Adiabatic flow of boiling water through a horizontal pipe

1 AUG 1931 ADIABATIC FLOW OF BOILING WATER THROUGH

A HORIZONTAL PIPE.

by

James B. Holden

S.B. Massachusetts Institute of Technology, 1930 and

E. Ralph Rowzee

S.B. Massachusetts Institute of Technology, 1930

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Master of Science from the

Massachusetts Ins titute of Technology 1931

Signature of Authors

Signature redacted

Signature redacted

Certification of the Department of Chemical Engineering Professor in Charge of Research

Signature redacted

Chairman of Departmental

Signature redacted

Committee on Graduate Students

Head of Department

Signature redacted

Professor A. L. Merrill Secretary of the Faculty Mass. Inst. of Technology Cambridge, Mass.

Dear Sir:

Herein is submitted to you this thesis, in partial fulfillment of the re-quirements for the degree of Master of Science.

Very truly yours,

Signature redacted

Jams B. Holden

Signature redacted

E. Ralph Rowzee

ACHNOWLEDGMIT

The authors wish to acknowledge

their appreciation to Professor C. S.

Robinson and other members of the Depart-ment of Chemical Engineering for their interest and guidance in this research.

Subject . . . . ... . . . 1 Object . . .. .. . . .

1

Sumary . . .

1

Introduction .. ... ... 2 Summary of Procedure . . . 4 Results * . . . . . . . . . 6 Discussion of Results . . . 7 Conclusions .*** . ... .. 10 Recommendations... ... 10 Appendices A - Method of Procedure . . . . 11 B - Description of Apparatus . . 18 q Data. . . . . . 22 D - Calculated Data . . . 29 E - Calculations . ... .31%.

SUBJECT

Adiabatic flow of boili~g water through a horizontal pipe.

OBJECT

To determine the pressure drop in a changing two phase system consisting of water and steam as it flows through a horizontal pipe.

I

SUMMARY

Calculation of the friction drop in flow of

this kind involves the use of some sort of correction, which appears to be a function of the final velocity.

The range of investigation should be extended and a practical method of predicting results worked out.

In the usual problem of pressure drop in fluids flowing through pipes, no drastic changes in physical properties occur. If, however, a liquid at its

boil-ing temperature is allowed to flow through a pipe, there is likely to occur a change of phase, more or less com-plete, which will involve great changes in the

proper-ties of the fluid.

Suppose, for example, that the liquid is water

at its boiling point . As the water flows a short

dis-tance _{through the pipe, its pressure will drop because} of the friction effect. If the temperature has not

dropped to correspond to the lowered pressure, a certain

amount of the water will flash into steam. The fluid

is now a mixture of liquid and vapor with much changed

volume, velocity, viscosity, and density. _{As it flows}

on, more of it flashes; _{the changes in physical} proper-ties become greater. With these factors constantly

changing, the pressure drop is a variable quantity.

This case of fluid flow is of practical

inter-est since it _{comes up often in industrial apparatus,}

as in drawing off boiling liquids from evaporators or stills. It is probably of most importance, however, in the oil industry. Here, in pipe stills, changing

mixtures of oil and vapors are forced through consider-able lengths of pipe. Although it is known that the

friction effect becomes more pronounced as the amount of vapor increases, the mathematical relationships in-volved are not developed and it is questionable as to just how friction calculations on this case should be handled.

A thorough search of the literature in the forms of abstracts, periodicals, and theses revealed no in-formation on the subject. Furthermore, conversations with both chemical and mechanical engineers failed to

discover any such knowledge. It was finally concluded

SUoM[ARY OF PROCEDURE

As finally worked out and adapted the tecbnique of operation followed was quite simple. When the

apparatus had been heated up by blowing steam through it, the tank, with the air vent at the top open, was filled with cold water nearly to the top of the gage glass. The vent was then closed and steam blown in at the bottom of the tank to heat up the water. As

the temperature of the water rose, the pressure above it increased due both to the increased vapor pressure exerted and the effect of heating the air present

there. The pressure was kept from becoming excessive by venting the tank at intervals. The heating was con-tinued until a temperature about one degree above the

one at which it was desired to run was attained. The

steam was then cut off and the tank vented to boil the water and expel the greater part of the air present so

that the pressure in the tank would not be too much in excess of the equilibrium pressure for the

tempera-ture of the water. In the course of this operation, the temperature was dropped to the desired value. The vent was then closed and the apparatus was ready for

the run. Tbe outlet pipe was opened by unscrewing its cap and the fluid allowed to run out. The pressure in

