THROUGH Long, Narrow, Rectangular Ports,

FLOW OF STEAM ,

...THROUGH...

Long, Narrow, Rectangular Ports,...BY...

WILLIAM A. FRASER.

THESIS:

FOR THE DEGREE OF BACHELOR OF SCIENCE IN THE SCHOOL OF MECHANICAL ENGINEERING, COLLEGE OF ENGINEEING.

UNIVERSITY OF ILLINOIS,

1899.

/

VELOCITY OF STEAM THROUGH LONG NARROW RECTANGULAR PORTS.

The following experiments were made at the Central Heating plant at the University of Illinois^ to determine the velocity of steam flowing through long narrow rectangular ports; when the open­ing is regulated by a plain slide valve. The apparatus used in these experiments was designed to give as nearly as possible the same con­ditions that obtain in steam engines of the D valve type.

The apparatus is shown in the blue print page2,as it was mount­ed for experimenting on the bridge connecting the raultitubular and

tube.National waterAboilers, it is designed to withstand two hundred ^ _|i oOpounds steam pressure and the pattern making, moulding, machining 3 and erection was done by myself.

The drawing page 3 shows the apparatus in detail, it consists of a casting A,with a rectangular port P,1 x 10 inches and 6 inches long9passing through the center. It is closed and opened by a plain slide valve B,operated by valve rod C. The rod C passes through a stuffing box at D and is threaded with §" inch pitch so that one complete revolution of hand wheel H,will open or close the port g* of an inch. The thread engages in a brass nut F,which is securely fastened to the yoke G.

Steam from the boiler entered through a 2 inch globe valve in steam pipe j,into chamber lfwhich has the same function as the steam chest of an engine, it then passed through port P,into chamber K, which acts as the engine cylinder. From there it was conducted through a 2 inch gate valve in steam pipe L,to the low pressure heating main. The pressure in the steam chest was (Observed by the

4.6834

4

left hand gage in the blue print and the pressure was maintained constant by means of the globe valve in pipe J. This was easily accomplished and could be done no matter how the pressure in the boiler varied, as long as it was about seventy-five pounds.

The exhaust pressure was observed on the right hand gage in the blue print and was kept constant during an experiment by operating the gate valve in pipe L.

The initial steam pressure in all the experiments was sixty pounds; that being the highest pressure that could be maintained during the experiments. Fifteen different experiments were all that could be obtained with the boiler used.

The 100 horse power multitubular boiler in the Central heating plant was used to furnish the steam for the experiments. The ap­paratus as shown in the blue print was connected to the boiler main by about four feet of two inch pipe and had an angle globe valve at the point where it was connected with the steam main.

The exhaust pipe was two inches in diameter and entered the low pressure heating main through a two and one-half inch angle globe valve.

The quality of the steam was determined by a universal steam Earus calorimeter,'95 pattern,which was connected with the steam

I chest as shown on the left of the blue print. Temperature readings were taken every five minutes unless the fluctuation was too great, when a reading was taken whenever the temperature changed more than five degrees.

The weight of the steam flowing was determined by reading the height of the water on the glass gage at the beginning and end of

an experiment and finding the weight of water used from a calibra­tion curve for the boiler, then making corrections to this weight for moisture in the steam and for the weight of the steam that pass­ed out through the calorimeter All of the experiments were of from fifteen to thirty minutes duration. Before taking an experi­ment, steam was allowed to flow through the apparatus for at least ten minutes and the water from the chambers was completely drawn off through the drip cocks. This was to eliminate all errors due to the condensation and to insure uniform conditions during an experi­ment.

The data for the calibration curve was obtained by filling the boiler with water to within one inch of the top of the gage glass and weighing it out one inch at a time,down to the bottom of the glass. The heigth of the water was read on a seasoned oak scale, graduated to tenths of inches, which was placed beside the gage glass.

