That is, for a perfect heat engine, operating through a reversible cycle process, the efficiency of the machine is the ratio of the difference of the absolute temperatures of the sources of heat and of cold to the absolute temperature of the source of heat.

FORMULAS USED IN STEAM AND STEAM

ENGINES.

RELATION BETWEEN THE

PRESSURE AND TEMPERA

TURE OF SATURATED STEAM.

Let temperature, Fahrenheit; t =

absolute temperature = t + 460°;

absolute pressure (pressure above vacuum) in pounds per sq. in.

H= 1,081.94.305 t. (91.) Art. 1200.

SPECIFIC VOLUME OF SATURATED STEAM.

p V = 475, (92.) Art. 1203. in which

is the pressure in pounds per square inch, and V the volume in cubic feet of a pound of steam at the given pressure.

WORK DONE IN THE CYLINDER OF A STEAM ENGINE.

Let P = the pressure on the piston in pounds per sq. ft.; p = pressure on piston in pounds per sq. in.;

V volume swept through by the piston;

W = work in foot-pounds.

Then,

W = PV = 144p V.

(93.) Art. 1212.

RELATION BETWEEN CLEARANCE, CUT-OFF, AND NUMBER OF EXPANSIONS, OR RATIO OF EXPANSION.

Lete the number of expansions;

=

i= the clearance, expressed as a per cent. of the stroke;

TO FIND THE AREA OF A THEORETICAL DIAGRAM AND THE WORK REPRESENTED BY THE DIAGRAM.

Let A

=

total area of diagram in square inches;

initial pressure measured in inches;

volume at cut-off measured in inches;

L = work in foot-pounds;

a = net area of diagram;

Then, the work done per minute is PL A N foot-pounds. One horsepower 33,000 foot-pounds per min.

=

Therefore, the indicated horsepower of the engine is found from the formula

PLAN

I. H. P.

=

33,000

(98.) Art. 1268.

When the point of real cut-off, and the steam pressure

at the beginning of the stroke, are known, the M. E. P. may be found approximately by the following formula:

in which P= absolute steam pressure = gauge pressure +14.7 pounds;

e = ratio of expansion;

p = absolute back pressure.

p is usually taken as about 3 pounds for condensing engines, and 17 pounds for non-condensing engines.

RELATION BETWEEN LENGTH OF STROKE, NUMBER OF REVOLUTIONS, AND PISTON SPEED.

Let L = length of stroke in inches;

R= number of revolutions per minute;

S piston speed in feet per minute.

=

Lete

EXPANSION ENGINE.

ratio of expansion in high-pressure cylinder;

E total ratio of expansion;

E=

v = volume of cylinder receiving steam from the

V:

boiler;

= volume of cylinder exhausting into atmosphere or condenser.

Letting the letters have the same meaning as in the last formula, then either of the following formulas may be used:

Lett, t,

the temperature of departing condensing water; the temperature of entering condensing water; ts: = the temperature of the condensed steam upon leaving the condenser;

H = total heat of one pound of steam at the pressure of the exhaust;

W the weight of water required per pound of steam condensed.

W =

H-t,+32

t-t2

Cooling Surface.

(105.) Art. 1323.

Let S the required surface in square feet;
W total weight of steam used per hour.

Then, S.0944 W.

(106.) Art. 1325.

TO FIND THE WEIGHT OF A FLY-WHEEL.

Let V the greatest velocity of the crank-pin in ft. per sec. ;

1

=

V1= the least velocity of the crank-pin in ft. per sec.;

V1 = average velocity of crank-pin in ft. per sec.;

0

W required weight of fly-wheel in pounds;

= =

H = the number of foot-pounds per sq. in. of piston

A

n

E=

W

represented by the excess of crank effect over the resistance;

area of piston in square inches;

ratio between radius of fly-wheel and length of crank;

FORMULAS USED IN PRINCIPLES OF

REFRIGERATION.

Let 2,

=

=

TRANSFER OF HEAT.

heat delivered to condenser in B. T. U.;
heat taken from body cooled in B. T. U.;

W = work in foot-pounds done by engine on working

fluid;

J = 778 mechanical equivalent of heat.

or

Let H

h

=

REFRIGERATING CAPACITY.

B. T. U. abstracted from cold body in 24 hours; = B. T. U. abstracted from cold body in 1 hour; F = refrigerating capacity, expressed in tons.

THEORETICAL MAXIMUM EFFICIENCY OF A HEAT ENGINE.

Let E theoretical maximum efficiency;

Q1 = heat given up by the hot body in B. T. U.;
Q1 = heat rejected to the cold body in B. T. U.;

T, absolute temperature at which heat is delivered

=

to condenser;

absolute temperature at which heat is abstracted from cold body.

In the last formula, J and I have the same significance

as in formula 108.