-5-the tank was held constant by admitting steam into -5-the space above the water in the tank. Readings of the temperature and rate of fall in the tank were taken at one-minute intervals.

RESULTS

(With expansion loss based on upstream density)

Calculated pressure drop #/in.*' 6.747 6.520 2.945 5.841 4.627 6.523 Observed pressure drop #/in." 6.07 6.07 6.07 7.67 7.67 7.67 Pressure drop correction -0.677 -0.45 +3.135 +1.829 +3.043 +1.147 Final velocity f t./sec. 96.5 92.3 41.45 78.5 62.1 88.3

(With expansion loss based on downstream density)

Calculated observed Pressure Final

pressure drop pressure drop drop velocity

#/In.g

#/in.A correction Uf

#/in.*

ft./sec'. 4.506 6.07 +1.564 96.5 4.495 6.07 +1.575 92.3 1.696 6.07 +4.374 41.45 3.702 7.67 +3.968 78.5 2.823 7.67 +4.847 62.1 4.205 7.67' +3.465 88.3 Run No. 4 6 11 7 9 10 Run No. 4 6 11 7 9 10

4-Tj *11

. .. ...

OF

CoRRECTIONS c

versus

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4

DISCUSSION OF RESULTS

The amount of data taken in this investigation was, unfortunately, rather small. This was not clue

to any difficulties encountered in the experimental part of the work, which was a comparatively simple

procedure, but rather to the laborious and

drawn-out calculations necessary. Because of the lack of

time, the authors were obliged to limit their range

of operation to a very narrow band of conditions.

However, the data taken seems to have some correla-tion and justify the procedure adopted.

It is obvious that the phenomenon involved

here is an integral of operations taking place over

differential lengths of pipe. It was, therefore,

necessary to use mathematics of the same nature to

calculate the results. In the absence of an in-tegral to express what happened, it became necessary to resort to a stepwise method. It was assumed that the fluid flowed for a small distance without change of phase and that at the end of that distance all the flashing due to the pressure drop over that

distance took place. By a few preliminary calcula-tions, it was decided that computations of one inch steps would give reasonable accuracy. The error

in-

-8-volved by using one inch instead of one-half inch steps was one or two percent. However, a consideration of the time available made that increase in accuracy unde-sirable.

When the pressure drop in the pipe had been calculated by this method with the aid of the friction factor plot on page 87 of "Principles of Chemical

Eng-ineering" by Walker, Lewis and McAdams, it was still necessary to calculate the expansibn loss at the exit

of the pipe in order to get the total calculateddrop. This exit loss was figured from the formula on page 90

of the above book. It is obvious that the density to be used in this formula is neither the upstream nor

downstream density but some value between them. Compu-tations were made using both these two limiting values.

None of the total calculated drops thus obtained cor-responded to the actual drops involved, but it was

found that, when the corrections necessary to make them check were plotted against the calculated final velocity, the correlation was too good to be a matter of chance. The corrections vary both with temperature and with the

final velocity. As plotted, the curves are straight

lines and parallels for different temperatures. Apparent-ly, either set of lines may be used for the correction,

but as has been already explained, the true condition

is somewhere between the two limits.

The present investigation rests here. Future work should consist of two parts. * The range covered

should be extended for both temperatures and velocities. The latter may be varied by an adjustment of operating pressures and sizes or lengths of pipe. Secondly, a

convenient correlation and a simplified, practical

method of using the obtained data in predicting results should be worked out.