The curve Figure 2 was plotted from this data,with inches on the scale as abscissa and hundred pounds of water as ordinates.It covers the range through which the height of water changed during the experiments. The curve in figure two was used in determining the weight of steam for the experiments. Before beginning an ex­periment the boiler was filled up to within about three inches of the top of the gage glass and after the pressure was raised sufficient­ly the steam was allowed to flow through the apparatus. The height of the water was read at the beginning and end of the experiment.No water was put into the boiler during an experiment and all open­ing aside from the port were tightly closed,so that no steam could

6

escape from the boiler without going through the apparatus.Experiments were made with port openings of^g , Jr, and "inches.

The experiments with the Jr inch opening were taken with sixty pounds steam chest pressure and a drop in pressure on the exhaust side of from five to forty-five pounds in steps of five pounds; making in all eight experiments. For g" inch port opening the experiments were taken with an initial pressure of sixty pounds and dropped five to twenty pounds; four experiments in all. With the ^ inch port open­ing only two experiments could be taken with a steam chest pressure of sixty pounds and exhaust pressures of fifty-five and fifty pounds. One experiment with the Jp inch port opening with an initial pressure of sixty pounds^exhausting against fifty-five pounds was all that the boiler would furnish steam for. For the same port opening and back pressure five or more experiments were taken mak­ing eighty in all. The mean of five was taken as the result.

The following form of logs were kept during the experiment:

77>?7 e

_ZLog ofjE7x/oe/~/fr>e.n/~ 7/®- /•''a/ar/snefe/-

T/fB/r 710

//t/7/a/

/in

/Tx/rtfc/sf-

//7 /ourre/s

//e/p/rf 0/ b/a/en //7 Gape G/ass /// 7/tcAes

7~e./n. //1 C

7Vo. J

/0-*0~ 6# 4 0 £ 7 £&4/O-0o 6 0 4-0 £ 0 4

6 0 4 0 £ 3 ///- 0O 6 0 4-0 £ 3 6// -o^r 6 0 4 0 # 4 0 £ 0 8//-/0 6 0 4 0 3 0 0

6 0 4 0 7 0 S £ 4 3 3 0 0

7.

By means of the calibration curve the weight of water evapor­ated per minute was obtained. This weight corrected for moisture and the steam passing through the calorimeter gives the pounds of steam passing through the port in one minute. The area of the port being known and the volume of the steam being calculated for the pressure; the velocity

Where^= velocity in feet per minute.W = weight of steam passing per minute in pounds.A — area of port opening in square feet.D = weight of steam per cubic foot.

8 .

THEORETICAL VELOCITY OF STEAM PASSING THROUGH AN ORIFICE.When steam flows through an orifice like a port, heat is neith­

er added nor extracted and the expansion follows the adiabatic cur\e and there is a gradual change of pressure from p to p where ^ is the lower pressure.

The volume also changes with the pressure from v to vA .7~Ae w - or A of* ff?& -*7 of e c- w / 6 5 /s .

Z = Tq&q =Heat units required to raise the temperature of the water from 320 to the temperature of the steam at p & p2pressures./dinner latent heat, x & x±= Quality of the steam.The numerator is the heat dissapearing during expansion, which is equal to A L-A =mechanical equivalent of heat.L=outer work.

The pressure of the steam in the boiler exerts a force which not only overcomes the pressure on the outside of the ori­fice but it also imparts a velocity to the steam. If =• -velocity o f the Ste.c\vr\ ,.Tz ,

11Where p v — work expended to force steam out of orifice and give it velocity ctr.

To this work must be added the work equivalent of the heat dissapearing during expansion.

Then

/OV tm ‘g z n

— ft *3

0.

Multiplying both sides by A and putting V = X/* + V" %/s/i'<r

- (5-o~J >5 = specific steam volume, c^-^pecific water volume.

£ + Xf+fl/°« * f°* 'b«,**) + (j° ~/°0 -A7*3 _Z2T

A <r{p-pa ) is so small that it can be disregarded._ y~ /7j» =outer latent heat.

/** =total latent heat. =anner latent heat.

