328 APPLIED MECHANICS . 
ro 
in the cylinder is proportional to the speed, and that all the surplus energy is 
stored in the fly-wheel, find the horse-power developed and the speed at the 
end of one minute. [U.L.] 
28. A punching-machine needs 4 horse-power ; a fly-wheel upon the machine 
- fluctuates in speed between 100 and 110 revolutions per minute; a hole is 
punched every three seconds, and this requires five-sixths of the total ene 
given to the machine during the three seconds. Find the M and the I of this 
fly-wheel. ‘‘M” is the kinetic energy of the wheel at one revolution per 
minute. t. 
29. In a gas-engine using the Otto cycle the indicated horse-power is 8 an 
the speed is 264 revolutions per minute, ‘Treating each fourth single stroke as 
effective and the resistance as uniform, find how many foot-pounds of energy must 
be stored in the fly-wheel, at mean speed, in order that the speed shall not vary 
by more than one-fortieth of its mean value. [Inst.C.E.] 
30. A gas-engine is provided with two fly-wheels, each weighing -114 cwts., 
and the radius of gyration of each is 1°87 feet. There is one working stroke in 
each four strokes. The diameter of the cylinder being 74 inches, the stroke 9 
inches, and the mean revolutions per minute 250. The mean pressure during 
the firing stroke is 88°7 Ibs. per square inch, during the compression stroke 15°1 
lbs,, during the exhaust stroke 4°4 Ibs., and during the suction stroke atmos- 
pheric. If the resistance overcome is constant, find the percentage variation of 
speed of the engine. (U.L.] 
31. A gas-engine drives a number of machines in a workshop. The work 
done on the piston during the working stroke is ¢ times the work done during 
the four strokes which make a complete cycle. The engine works for some 
time at 60 horse-power, and at a mean speed of 200 revolutions per minute. 
Immediately after an explosion in the working stroke has taken place, machines, 
which absorb 20 horse-power, are cut off, the speed at the instant being equal 
to the mean speed. Find the moment of inertia of the fly-wheel so that the 
change in velocity during the working stroke is not more than 4 per cent., 
and then find the number of revolutions per minute at the end of the fourth 
stroke, [U.L.] | 
