0
0.00941 0.00950 0.00968 0.00958 0.00958 0.00958 0.00958 0.00958 0,00958 0.00950 0.00958 0,00958 0.00958 O.OOb58 0.00958 0.01281 0,01273 0.01273 0.01281 0.01273 0.01273 0.01281 0.0055 0.00550 0.00550 0.00566
0.01355 0.00606 0.00950 0.01477 0.01011 0.01213 0.0186 0.0243 0,00286 0.0279 0.0285 0.0356 0.0392 0.0370 0.0324 0.0079 0.01597 0.0257 0.0216 0.0314 0.0378 0.0346 0.0208 0.0263 0.0318 0.0089
0,0190 0.0155 0.0175 0.0210 0.0165 0.0190 0.0230 0.0260 0.0240 0.0290 0.0300 0.0355 0.0405 0,0388 0,0345 0.0260 0,0345 0,0460 0.0425 0.0540 0.0635 0.0585 0.0145 0.0175 0,0210 0.0085
Rerun, All Pipe Level 0.00870 40.0 37.5 0,0095 0.02122 39.8 38.0 0.0095 0.00958 0.0293 40.2 38.0 0.0346 0.00958 38.0 40.0 0.00958 0.0445 38.5 39.9 0.00958 0.0384 38.5 39.9 0.01272 0.0354 38.5 40.0 0.01281 0.0455 38.5 39.8 0.01272 0.0281 38.5 40.0 0.0160 38.0 0.01272 40.2 At 40 lb./sq. in. system pressure.
217 218 219 220 221 222 223 224 225 226
*
TABLEVII. Point
No.
woil
1 2 3 4 5 6 7 8 9 10
Lb./sec. 0 005 0.010 0.015 0,020 0.025 0.030 0.038 0,040 0.045 0,050 0.055
11
0.0280 0.0195 0.0220 0 I0280 0,0245 0.0270 0.0345 0.0415 0.0390 0.0455 0.0480 0.0565 0,0600
0.0575 0.0540 0.0295 0.0440 0.0635 0.0540 0.0725 0.0745 0.0760 0.0320 0.037 0.043 0.022
0.0165 0.0235 0.0300 0.0350 0.0460 0.0390 0.0595 0.0715 0.0485 0.0325
DATAFOR FIGURE 10
__ B f c vcurve 01. Ratio A curve^ Curve c 2 37' F., Vol. Ratio Vol. Ratio Vol. Ratio Pipe 32O F. 42O F . 37O F. Sloped1:6 0.00968 pound of air per second 0,090 0.082 0.087 0.077 0.145 0.128 0.134 0.122 0.180 0.156 0.162 0.150 0.205 0.172 0.178 0.167 0,226 0.179 0.184 0.190 0.244 0.195 0.200 0.190 0,260 0.204 0.210 0.198 0.274 0.205 0.211 0.217 0.212 0.218 0.224 0.218 0.224 0.230 0.224 0.230 0.236
Curve
Run No.
t
Wair
OF.
Lb./sec.
401 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
68 65.5 67 68.5 70 70 58 61 62.5 62.5 64.0 65 64 62 68 62 65 67 68 70 70 70 70 63 64 64 64 64 64 70 72
0.00648 0.00640 0.00639 0,00629 0.00618 0.00635 0.00635 0.00640 0.00635 0.00640 0.00650 0.00640 0.00650 0.00630 0.00640 0.00640 0,00627 0.00630 0.00630 0.00620 0.00630 0.00630 0.00630 0.00635 0.00640 0.00640 0.00630 0.00636 0.00635 0.00650 0.00630
433 434 435 436 437 438 439 440 441 442
67 67 68 69 70 70 68 68 68 68
443 62 444 62 445 ~~.62 62 446 62 447 448 62 449 62 64 450"
~~
FVe W 2 = modulus which describes capillary waves Fr V4p The minimum velocity necessary to sustain capillary waves (3) on the surface of water a t room temperatures is 0.75 foot per second which is about one tenth of the minimum air velocity employed in these experiments. The effect of surface tension may persist a t fairly high relative interface velocities because of the splashing which occurs. Experiment may, however, indicate that not all of these variables are effective. A preliminary calculation of Reynolds modulus for the air and oil was made from the volume ratio data presented in Figure 9 and the corresponding pressure drop data from Figure 3. The significant dimension, D, was defined as
-
Vol. Oil AP* Abs. Viscosity AL Vol. Pipe Lb./(ft$(sec.) Lb./ Lb./sec. ( X 1 2) (sq.in.)(ft.) Woil
Oil No. 1 0.00812 0,00435 0.0179 0.0224 0.0206 0.0135 0.0145 0.00832 0.0211
0.0442 0.0492 0.0441 0.0415 0.03115 0.0217 0.0185 0.0134 0.00974 0.00486 0.00227 0.0165 0.0381
5.56 6.15 5.80 5.47 5.18 5.18 8.25 7.30 6.90 6.90 6.50 6.25 6.50 7.02 5.56 7.03 6.25 5.80 5.56 5.18 5.18 5.18 5.18 6.77 6.50 6.50 6.50 6.50 6.50 5.18 4.76
0,030 0.0213 0.0489 0.0585 0.0453 0.0406 0.0456 0.0612 0.0303 0,0353 0.0497 0.0711 0.0212 0.0239 0.0636 0.0719 0.0839 0.0988 0.1022 0.1105
....