Substituting these values in IV.

+ *r - * > n ^

+xr-x,r,YF

*3 = 3 Z .Zi = 77Z ________

ur = / %-%•

Since p p2 and x are known. a, q,y)r and /T'can be found in table.6 6 r- r ,+

1Z2T

X/ ji.7 ;

T' and ^ are given in the table.Prom formula VII the theoretical velocity of saturated steam

and steam with two percent moisture were calculated and the re­sults are given on the following pages*

/o.

The data and results of the experiments are given in the follow­ing tables;

Table 1. pp/jgives the velocity of steam calculated for theoretical flow and from the data obtained by experiment the results above and to the left of the double lines were obtained by experiment while those to the right were taken from the curves drawn by comparison with the ones plotted from the experimental results.

Table 2.pp /-fto Ogives the results as obtained by ex­periment .

The curves Figures 3 to 9 were plotted from the results of the experiments and are explained on each diagram.

An inspection of the curves Figures 4 to 9 shows that there is a marked change in the velocity of the steam when the exhaust pressure falls to between forty and thirty-five pounds,for a j i " p o r t o pen m y th e v e lo c i t y fo r . -from f i f t y - f i v e to t h i r t y - f i v e poundsexhaust pressure can be approximately calculated by the formula

U r = 3 + f / T T

LaT =velocity in feet per minute.f-f ^height in feet of a column of steam, of the pressure of

the steam in the steam chest, which would produce a press­ure equal to the difference of pressure on the two sides of the port.

For each one-sixteenth inch increase in the port opening the velocity increases about four per cent.

When the exhaust pressure falls below thirty-five pounds there is but a slight increase in the velocity and for a formula there would have to be a change in the constant for each change

in the exhaust pressure,

/ 3.

7~a6/e 7Vo /.

/ressur±s/nitia/ £*Aaust

/ /reare/im Ve/ac/ty Saturated tit earnSee/.y>er- m"i

7Aeoret/ealVe/oer/y Steam 98 Qaa/itvSeetter

Ve/ocz/y 0/ 3team /n feetyaer mmute /7aw/ny 7/rrauyA 7ony,/Yarrow, /7ectanyu/ar 7 r/s. 73y /Txyer/nrent an a/ Can7y°or/aor (pi/o// ty -38

Yen* ft? ot tort /o" 14/477 ** Ae/aw '** "reAts7/A 4-

83 /4 3

8 2

6 0 - 3 3 323oo 3/300 2 2 0 0 0 2 2 600 232oo 24ooo 2 Sooo 27ooo

6 0- so 462So 4 4 3oo 34ooo 33~ooo 338oo 362oo 37600 3S>ooo

6 0 - 4 3 36800 33730 4 0 0 00 4 /0 0 0 4/900 42300 4 4ooo 433oo

6 0 - 4 0 6 6ZS0 6fSoo 438oo 43ooo 439oo 46300 482oo 30000

60-83 7S6oo 74000 462oo 47800 48600 49300 3/200 333oo

60-30 8 ?£oo 83700 48Soo Soooo 3/200 323oo 342oo 36 600

60-23 34-000 32000 So 8 0 0 322oo 33&oo 3 3 0 0 0 372oo 6 ooo 0

6 0 -2 o/O 3 3oo/0t 80 0 S2 70 0 344-00 36ooo 37 300 6 0 2 0 0 6 3 Ooo

60-737/28007/0 330 34 600 36 4oo 38200 6 0 00 0 6 3 ooo 6 6 Ooo

60-/3 72280 0 720800 36 S 00 384oo 6 0 2 00 6 2 Ooo 6 3300 68200

60-3 733 000 730 600 38 0 00 6 O/oo 62 700 6 4 000 6 7800 7 /0 0 0

6 0 - 0 744300/ 4 0 s00 3^2 00 678o 0 6 4 ooo 6 6 ooo 63300 733oo

74

7 ^ /b U 7Yo. 2 .

2x/>er/~/nerT/y* .

