Fig. 110. Let the gauge pressure in the boiler be constantly 90 lbs. per square inch.

Conceive the dimensions of the tube to be such that the weight of steam discharged per second to be unity. Then in one second the rectangle of steam a""ob""oc""olo expands from the pressure Oa1 and volume ab1, Fig. 110, to the pressure DE and volume OD, and simultaneously it moves from g1 to gr. Conceive that when occupying the positions 91, 92, 9, the steam is at the

Zero Press.

Oar, Fig. 110. Then the volumes

vvv'v'e are represented by aba, asbз

6

ab, Fig. 110, b1E being an adiabatic curve. The phenomena occurring during one second are then as follows:

(1) Unity weight of water is vaporized in A, requiring the expenditure of heat from the main source equal to

H= total heat of evaporation for 90 lbs. pressure.

The unit of weight thus vaporized displaces abocado, causing the latter to force go to g. Thereby there is performed the work Oa,b,k, of which the part Oa,b,k is expended against the atmosphere and a,a,b,b', creates velocity in g. We have thus expended a portion of H, but have not lowered the latent heat or temperature of g1, since Regnault's value for H includes the work of forcing the steam out of a boiler at constant pressure.

(2) g, becomes g2, and thereby the work kbbak, is performed, the portion kb'k, overcoming the resistance of the atmosphere and bbby creating velocity.

(3) 9 becomes 93, 9s becomes g

96 becomes 97, and

Summarizing these effects we have the distribution of heat as

follows:

2

Let V2 the volume of a pound of saturated steam for the pressure DE, and He = the total heat of evaporation for this

pressure.

In forcing the steam from the boiler there is performed upon the steam a,a,b,b', units of work and upon the atmosphere Oab'-k units of work.

By adiabatic expansion to condition E, heat is abstracted equal to kb,ED. By proper transformation the value of this area may be written,*

*The work kb1ED =

V1

p du, in which u is any volume of the mixture after

latent heat per pound of steam at p1 in foot-pounds per Reg

kb1ED = H1 — Oаab1k — (H2 - DE × V1⁄2) + Q,. '. . (1.)

*

Н

in which Q is a quantity representing heat supplied by the liquefaction of a certain portion of steam in accordance with the law of adiabatic expansion.

7

If now we consider that the work a,a,b,b', is available to tend to counteract the effect of Kb1ED, we may write :

Kb1ED-a,a,b,b'2 = H1
H1 — Оubk — (Hx − DE × v2) + Q'

(2.)

In which is a value representing liquefaction less in amount

= b',b1E + Kb'2ED + Oa‚b'2K + a‚a‚b‚b‚ — a‚a‚b‚b‚ -- DE × v2 - (H1 - HE)

= b'‚b1E + Kb'2ED + Oα„b'„K — DE × v2 − (H1
- v2- – HE)

in which

H' = latent heat per pound of steam at p1 foot-pounds.
H" = latent heat per pound of steam at p2 foot-pounds.

Add and subtract H" in (4).

Then,

kb, ED = J(t, − t2) + H" (

=

tą, in which t, and t, are temperatures above 0 on Fahrenheit

scale. Hence (5) may be written,

in which H, and HE are total heats by Regnault's tables in foot-pounds.

(7.)

is the proportion of v2 which liquefies and is equal to Q in (1);

Equation (3) divided by the latent heat of steam for the pressure DE gives the proportion of moisture in the steam represented by the portion g of the jet, Fig. 109.

For any other portion of the jet as ga, which is at the pressure Oag, we may conceive the action to be the same as though a jet flowed into an atmosphere at a pressure Oa, since g, absorbs only the dynamical effects represented by the area açab1b ̧ which lies above abs. In general, therefore,

Let p1 be the absolute boiler pressure.

P2, any lower pressure.

V1, the volume of a pound of saturated steam at P1.

Va, the volume of a pound of saturated steam at p.

u2, the volume of a pound of steam expanded from p1 to p2 adiabatically.

H1, Total heat for P1.

Ha, Total heat for p..

Table I. shows values of Q'.

for p1 = 105 and p2 ranging from 15 to 70 lbs. Also

for p1 = 70 and p2 = 15 and 33 lbs.

From the table it appears that the value of Q' becomes zero for a value of p, nearly corresponding to the back pressure which gives the maximum outflow measured by weight. Both theory and experiment prove that this pressure is that of the steam at or near the extremity of the nozzle or tube.

*

Hence it follows from the above deductions that steam as seen close to the end of the tube through which it issues into the atmosphere is neither sensibly superheated nor below the condition of saturation. Hence dry steam, if allowed to flow through an orifice into the atmosphere under conditions such that it attains its maximum velocity at about the instant of exit into the atmosphere, appears invisible for a very short distance from the orifice as per photographic views of the paper. The slightest obstruction to its outflow, created by throttling, superheats the steam and less than five thermal units produces the considerable increase in the length of the invisible portion of the jet, shown by photographic Fig. 68. The jet is similarly sensitive to the presence of moisture as shown by photographic Fig. 64.

* See Rankine's Discussion on the "Outflow of Steam," Engineer, 1869.

TABLE 1.

SHOWING SUPerheating oF STEAM JET DUE TO ITS VELOCITY OF FLOW INTO THE ATMOSPHERE.