512 APPLIED MECHANICS 
square inch of high pressure piston to the same scale as the high p: e 
diagram. These various conversions were discussed in Art, 272, Pp. 314. 
Adding together the corresponding ordinates of these corrected diagrams | 
would give the total effective pressure on the three pistons per square 
inch of high pressure piston. 
It remains to construct the diagram which shall show the horizontal 
thrust on the cross-head due to the action of the compensating cylinders, — 
This is shown by the dotted curve % 
DE (Fig. 822) constructed on the 8 h aa 
base XX. To construct the curve '*8 a a 
DE, the first step is to find the 144 Pa 
, P 
pressure on the rams per square 49 
inch of high pressure piston. de 2 EA 
This amounts to nm | 4 
O-7854x OXI poe pe A 
07854 x 142 thie Pe nD 
per square inch for each ram, * Kye mays) 
neglecting the effect of the piston-  °X side what dae 5 
rod. As there are two rams, the 24 seat 
total effect is equal to 131°4 Ibs. 4g H18y 
per square inch of high pressure 72 Base 
piston on one ram. Referring a te (, 
now to Fig. 822, O is the axis of %*>-4@ te 
the trunnion of one ram, and XX_ 120 D: 
is the line of stroke of its gudgeon. Fic. 822. 
When the gudgeon is at F, the 
axis of the ram is OF. On OF make OH equal to 131°4 lbs. to the 
pressure scale of the high pressure diagram. Draw the horizontal line 
HK to meet the vertical line OK at K, then HK is the horizontal thrust — 
exerted on the cross-head by the rams. Make the ordinate FL equal to 
HK. Lisa point on the curve DE. For the first half of the stroke the 
horizontal thrust of the rams on the cross-head is reckoned as negative, 
since it is opposing the motion of the cross-head. 
The upper boundary line of the final diagram, shown shaded in Fig. — 
822, is determined by laying off the sum of the respective ordinates of — 
the corrected curves in Fig. 821 above the curve DE in Fig. 822. For 
example, ab=cd +ef + gh. 
The ordinates of the final diagram represent the resultant horizontal — 
driving force on the pump piston per square inch of high pressure piston. 
The total resultant driving force is of course obtained by multiplying the 
force shown by the shaded diagram by the area of the high pressure — 
piston. In constructing these diagrams, the effect of the various piston- — 
rods in diminishing the effective areas of the pistons has been neglected. 
Direct driven steam pumps are generally of the duplex type, there — 
being two sets of steam and water cylinders side by side with one common 
delivery pipe. 
442. Centrifugal Pumps.—The ordinary form of centrifugal pump — 
consists of a wheel, disc, or runner, provided with a number of vanes, — 
which revolves within a casing. When fully charged with water the 
revolving wheel carries the water round with it, and the centrifugal force — 