Again because of the lack of time, three runs were not calculated. however, _{these runs (numbers 13,}

16, and 17) were seen, by preliminary calculations, to

be very similar to runs already computed. The results of these preliminary calculations are included under Calculated Data. These runs should, at some time, be completed.

-10-CONCLUSIONS

1. The friction drop in a two phase fluid con-sisting of boiling water and steam cannot be calcu-lated from the usual formulae and data for single phase fluids without correction of same sort,

2. It appears that this correction is a func-tion of the final velocity.

RECOMME1DATIONS

1. This research should be continued to cover a wider range of temperature and velocities*'

2. A convenient correlation of the data should be worked out with the development of a practical

method of predicting results in fluid flow of this type.

APPENDIX A

METHOD OF PROCEDURE

The procedure followed in obtaining the data

for this thesis follows in detail.

The apparatus being heavily lagged to prevent heat loss during runs, it was necessary to heat it at a temperature approximating that of the subsequent

runs in order to bring the whole to a state of temper-ature equilibrium. To insure equilibrium, steam was blown through the apparatus for not less than twelve hours before runs were to be made. It was blown in

through the steam line at the bottom of the tank and with all other. exits to the tank closed, was

exhaust-ed through the horizontal pipe which was left uncappexhaust-ed. The temperature in the tank during the heating-up per-iod was about 220 0_F.

At the conclusion of this preliminary heating period, the steam was cut off, the outlet pipe capped

and the air vent at the top of the tank opened. Water was run in until the tank was about three quarters

full. At first, it was thought that for purposes of

exhausting all air from the tank,it should be

complete-ly filled with water and the steam lines opened f or a

in running, it was f ound that the steam contained air which collected slowly, building up an air pressure

as the water was heated. So, it was decided tb fill the tank about three-quarters full* turn on the steam through the line at the bottom of the tank until the desired temperature was reached, and when the steam

line had been closed, to vent the tank to allow the air to escape.

This was done. With all exits to the tank closed, the steam line at the bottom was opened and the water heated up to the rdquired temperature which

in one set of runs was 23ou]". and in the other 2340F.

The heating up of the water required about twenty

minutes. After the pressure started to build up (ob-served on the manometer) the tank was vented at inter-vals by means of the valve at the top of the tank.

This was done to prevent the building up of the pres-sure to too high a figure due to the air coming in with the steam.

When the temperature reached a figure about one degree higher than the desired temperature, the steam line was clased. (It was carried slightly higher than desired so as to provide opportunity to get rid of the air by venting the tank for several minutes.) It was

-14-found that when the temperature reached the desired point, the water in the tank boiled. After the steam was cut _{off, this was allowed to continue so as to}

allow the collection of any air which might be present in the air space at the top of the tank. Due to con-densation of the steam used in heating up the water, the tank was at this point nearly full of water.

When the boiling stopped, the tank was vented by opening the valve at the top. This permitted the air to escape and with the release of pressure, the

water started to vaporize thus reducing the temperature of the water slightly. _{This was allowed to proceed} until the temperature dropped to the desired point.

when the vent was closed.

As the desired temperature was reached, the outlet pipe was uncapped and a mixture of steam and

water flowed out at an apparently very high velocity. The water level in the tank began to drop and soon

after the pipe was uncapped, the level dropped down so that it could be observed by means of the sight

glass. _{The water was allowed to flow for two or}

three minutes to establish steady conditions and as the water level arrived at the 60 cm. _{mark on the scale,}

readings were taken, the steam valve was cracked just enough to hold the pressure constant and this valve was adjusted constantly until the end of the run. By this means, it was possible to hold the pressure constant to within one millimeter. Readings of the time, temperature, and height of water were taken every minute until the

level of water approached the level of the outlet pipe at which point the run was considered complete. From the

first reading, about six minutes were necessary to com-plete the run. In practically all runs, while the

water-steam mixture was exhausting through the outlet pipe, a

slight bumping or boiling was noted in the tank. It was

concluded that this was due to the fact that the upper layer of water bad _{not had time for equilibrium to be}

re-stored since the closing of the valve on top, and that a slight amount of the water was still vaporizing. This

was of no importance, however, as the run was considered over when the water level was still approXimately 10 cen-timeters above the outlet, and the thermometer .indicated

Before any runs were made the outlet pipe was

made level by adjusting its position in the box

which supported it and checking this level with a spirit level. Its position in the box was fiXed and left undisturbed.