7?rz-0f>e/7/rt4 //fc />e7

Tress i/z-e. ZZx/?ausfod /7oa,n$f-

(pi/a//fyor*

lSZea/n

V/e.p/r/ of- Wafer fra/oo/-afe4 Jke/- /n/r.

Me/pAf of SZean, /,e* s/ey t/roupl /hr Aybr,ot>\

Vf/ocz/y /<v Too/

/ ~ w

//

76 3 3 .3 8 3 3 7<3 7 7 .3 4 2 2 8 3 8

2/

76 3 3 . 9 8 / 7 7 7 7 6 .2 9 2 / 7 5 2

3/

7 6 3 3 . 9 8 5 9 / 8 / 7 -3 / 2 2 7 9 8

4/

7 6 v ^ j T . 9 8 3 3 7 6 7 7 3 o 2 2 785

s/

7 6 3 3 . 9 8 0 3 7 6 7 3 2 9 2 0 / 3 5

6/_

/ 6 s o .9 8 /8 2 6 2 3 3 2 3 3 2 0 0

7/ .

76 <5o . 3 7 8 9 2 6 2 8 4 3 33 050

6_ z .7 6 <3~o • 9 8 / 7 2 9 28 .08 36 98o

9 / 6 <30 • 9 8 2 ? 2 7 2 6 .7 3 3 53 oo

/ o_z.

7 6 <30 .9 8 / / 2 ,8 2 7 0 7 3 5 6 5 3

///

7 6 4 3 . 9 8 o o 3 2 . 3 3/. 4 / 4 / 3 3 0

/ 2/

7 6 4 3 .9 8 02 3 2 30. 96 40 780

/ 5/

7 6 4 3 • 9 8 0 8 3 2 30. 9 8 50 8o o

7 5 7 6 4 3 .9 8 / / 3 2 . 3 3 / 4 8 4 / + 5 o

~7~aa&. / 4

7~a6/e 7Vo- £ C-on.

4xyoe/-/~

/nesif-

Z/o.

Y=>ortOjO&O/naZocZZs

Treasure 7'xYausfy7?p#/s7,s7jYc/u /ids

(j)oa//7yo f

\5/-eo/?j

We/yAl of Wafer fvayofo/et/ Joer m/n

We/fA/- *f

6/eom y>Oi-

siny tirtuyj, 8rtf t Ot in

Yt?/oc/fy

//7 T^pf-

7>e/- *vnti.

Z S-J~/ 6 4 4 .3 8 Oo 3 7 3 3 0 .7 7 7 0200

76 7 Z 4 -o . 3 8 o J - 3 3 . 3 3 2 .7 0 - 7-2737

7 7/

/ 6 4 o .9 8 0 2 3 4 32. 33 7 3 3 6 o

78/

7 6 4 0 s>8o<r 3 4 .3 - 3 3 .7 3 77023-

79 _Z _76, 4 o .9 8 2 7 3 7 3 3. 7 3 7 6 o

2 o_Z .

76 4 0 .9 8 0 2 3 7 3 2 .2 3 73 3 6 o

2 /_ Z _76 3 4 . 9 6 2 7 3 7 3 3 7 3 76o

2 2/

76 3 4 -0 7 8 6 3 3 3 3 -8 3 7 7 6 o o

2 3 Z 6 3 4 . 9 8 oo 3 < r 3 3 .9 o 7 7 63-0

2 7 76 3 4 . 9 8 2 0 3 7 33193 7 7 3 2 o

23~ 76~ 3 4 . 9 9 / / 3 7 3 6 .6 7 787oo

2 6s

7 6 3 0 . 9 9 4 Z 3 7 - 4 3 6 .9 3 4 8 6 7 0

£ 7 76 3 o . 3811 38 . 3 7-28 7 9 /o o

2 8/•

/ 6 3 o .9 7 3 3 3 7 3 33T.87 7 7 2 oo

2 97

7 6 3 o ■ 98oo 3 7 -3 3 6. 3/ 7 7 8 2 o

~7ay e. 7 &

7*£/e 7~/o. 2 con.

