eT SSF a 
s0 
25 
PISTON AND ORANK EFFORT DIAGRAMS 327 
_ twisting moment diagram, as in Fig. 510, in pound-feet per square inch of piston 
area. 
- (6) Determine the coefficient of fluctuation of energy and the coefticient of 
, fluctuation of speed. 
_t-—-- One revolution. —- —-->«- --— One revolution.- - - - > 
ee Ne Pte \ CN 
______\_ || Average Turnis 
Fie. 510. 
18. A fly-wheel, whose radius of gyration is 5 feet, weighs 4 tons. How 
many ft.-lbs. of energy will this wheel take up in changing its speed from 99 to 
101 revolutions per minute ? 
19. A certain fly-wheel gives ont 6500 ft.-Ibs. of kinetic energy in changin 
its speed from 170 to 168 revolutions per minute. What is the kinetic energy 0 
this wheel when its speed is 172 revolutions per minute ? 
20. What must be the weight, in lbs., of a fly-wheel, 15 feet in diameter, 
whose mean speed is 120 revolutions per minute, if the total fluctuation of 
speed is 7 per cent. of the mean speed, and the energy taken up between the 
minimum and maximum speeds is 12 foot-tons ? 
21. A steam-engine indicates 10 horse-power. The fluctuation of speed is 
gy of the mean speed, and the mean speed is 100 revolutions per minute. The 
fluctuation of energy is ; of the work per revolution. What must be the 
weight of the fly-wheel for this engine, assuming that all the weight is concen- 
trated at a distance of 2 feet 3 inches from the axis of the wheel? 
22. Calculate the moment of inertia of a fly-wheel (in ton and foot units) 
which will give up 20,000 ft.-lbs? of energy as its speed changes from 130 to 128 
revolutions per minute. 
23. The mean speed of a be Peg is 85 revolutions per minute, and the 
coefficient of fluctuation of speed is s{5. What are the minimum and maximum 
speeds? If the coefficient of fluctuation of energy is 0°07 and the indicated 
horse-power of the engine is 1600, what must be the moment of inertia of the 
fly-wheel (in ton and foot units) ? 
24. A cast-iron fly-wheel is in the form of a disc 6 inches thick and 4 feet 
6 inches in diameter. Taking the weight of a cubic foot of cast-iron as 450 Ibs., 
what is the kinetic energy of this wheel in foot-tons when it is running at 200 
revolutions per minute ? 
25. A fly-wheel weighing 60 tons has a radius of gyration of 15 feet. The 
indicated horse-power of the engine is 3000, the mean speed is 75 revolutions 
per minute, and the coefficient of fluctuation of energy is 0°06. What is the 
coefficient of fluctuation of speed ? 
26. A 1000 horse-power engine, running at 240 revolutions per minute, has a 
wire-wound fly-wheel whose mass of 70 tons may be considered as concen- 
trated at a radius of 10 feet. ress the energy stored in this fly-wheel in 
terms of the work done per revolution. Steam being shut off, find the moment 
of resistance which will reduce the speed from 240 to 120 revolutions in 
two minutes. — [U.L.] 
27. An engine developing 80 horse-power has a fly-wheel 10 feet mean 
diameter, weighing 4000 Ibs., and making 120 revolutions per minute. The load 
on the engine is reduced to 60 horse-power. Assuming that the governor fails 
to act, that the speed increases at a uniform rate, that the horse-power developed 
