324 APPLIED MECHANICS 
on the crank shaft, (a) with infinite connecting rod, (b) with connecting-rod 
45 inches long. a 
9. Referring to Fig. 503, cal- 
culate T, the effort on the crank Forward stroke. 
pin per square inch of piston "sa eee 
when 6=75°, when 0=135°, and 
when «=5 inches, assuming an 
infinite connecting-rod. 
10. Same as preceding exer- 
cise for both forward and return 
strokes, but taking the connect- 
ing-rod 45 inches long. 
11. The cylinder of a vertical P (ac+2)=560. 
steam-engine is 45 inches dia- : a 
meter, oak the stroke is 4 feet. Return stroke = 
The connecting-rod is 8 feet Fic. 503. 
long, and the effective weight of 
the reciprocating parts is 10,000 Ibs. The speed is 100 revolutions per minute. 
When the crank is 30 degrees from the top dead point the steam pressure on the 
top of the piston is 190 lbs. per square inch, and on the bottom 85 lbs. per square 
inch. Find the effective force transmitted along the piston-rod and the turning 
moment on the crank shaft when the crank is in the above position. [U.L.] 
12. Construct the rectangular diagram of combined crank effort for a two- 
cylinder engine, the cylinders being of equal size, and the cranks at right angles 
to one another. The piston effort diagrams are given in Fig. 503, and the con- 
necting-rods are 45 inches long. Find the coefficient of fluctuation of energy 
for this engine under these conditions. 
13. Same as Exercise 12, except that the inertia of the reciprocating parts is to 
be taken into account, the weight of these parts being 
3 Ibs. per square inch of piston. The engine is a 
horizontal one, running at 150 revolutions per minute. 
Stroke of piston, 20 inches. 
14. Considering Fig. 503 to refer to a vertical engine 
in which the weight of the reciprocating parts is 3 Ibs. 
per square inch of piston. Construct the rectangular 
diagram of crank effort, taking into account the weight 
and inertia of the reciprocating parts, and find the co- 
efficient of fluctuation of energy. Length of connect- 
ing-rod, 45 inches. Speed, 130 revolutions per minute. 
15. Show, (a) that with constant pressure P on the 
piston and infinite connecting-rod the polar crank 
effort diagrams for one revolution are two circles of 
radii r=}$P, as shown in Fig. 504; (0) that with two cylinders of the same size, 
constant pressure P on each 
piston, infinite connecting-rods, 1 
and two cranks at right angles, 120 sats 
the polar diagram of combined PS BS ab 
crank effort for the two cranks 499 Mine | l-4" 
for one revolution is bounded Pat =F } 
by four arcs of circles of radii go pete | ; 
R=r,/2, the centres of the La 7 
circles of radii R being situated  60}-\+-7- it 
at the corners of a square of , 
side=2r, as shown in Fig. 504. 40b44=505 ee 
16. The following __par- Ra-tdotd-t4- ; 
ticulars* relate to a vertical 2 
triple expansion steam-engine: 
Diameters of cylinders, 18, 27, _ 
and 44 inches. Diameter of J 
High Pressure. 
piston-rods, 4:75 inches, Stroke 
of pistons, 16 inches. Length Fig. 505. 
* Kindly supplied by the makers of the engine, Messrs. W, H. Allen, Son, and 
Co., Bedford. 