Tlxyer-/-m e n f

T/o

T a r fOyen/ny7/?cAe s

Trej^ure 3* Aaujtej7/772,4/

(j>ua/,tyof

Steam

We/y/}f a/ Wafer- fva/toratea /jet min.

We/fAf of Steamyas- J/aa /ArovpJ, fortyer/ni^

fc/oc/fy /h Teet ye r min.

3 0/

76> 3 0 .3 7 3 6 3 7 O ' 3 6 .3 0 4 7 8 0 3

3 //

76 2 S . 3 3 oo 40. 3 8 .7 9 3 / 0 9 0

3 2 , 7& 2 /T .3 8 / / 39. <r 3 8 . 7 3 3 O800

3 3/

76 2 3 ~ . 330* 40- 3 3 9 .3 0 3 /7 3 o

3 ? 76 2 3 ^ . 37 39 4 /. 3 9 . 7 3 3 2 3 3 o

3 3 76 2 d T . 9930 3 9 .2 3 3 8 3 6 3 0 780

3 0/

76 2 0 . 99/0 4 0 .7 3 39. 98 32660

3 7 // 6 2 ,0 • 3 8 7 + 4 0.30 3 9 .2 3 3/670

3 6/

/ a 730 • 3862 40 .3o 3 9 .3 * 32 030

3 3-Z .76 £ o . 3 8 * 8 4 2 .2 3 4 7 2 0 3 * 2 / o

4-3_z.

7 6 2 0 - 3 8 * 8 4 / .2 o 40. / / 3 2 9/2

4 //

7 6 7<7 ■ 9896 4 2 .2 3 4/. 4 / 3 4 3 * 0

4 2/

S S S ■ 9803 3 4 .3 3 3 .4 4 2 2 0 2 0

4 3/

s 3 S - • 9 8 /4 3 4 3 2 . 96 2 / 7 o o

4 * s~ ■ 3 8 / / 3 3 - 3 3 -9 4 2 2 330

© / /

/g7/e 7Vc. K? CO/7.

Sxper/ - fiie/tf /Yo.

f^ortOprefijfip/ ft c he s

Tre&sure.Sx/utuatae!/fao/nst'J&ovstc/ s

(pUfiZ/Yp

iSfeczm

We/?//- of Wzffer- /rvofcro te<) p e r zn/n.

Mrsp/rtot steqsn prat S/tio fziz-aap, forfprez-zni,

Ve/aci/?; //7 Feef- t. per fit zn.

4 S/

8 s s . 9 8 0 6 3 7. OO 3 3 .8 9 2 3 6 3 4

4 6/

8 S S . 9 d o o 3 6 .2 s 3 3 / 2 2 3 / 3 0

4 7 8~ S O ■ 9 7 83 3 2 .0 0 3 0 .4 ? 3 3 2 3 0

4 8/

8 S O , 98 o s ' 3 2 . oo 3 0 .3 9 3 3 3 2 0

4 9 S O . 9 8 o s 3 8 . o o S 6 4 7 3 7 / 9 0

S o/

8 s o ■ 3808 S 7-So 36 .0 0 3 6 870

S / 8~ s o .9 Q o o 3 7 oo 3 3 8 6 3 6 o o

S £/

8 4 S ■98/4 77 3 o 6 9.77 4 / 94 S

S 3 i r 4 S , 98oo 7 / 3 0 6 9.6 7 4 /8 o o

S 4/

8 4 S ■ 97-86 7 /o o 6 9.0 3 4 /2 o o

s < r/

8 4 S ■ 98oo 70. o o 6 8 / 9 4 0 8 o o

S 6/

8 4 S • 9 8 oo 6 9. So 6 8.o o 4 o 6So

S 7/

8 4 0 . 9 S Z 7 70. so 6 8 .8 7 4 3 3 So

S 8/

8 4 0 . 98// 737SO 73-78 4 8 S 8o

S 3 8~ 4 0 9 8 2 7 70 .o o 6 8 .3 0 4 4 9 o 0

7~aje. /6

TaA/e 7Vo. 2 O 0/7.