0.188 0.188 0.188 0.188 0.188 0.188 0.188 0.267 0.267 0.267 0.267 0.267 0.267 0.161 0.275 0.275 0.275 0.275 0.275 0.319 0.282 0.282 0.293 0.246 0.243 0.210 0.196 0.157 0.038 0.231 0.293
0.00640 0.00635 0.00638 0.00639 0.00638 0.00638 0.00635 0.00635 0.00631 0.00640
Oil No. 2 0.0585 0.0535 0.0511 0.0446 0.0363 0.03165 0.0224 0.01785 0.0121 0.00766
3.22 3.22 3.12 3.06 2.96 2.96 3.12 3.12 3.12 3.12
0.0945 0.0827 0.0767 0.0669 0.0564 0.0491 0.0415 0.0337 0.0265 0.0205
0.333 0.340 0.338 0.310 0.295 0.264 0.257 0.222 0.201 0.169
0.00635 0.00630 0.00630 0.00635 0.00636 0.00636 0,00636 0.00636
Water 0.0660 0.0576 0.0521 0.0464 0.0374 0.0278 0.022 0.0152
0.0715 0.0715 0.0715 0.0715 0.0715 0.0715 0.0715 0.0715
0.0224 0.02025 0.0179 0.0155 0.0129 0.0098 0.00689 0.0054
0.206 0.198 0.193 0.183 0.169 0.150 0.137 0.121
2
General Comments Generalization of these results cannot be made without many more data. Tentatively the following generalized variables are proposed:
-=-
TABLEVI. DATAFOR FIGURES 7 AND 11
B+C 0,008 0.017 0.024 0.033 0.042 0.049 0.056 0.063
VOL. 31, NO. 4
0.0111 0.0162 0.0257 0.00582 0.00547 0.0246 0.0273 0.0341
0. OSoi
..... ... .... ..... ... .... .... .... .... ....
*
Corrected t o 40 Ib./sq. in. gage. Balance of data, runs 159 to 167,tabulated with data for Figu.res 4 and 9 in Table 111. (1
4 A / P , where A is the cross-sectional area of flow for the particular component and P is the corresponding wetted perimeter. The idealization which places all of the oil in the lower portion of the pipe was employed. P for the oil was considered to be the portion of the pipe wetted by the oil; P for the air was taken as the portion of the pipe wetted by the air, augmented by the chord which defines the air-oil interface. The results are presented in Table VIII. Inspection of this table reveals the fact that the effect of a change of wetted perimeter and cross-sectional area with oil rate does not affect Reynolds modulus for the air appreciably but changes that of the oil to a greater extent. To the first approximation it may be concluded that for the same oil rate the pressure drop varies directly with the rate of air flow. The greatest error is made a t low oil flows by the use of this artifice. For the data presented in Table VIII, the error will be about 15 per cent for an oil flow of 0.01 pound per second. The data also indicate that the pressure drop a t equal oil rates are more nearly proportional to the air rate (that is, air Reynolds modulus) than the pressure drop a t equal Reynolds modulus for the oil.