The amount of lagging calculated to be

nec-essary to insure adiabatic flow (3 inches on the

tank and 2 inches around the outlet pipe) proved

sufficient as no temperature change was observed during most of the runs and in those in which a change was noted, it was so slight as to render it negligible.

It was found that to establish equilibrium conditions for the whole apparatus, it was necessary to make one or two runs before the conditions be-came sufficiently constant for the data to be re-lied upon.

A part of the preliminary work on the

appara-tus consisted in the calibration of the tank and of the thermometer used.

The tank was calibrated by filling it with

water and allowing the water to run through the out-let pipe into a pan which was supported on a plat-form scale. For each drop of five centimeters in

flow-ing out was weighed. This was done for two tankfuls of water, the second calibration being somewhat better due to more careful procedure. The calibration showed

the pounds of water per unit height of the tank to be esentiaLly constant.

The thermometer was calibrated over boiling

water. Its stem was immersed in the vapor approximate-ly the amount it would be immersed in the water in the tank. A number of check readings were obtained at the point of boiling water, and the reading corrected for atmospheric pressure as read from a barometer.

-18-APPENDIX B

A

IA a

II

yr.

2

r

w

*1

tq A

a

I

I

r

U

"'HE.

0 1

K

DESCRIPTION OF APPARATJS

The apparatus used for this work consisted of a galvanized iron cylindrical tank of approximately

18 gallons capacity, 1 foot inside diameter, and three feet in height, constructed to withstand a pressure of

50 pounds per square inch. It was set in a vertical position and supported on legs two feet high. A few

inches from the bottom of the cylinder was a horizontal 1" outlet into which a standard 1/4" iron pipe, 7 1/2 feet long was screwed by means of bushing. This pipe served as the outlet for the water-steam mixture, and reached into the center of the tank. The pipe was supported by a wooden box set on legs and was fixed

in a level position in the box. Leakage was prevented by means of a lock nut being turned up over valve stem

packing until it fitted tightly against the bushing.

Directly above this outlet, was another

horizon-tal tap into which a thermometer was fitted by means of

a rubber stopper. The thermometer was used to obtain the temperature of the water in the tank and was cov-ered with a pipe guard to prevent breakage.

Set into the bottom of the tank were two fittings, the one at the center to provide an inlet for the steam

which was used to heat the water to tIe boiling tempera-ture, the other was connected to the water line.

At the same level and placed at an angle of 9o to the outlet pipe was a horizontal tap connected to

a manometer for the measurement of pressure in the boil-er. The manometer contained mercury and had a range

of approximately 24 inches. On the opposite side of the tank from the manometer tap were two gage glass

connections into which a 50 inch gage glass was insert-ed. This was for the determination of the volume of water flowing from the boiler in a given length of time.

The glass was backed by a meter stick for measur-ing the drop in level of the water. These measurements were necessary to calculate the initial velocity of the water in the outlet pipe.

on the top of the cylinder was a vertical tap _to which an air vent was attached for the purpose of

ex-hausting the air collecting in the vapor space before

the start of a run. A horizontal tap near the top of the tank was used as a steam inlet in order to keep a constant pressure in the boiler as the water flowed out.

The boiler was lagged with a three-inch layer of standard magnesia blocks, the blocks were bonded to-gether with a paste made from loose lagging mixed with

water. The outlet pipe was also lagged by filling the wooden box, which supported it, with loose lagging.

This provided a three-inch layer of lagging around the outlet pipe also.

The two steam lines were connected to the 20-pound steam line in the laboratory. In the line was installed a steam trap to remove most of the moisture from the steam. After the trap, the line divided, one branch going to the steam tap at the bottom of the tank,

the other to the horizontal steam tap at the top. In each of these lines, a globe valve was installed to.

regulate the flow of steam and the pressure on the boil-er.