3 pen - sne/t//yo.

forf-OjPen/Hj//7 C A & £

Treasure.7x/rausftrc///aa/trat-Sfieuntfis

(pua/ifyo7

3/ea/n

Weyl)t 0/ Weter- Tyoforafe j?er /*7u1.

tye/yAt a/ Steam joqs S/HJ fArouyi Aort J°er min.

Ve/ocity srt/eet- f>er thin.

6 0 6 4 0 3d// 7370 ?3. 78 48380

6/ £ 4 0 ■ 2760 72.60 70.02 46 /ZO

6Z £ 4 0 . 9893 7 7 -3 0 70. 3o 4 6 6 2 0

6s 6 3<r . 9 8 /0 73-00 7 / 9 3 4 7 4 / 4

6 4 6 3 3 3 8 / 0 73. OO 7 3 ./ O 4 8 4 2 0

6<3 6 3 <7 . 9 8 9 0 72,00 7 / Z / 4 7 o o o

6 6_3_76 S 3 . 9796 4 9.36 4 8 o 9 2 3 /7 0

6 79_

76 3 3 .9 7 9 3 3 o .o o 4 8 .6 o 2 3 3 4 0

6 63

76 3 3 .9 7 9 3 48 00 46 -60 2 2 4 6 o

6 a 7* 3 3 .9 8 / / 49. 00 4 7 6 9 2 2 940

7o3

/ 3 3 . 9 7 9 3 3 o .00 4 8 .6 0 2 3 3 40

7/3

/ 6 3 -0 . 9 8 / 7 83.00 83 03 3346 0

7 23

/ 6> 3 o . 9836 89.oo 67/4 37230

7 * 7& 3 0 . 9 8 2 3 8 3.00 83. /o 334Xo

3/6 3 0 > 9792 84.0 0 8/83 34 940

y e / 3

~7ajb/e. 77 o . 2 co/7-

£y>e/-/'-/rre/rt

7/o.

/o rf-Oyehincj//?c7es

Treasure*7*/>auJitff4S yy jn s t

6j notify

\5featn

Weight- of WaterEvaporatedye r nun.

We ip f t of steam y>as- a/y throupi, tort ysrn?in.

Velocity in fee f yoernu'n.

7 S3

7 6 S o . 9823 8 3 7 0 0 8 3 ./ 0 93T+80

7 6/

4 s s . 9 8 + 2 76.oo 7+ <76 2 + 9 3 0

7 7/

s s • 9836 72oo 7 0 7 Z 2 3780

76 + s s ~ .9 8 2 7 7+.oo 72.3 Z 2 3 8 /0

7 s/

.38+2 7&.oo 7 + S O 2 + 3 S o

<9o ^ 3 ~ .9 8 <7o 737o o 7 3 .o o 2 + 000

~7&<7e'

PA e ore /zca/ l e/a c/iy oA Ozeazzz

f/cn vzzzy / A rs tz ^ A a/7 O d z/zce ,

fe e ,/ - y o e r P /zZ7 i//e -

/si / Azof / Pre s z/re 60 Pz> vzzfs---------6z?/zzr#f er/ J/ev/rz

Q zzzz/zA y 3 6 P>

S S do S S 40 3 d 30 2 d Z o /S ' SO S' o Z^ess u re /TxSrai/tfee/ /7y<?//76/-

/fl

flfl

/-&

&■

/-^

oe

r /7

7//7

.