APRIL, 1939
INDUSTRIAL AND ENGINEERING CHEMISTRY
433 ~~~
TABLE VIII. -Air
Flow Rate
v01:
Oil Rate
ratio
a
0,137 0.182 0,203 0.217 0.227
Lb./Sec. (7.5 Cu. Ft./Min.)-
Doil
Dair
AoiI
Aair
In.
In.
0,290 0.357 0,372 0.384 0.395
0.552 0.530 0.521 0.517 0.510
Sq. ft. 0.000286 0.000380 0.000424 0.000454 0.000472
Sq. ft. 0.00180 0.00170 0.00166 0.00164 0.00161
Lb./sec. 0.01 0.02 0.03 0.04 0.05
= 0.00958
REYNOLDS MODVLUS FOR AIR AXD OIL^
Visoosity of oil = 0.00715, viscosity of air
-
Reoil
Reair
-Air VO!. ratio
Ap/AL
Flow Rate
Lb./
(sq. in.)(ft.)
125 219 303 394 487
21,200 21,500 21,700 21,700 21,800
0.0177 0.0240 0.0303 0.0382 0.0480
0.193 0.255 0.288 0.313 0.333
= 0.00634
In.
In.
0.358 0.423 0.453 0.480 0.492
0.524 0.496 0.482 0.470 0.458
Lb./Seo. (5 Cu. Ft./Min.)-
Aoil
Asir
Sq. ft.
Sq. ft.
Dair
Doil
0.000403 0.000531 0.000600 0.000652 0.000695
Reoil
Reair
Ap/AL
Lb./
(sq.
0,00168 0.00156 0,00148 0.00143 0.00138
104 186 264 342 412
14,300 14,650 14,950 15,050 15,200
in.) (ft.)
0,0103 0.0140 0,0184 0.0250 0.0330
0.00001, 155 lbs./(ft.)(sec.) a t 32O F.
TABLE IX. DATAFOR FIGURE 12 Traotion of Air on Oil Oil Rate Lb./sec.
Horizontal 1:6slope Lb./sq. ft.
0.010 0.015 0.02 0.025 0.03 0.035 0.04
0,019 0.021 0.023 0.024 0.028 0.030 0.032
Power per Unit Length to .Overcome Actual (as Gravity 1:6 slope difference) Only Ft.-lb./(sec.) (ft.)
Power per Unit Length
.- Hori-
zontal
c
0.029 0.030 0.032 0,036 0.038 0.041 0.040
--
0,0225 0.0257 0.0294 0.0344 0.0378 0,0420 0.0423
0.00166 0.00250 0.00332 0.00416 0.00500 0.00583 0.00664
have been made. The oil was again considered to flow quiescently in the lower portion of the pipe. The force required to move the air per unit length of pipe may be written as: (2)Asir
(air perimeter) $-
= Tdry air-pipe X
Tair-oil
X
(chord length)
(6)
This equation was employed to calculate the traction between the oil and air a t the interface for 0.00958 pound per second (7.5 cubic feet per minute) air flow, a t various oil flows for the horizontal and 1:6 sloped, 1/2-inch pipe. The corresponding volume ratios were obtained from the curves in Figure 10; and the air perimeter (air in contact with pipe) and chord length were then computed. The power per unit length required actually to lift the oil up the sloped pipe was computed from the equation
OIL RATE-LBS./SEC.
FIGURE 10. FRACTION OF PIPEVOLUME WHICHIs FILLED WITH LIQUIDAS A FUNCTION OF OIL RATEFOR PIPELEVEL AND WITH 1: 6 SLOPE Oil 3, 31.4' A. P. I., 60/60; air rate, 0.0098 po,und per second; pressure, 40 pounds per square inoh gage. Half-inch iron pipe Curve Symbol -ViscositySlope Lb./(ft.)(sec.) 'F. A A 0,00640 37 1:6 0.00754 31 Level B 0.00534 42 Level C 0 +
A
-k 2
c
Additional equilibrium volume ratio of 1: 6 slope with respect t o horizontal pipe
Inspection of the extrapolated pressure gradient to an air rate of 0.01272 pound per second for various oil rates (oil No. 3 at 42" F.) in Figures 3 (curve IV) and 4 (curve 111) for 1/2- and 3/4-inch pipe, respectively, allows a computation of the effect of diameter. For oil rates of 0.01 and 0.06 pound per second the pressure gradient varies approximately inversely as the diameter to the fifth power. Exactly, the ratio of diameters (0.824/0.622)5 = 4.00, and the ratio of the pressure gradients is 4.17 and 4.00 a t 0.01 and 0.06 pound per second, respectively. For single-component flow in a round pipe and in the turbulent region, Equation 5 indicates that the pressure drop varies as the diameter to the 19/4 power. As a first approximation the pressure drop in a horizontal pipe with a given oil rate and a fixed air-oil ratio may be predicted from present experimental data on a given pipe size by a multiplying factor which is the inverse ratio of the diameters to the fifth power. Preliminary computations on the power required to force a liquid through an inclined pipe (slope 1:6)
W-I
$3.