The length and size of pipe used was calculated roughly (using average values) from Berno-gillit s equa-tion as the most practical length and size to be used when operating the boiler at an absolute pressure of

about 20 pounds per square inch and exhausting to at-mospheric pressure.

On page. 1e will be f ound a photograph of this apparatus. Reference to it may be an aid in under-standing the foregoing description.

-22-APPERDIX C

Gage Glass Reading (cm.) 69.00 63.95 60.00 55.00 49.85 44.95 40.05 35.00 30.20 25.05 20.00 15.05 10.00 Differential Reading (11) 5.05 3.95 5.00 5.15 4.90 4.90 5.05 4.80 5.15 5.05 4.95 5.05 Diff erential Weight of Water (W) (Pound5) 8 6 8 8 7 7 8 7 8 8 8 8 1/4 3/8 1/16 3/16 7/8 13/16 1/16 16 1/4 1/8

W/H

1.634 1.613 1.61 1.59 1.61 1.596 1.595 1.60 1.60 1.61 1.615 1.61

-24--DATA

Calibration of Thermometer-Date Time Barometer Temperature Reading of thermometer in condensing steam Corrected barometer Boiling temperature at barometric pressure Thermometer correction April 14, 1931 10:30 A.M. 768.4 mm. 25.8

*0.

210.50_F. 765.17 m. = _{1.007 Atm.} 212.35OF. Add 1.80_F.

Manometer Reading cam. of Mercur7 Right Left 74.6 74.5 75.0 77.0 76.0 46.4 46.5 46.0 44.0 45.0 Run No. 0 1 2 3 4 a 6 Time min. 0 1 3 4 5 5-30 0 1 2 3 4 5 5-55 0 1 2 3 4 5 6 6-28 0 1 2 3 4 5 6 228.0 228.0 228.0 228.0 228.0 227.5 227.5 Temperature OF. 225.5 225.5 225.5 225.5 225.0 226.5 226.5 225+ 226+ 226+ 226.0 227.0 227.0 227.0 227.0 227.0 227.0 227.0 228. 228. 228. 228. 228. 228. 228. 60.0 51.3 42.6 33.8 24.9 16.0 7.2 Height of Water Om. 60 10 60 10 60.0 51.8 43.5 35.6 28.0 20.4 13.3 10.0 60.0 50.8 41.3 31.9 22.3 12.9 3.4 1 2 4 5

-26-Manometer Reading Run No. ercury Left 44.5 39.9 6

rM.

of Right 76.5 81.1 81.3 81.1 81.1 Time min. 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0-1 2 3 4 5 6 39.9 Temperature Height of "F. Water Om. 228.0 228 .0 228.0 228.0 228.0 228.0 P228.5 232.5 232.5 232+ 232+ 232+ 232* 233.0 232 232 232 232 232 232+ 232+ 232+ 232+ 232+ 232 232 232 233 232 232 232 232 232 232 233 60.0 51.1 42.4 334.5 24.8 16.1 7.4 60.0 51.7 42.5 33.1 23.6 14.3 5.0 60.0 51.0 42.2 33.7 25.2 16.8 9.0 60.0 51.0 41,9 32.5 23.3 14.0 4.7 58.0 48.8 39.4 30.0 20.5 11.5 1.5 39.7 39.9 7 8 9 10

Manometer Reading am, _{of mercury} Right Left 77.0 77.1 77.1 80.0 81.1 44.0 43.9 43.9 41.0 39.9 Rn No. 0 1 2 3 4 5 0 1 2 3 Time min,. 0 1 2 3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 228+ 228+ 228+ 228+ 228+ 228+ 228 228 228 228 Temerature F. 228 228 228 228 228 230 228.5 228.5 228.5 228.5 228.5 228.5 228.5 228 228 228 228 228 228 Height of Water Cm. 50.0 41.1 32.2 23.2 14.2 5.4 60.0 51.5 43.3 34.8 26.8 18.7 10.5 50.0 40.7 30.9 21.3 12.0 2.5 60.0 50.4 40.9 31.5 21.1 11.5 43.0 30.7 18.5 16.4 11 12 13 14 15

