322 APPLIED MECHANICS 
energy of a given wheel is therefore equal to the square of the speed, in 
whatever way that speed may be stated, multiplied by a constant, and 
for certain problems this simple rule is useful. 
If I is the moment of inertia of the wheel, in Ib. and foot units, then 
I= WR?, and from this and the foregoing formule the following formule 
are readily deduced, namely, K = Wet ae 
: : 2gR? 29g 6029 © 
If during a period or cycle of the working of a machine the minimum 
and maximum speeds of the fly-wheel are N, and N, revolutions per 
2 
minute respectively, then the fluctuation of energy is 30%) (x: - Ni). 
The difference between the maximum and minimum speeds is called 
the fluctuation of speed, and the ratio of the fluctuation of speed to the 
mean speed is called the coeffictent of fluctuation of speed. If N is the 
mean speed in revolutions per minute, and ¢ is the coefficient of fluctua- 
tion of speed, then ona oN, It is usual to assume that the mean 
speed is the arithmetical mean of the maximum and minimum speeds, so. 
that 2N=N,+N,. Hence NZ -Nj=(N,+N,)(N,-—N,)=2cN?. 
If U denotes the work done per period or cycle in ft -lbs., and & 
denotes the coefficient of fluctuation of energy, then the fluctuation of 
energy is kU, and kU = i he cd 
een he 6029 6029 
If H is the horse-power of an engine, then the work per revolution- 
is segs where N is the speed in revolutions per minute. 
The following are some values of ¢, the coefficient of fluctuation of 
speed, found in practice :— 
Pumps, and shearing and punching machines . . 3 - 0:05 to 0°03 
Flour-mills - : : . : ; ; : ‘ - 0°04 to 0:03 
Looms, paper-making machines, and ordinary machine tools. 0:03 to 0°025 
Spinning machinery . A . : . ‘ : r . 0°02 to 0°01 
Dynamos . = ‘ : ‘ 5 : ‘ . é : - 0°007 
Exercises XIX. 
1. The piston of a steam-engine is 30 inches in diameter, and the stroke is 
40 inches. Instead of a piston-rod there is a trunk 12 inches in diameter which 
works through the front end of 
the cylinder. The indicator dia- 70 
grams for this engine are given in ig 
Fig. 501. The full line diagram 6° 1 BF g 
is from the back end, and the sol Ne b. 
dotted line diagram from the \ Be, rie. : 
front end of the cylinder. The 49 Bee een s 
pressures marked are in Ibs. per N--T - 
square inch. Reproduce these 30 
diagrams, making the length 5 $ 
inches, and the pressure scale 20 ot 
1 inch to 20 Ibs. per square inch. 10 = fo ine 
Reconstruct the diagrams on a 
straight base to show effective pres- 
sure on the piston, in lbs. per square Fre. 501, 
inch of the larger face of the piston. 
What is the effective pressure in lbs, per square inch of the larger face of the 