n o
0 00
g=
0
0 0
*'
A
0
A
g o u E m 2: +s > .20 /
#zE
8 :: uo
0
1
0 3
.I-
'F,/
/
,I
I
/'
/'
0
INDUSTRIAL AND ENGINEERING CHEMISTRY
434
.014
VOL. 31, NO. 4
Nomenclature
I
A O
/
c
’
D g
G L P
P t
= area, sq. ft. = chord length, ft. = significant dimension, ft. = gravitational constant, ft./(sec.) (sec.) = Vp = mass rate per unit area, lb./(sec.)(sq. ft.) = length, ft. = pressure, lb. per s in. or per sq. f t . = wetted perimeJei-,%. = temperature, F. mean velocity, ft./sec. = weight rate, lb./sec. = finite difference, used to indicate that the variable represents an average = density, Ib./cu. ft. = surface tension, Ib./ft. = traction, lb./sq. f t . = viscosity, (lb.)/(ft.)(sec.)
v =
w
A P
u 7
P
Dimensionless moduli: v
‘0
.01
.02
.03
.04
.05
.06
.07
.OL
OIL RATE-LLBS/SEC
FIGURE12. POWER PER UNIT LENGTHREQUIR~CD TO LIFTOIL UP A SLOPE OF 1: 6 AS A FUNCTION OF OIL RATE
-
Air rate = 0.000958 pound per second; A power to overcome gravity; B = actual power required
These results may be compared with the power per unit length required to overcome gravity as illustrated in Figure 12. The actual power is somewhat higher, which is roughly indicative of the inefficiency of the lifting process although the computations are subject to the definition of the ideal air-oil interface. The supporting data for Figure 12 are listed in Table IX. The authors have attempted to present experimental evidence which will allow the design of two-component flow systems of dimensions and properties not too far removed from the experimental range covered. Further experimental data are needed to extend the range of applicability of the results and to establish the basic variables.
Acknowledgment The results of this paper were obtained as a part of the Orchard Heater Investigation Project of the Division of Agricultural Engineering, University of California; H. B. Walker lent his support and encouragement; F. A. Brooks and Coby Lorenzen aided the project by advice and assistance. E. D. Howe, V. H. Cherry, H. L. Eagles, and other members of the staff of the Department of Mechanical Engineering a t the University of California aided the authors on the portion of the work done in Berkeley. The latter experimental installation was accomplished with the aid of the WPA Mechanical Engineering Research Project No. 8850. V. N. Tramontini, L. J. Mohler, J. W. Krug, 0. C. French, and A. L. Coons conducted the experimental work and performed computations. EXTRA HEAVYSTEEL PIPEBENDS USEDIN THE BLOWLINESAT THE BOTTOM OF THE DIGESTERS IN A KRAFTPAPER FACTORY Cour:ery, arinnell Company, Ino.
f = friction factor Re = Reynoldsmodulus = VDp/p Fr = Froude’s modulus = V 2 / g D We = Weber’smodulus = ug/V*Dp
Literature Cited Bakhmeteff, “Mechanics of Turbulent Flow,” pp. 31 and 32, Princeton University Press, 1936. O’Bannon, L. S., J. Am. SOC.Heating Ventilating Engrs., 30, 225-34 (1924). Page, Leigh, “Introduction to Theoretical Physics,” p. 222, New York, D. Van Nostrand Co., 1930. Walker, Lewis, McAdams, and Gilliland, “Principles of Chemical Engineering,” p. 77, New York, MoGraw-Hill Book Co., 1937.