-28-Manometer Reading efn, of Merdury Right Left 76.5 77.0 44.5 44.0 Time min. 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Temperature O*. 228 228 228 228 228 228 228 228 228 228 228 228 228 228 Height Water em. 60.0 51.6 43.5 35.1 26.8 18.5 10.3 60.0 51.2 42.4 33.3 24.4 15.2 6.2 Run No. of 16 17

APPENDIX D

Run NF. 4 6 11 7 9 Initial temp. t *F. 230 230 230 234 234 234 230 230 230 Pressure in tank P1 21.60 21.41 21.60 23.14 23.14 23.14 21.65 21.42 21.60 Equili-brium Pressure Pt 20.77 20.77 20.77 22.37 22.37 22.37 20.77 20.77 20.77 Entrance loss #Iin.2 0.115 0.0995 0.103 0.115 0.103 0.115 0.118 0.089 0.105 Eff ective

< ,

P length

#/n.

inches Initial Velocity U ft/sec. 6.0 5.585 5.675 5.94 5.875 5.99 6.05 5.27 5.71 3.042 3.115 1.423 2.861 2.297 3.143 Expansion loss based on Down- Up-stream stream density density

#in.

2 _#/in. 1.464 3.705 1.38 3.405 0.273 1.522 0.841 2.98 0.5255 2.33 1.062 3.38 Pt . 14.7

#/An.2

6.07 6.07 6.07 7.67 7.67 7.67 6.07 6.07 6.07 Final y elocity u _f 96.5 92.3 41.45 78.5 62.1 88.3 42.25 47.9 35.15 45.4 43.0 46.1 39.5 42.5 36.7

APPENDIX E

-32-METHOD OF CALCULATION

The calculations were based on the following line of reasoning.

Knowing the initial pressure and temperature, the area of the outlet pipe, and weight of water flow-ing per unit time (obtained from drop in level of water and tank calibration) it was possible to calculate the initial velocity in the outlet pipe. Knowing this, it was possible to calculate the entrance loss in head by

the equation found in Walker, Lewis, and McAdams on page 91.

In every ran, the pressure in the tank was

above that corresponding to the temperature of the water, so it was necessary to calculate through what length of pipe the liquid would have to flow to reduce its

pres-sure to the equilibrium value. This was done with the use of the Reynolds number and the Fanning equation.

This remainder of the pipe after the subtraction of the amount just mentioned was called the "effective length"

as it was during this portion of the pipe that the liquid flashed and two phase flow occurred.

To calculate the velocity and pressure drops down the effective length of pipe, inch by inch calcu-e

lations were used. It was assumed that the pressure

drop and velocity during the first inch would be the same as if water were flowing alone. With the aid of the steam tables (assuming adiabatic flow), the velo-city at the end of the first inch and the pressure drop for the second inch were calculated. This was continued inch by inc# to the end of the pipe.

By means of the equation for expansion loss on page 95, Walker, Lewis, and McAdams, the pressure drop due to loss in momentum was calculated in two ways , In

one method, the downstream density of the water-steam mixture at atmospheric pressure was used, and in the

other the density of the mixture at the end of the pipe.

Reference to the following calculations will help make this explanation more clear.

CALCUIATIONS

Run

#9

Differential reading on manometer - 41.2 cm. Hg.

Correction for height above outlet pipe - 32.6 cm. H20 2.4 cm. Hg. Pressure at outlet pipe = 41.2 x 2.4 x 14.7 + 14.7

= 23.14 #/sq.in. Abs.

Temperature of water = 234 *F.

Rate of drop of water level in tank = 60 - 4.7 =9.22 cm/min.

= 9.22 x 1.607 = 0.247 #/sec.

60

Area of standard 1/4" iron pipe = (o)a x

=

0.000706 ft.*2

4x 144-Density of water at 234 OF. = 59.30 #/ft. 8 Velocity of water at entrance to pipe = ul

0.247

=

5.875 ft/sec.