£Tx6a vsf / /'essur-e*

' X

i§$VX

:-■--r/yur& <x

Ye/oc/Vv of f'/eo's?? ffroaoXy /do/'/l & x /&"

/ f3/ ffx/?ex//?7 &/7 f a/jY CsaVfw±j<?/7/ Qi/af/fy zzs 7% ^/ //7/Y/a/ /yressvr& 63

ffxfousf f resoi/x-e.J S - 3 0 Jdo S 3 - / O 3~ O

P/y ure 6V e / a c p y o f 3 / - e 4/77 / A r e * / 4 /7

ParA3/ Px/yer/me/iA a/7W Pempar/sor?Quu/zY/ fo //77V/4 / Pressure 60

PxAausf Pressure,'T'o s~ *?o 3<s~ 3 0 £ ,0 7 3- ro 3 - o

Z700

ZlZ

&Z/

yer

/T7//7

\

\1

7yyM/ c/fy 0 /Z a / i

C /./?& /'//7 7

Ve/oF o r

#

Z/7/

'& 7\ J Z e 0 / 7 7 Z Z 7 r s c y y Z 7

0 "

e / 7 Z 0 /7 * Z 7^/77/70 r / 5 0/7

'a Z Z f y c9 6 7

Z Z & Z T T r e s s u r e

4 x ^ / Z ^ r& s s u re sS ’i f $-o ■?£- 3S~ 30 £6~ £ 0 ss~ yo S ’ o

s

$

PORT OPENING FOR DIFFERENT PISTON SPEEDS.

in deriving a formula for the area of port opening the factors to he taken into account are; velocity of the steam for the given width of port, piston speed, diameter of cylinder, point of cut off and the ratio of the lengths of crank to connecting rod. The width of the port, ratio of crank to connecting rod, piston speed and diam­eter of cylinder are either fixed or assumed in each engine design. The point of cut off varies for each change in the load, and the the port area must be large enough to keep the steam pressure from falling more than ten per cent for maximum cut off.

The piston speed as taken for an engine is

y =piston speed in feet per minute./V revolutions per minute.£ -length of stroke in feet.

This piston speed varies at every point of the stroke between zero at the beginning and end and maximum speed near the middle of the stroke; hence some constant must be introduced to correct the piston speed for point of cut off taken.

The value of this constant is derived as follows:Let x = distance piston has traveled when cut off takes place.

T' - length of crank.= angle that crank has rotated through.

^ ir-yc)

JL - fraction of stroke that piston has traveled throughZ r

when cut off takes place.

jg-Q fraction of cranx circle that cranx pin has traveled when cut off taxes place.

If the angular velocity be taXen as uniform then the constant to be used equals

/_QOJL = 9 0

The port area multiplied by the velocity of the steam is equal to the piston area multiplied by the piston speed.Port area= 7 7 -4 * 0 V

■*f. ujr-

d =diameter of cylinder.V =piston speed in feet per minute.C =constant.os velocity of steam in feet per minute for given width of port.

Table 3 pp£9and Figure 10 pp#* gives the values and curve for the constant c^for different ratio of cranx to connecting rod and different point of cut off.

2>9

yct^/e 77o 3

Cuon/{Tl/ty/e.

74

Cut off

fcrt/o o.s yConstant

r Crctn

Cut off

/f to C r

Constant

onne-cf0.

Cltoff

7/7f /J (TCom Tent

oc7t

Cutoff Consto/it

/0 ° .003Z . / 6 &6> .009/ ■ 7648 ■ 0039 ./& 0 2 .0089 . 76,02

£ 0 ° ■ 03t>7 • 330 3 ■ 03 bo ■ 3240 ■ 0385 . 3/95 .03 50 . 3/50

30° ■ 0809 ■4854 ■ 0796, 4776 ■0784 - 4704 .07 74 ■ 4644

4 0 ° ■ /4o o ■ 6300 ./3 7/ ■6/70 73 58 . 6/// ■7342 ■ 6040

S 0 ° -2 //5 . 75/4- -208/ ■ 749/ 2054 ■ 7404 2032 73/5

c>0 ° .2920 . 876o .2878 ■ 8 6 3 4 ■ 2843 852 9 . 28/4 ■8442

/ o 60

(/r.ti- ?>