59~5 x 0.007066

Drop in pressure due to entrance loss = Ku

(K 0.5 from plot Walker, Lewis, and McAdams, page 92)

0.5 x

(5.875)8

=

_0.268

ft.

HaO

=

0.110

#/in.

2

2 g

Pressure inside pipe = 23.15 - 0.110 = 23.04 #/in.2 Pressure corresponding to 234"F. = 22.37

Length of pipe necessary 2fLUS Dxs - 0.36 x 5.875 x 0.952 = 8.39 h

_gd

_{z 24} f =

.0058

0.67 x 144 2 x

.0058

x L x (5.875)* x 59..27 0.67

=32.2

x144 _x

.36

L = 3.92 ft.necessary to bring pressure to 22.37

#/in.

2

Effective length of pipe = 7.5 - 3.92

=

3.58 ft.

=

43.0 in.

P

= pressure drop in first inch

=

0.67 = 0.01425 #An.

3.92~x 12

Using Marks and Davis Steam Tables:

Og = entropy of liquid at end of first inch = 0.344214

= entropy of evap. at end of first inch = 1.378 Let x = pound of water

1 - x = pounds of steam In adiabatic change:

x(.344214)+(l-x)(1.375042) = .3443

Using 7 place log tables x = .9999535

Ve

=

volume (18.104 x .0000465 = .000841 for steam

0.01687 x.9999535 = .01687 for water Total .017711 cu. ft. u = 5.875 x 0.01771

=

6.17 ft/sec. a~ *.1684 Duo = .36 x 6.17 x

.7I~X

3

=

8.39 z 0,94 AP* = 2 x .0058 x --

1

x (6.17)' x 0'"IT 32.2 x .36 x 144

=

pressure _{drop in s nd inch.}

5042.

=

.0058

-0

Adding this ,Pa to AP, and interpolating between 234 and

233'F. for values of 0 + (V/t): e

=

0.344200 (v/t)

=

1.378614 x(O.344200) + (1-)(1.378614) = .3443 x = *9999028 18.12 x .0000972 = 0.001762 0.01687 x *9999028=0.01687 Total 0.018652 cu. ft. u1 = 5.875 x 0.01863 = 6.5 0.00687 1 12 APs = 2 x .0058 x = x (6.5) 52.2 x 0. 6 x 144 * 2

Expansion loss = ul" - 2

=-Sg

x

= 0.01573

#/in.

2

Ah ft. *HaO

u,

=

uf = 62.1

'1 = velocity after expansion = 0

Ah = (62.1) 94.*3

=

60 ft. Ha0

Using downstream density of mixture:

AP = 60 x 1.261

144

=

0.5255

#/in.

2

Using density at end of pipe 17

0.17855

=

5.6 (0.17855 = specific volume at end of pipe)

AP = 60 x 5.6 = 2.33 #/in.2 MI4

ft/sec. 5.875 6.17 6.50 6.81 7.15 7.51 7.90 8.30 8.73 9.16 9.65 10.14 10.65 11.20 11.80 12.38 13.03 13.70 14.40 15.20 16.05 17.00 17.90 19.00 20.02 21.20 22.40 23.80 25.20 26.60 4-A2 o*2CjQ1 #/ 1n.2 0.01425 0.01494 0.1573 0.1648 0.1727 0.1818 0.1913 0.2010 0.2107 0.220 0.2334 0.2459 0.2576 0.2712 0.286 0.0300 0.03160 0.03317 0.03480 0.03693 0.03885 0.04110 0.04338 0.04590 U. 0 4 8 5 5 0.05125 0.05430 0.05763 0.06095 0.06480 31 32 33 34 35 36 37 38 39 40 41 42 43 Final 28.10 29.80 31.60 33.60 35.60 37.80 40.20 42.70 45.30 -48.2 51.2 54.5 58.1 62.1 Total 6P = #/in.2 0.0686 0.07283 0 .0771 0.08183 0.08670 0.09235 0.09830 0.1042 0.1112 0.1187 0.1260 0.1341 0.1430 2.297 ~~0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30