PUMPS 501 
Weight of water raised in one up stroke = 62-3al. 
Work done in one up stroke = 62:3alh = Pl. 
Therefore P =62-3ah. That is, the pull on the pump-rod is equal to the 
weight of a column of water, whose base is equal to the area of the bucket, 
and whose height is the total head. Hence when friction is neglected, 
P is independent of the diameters of the suction and delivery pipes. 
During the downward stroke no water is raised, and only friction has to 
be overcome. Strictly speaking, a volume of water is discharged during 
the down stroke equal to the additional volume of pump-rod entering the 
barrel, but in the pump under consideration this may be neglected. 
Considering the effect of the pump-rod, if a, = effective area of bottom 
of bucket = 0°7854d?, where d is the diameter of the barrel, a, = effective 
area of top of bucket (a, is less than a, by the area of the section of the 
rod), h, =suction head, h. = delivery head, then P= 62°3(a,h, + ayhq). 
434. Plunger Pump.—Fig. 801 shows a short stroke plunger pump 
provided with ball valves. S is the suction valve, and D the delivery 
valve. The action of this pump 
during the out or suction stroke: is 
the same as that under the bucket 
of the bucket pump when the bucket 
is ascending. During the in or de- 
livery stroke the air within the pump 
is compressed and a portion of it is 
discharged through the delivery valve, 
and when the pump becomes charged 
with water a volume of water equal 
to the displacement of the plunger 
is discharged through the delivery 
valve during each delivery stroke. 
By the displacement of the plunger is 
meant the volume equal to the area 
of the cross section of the plunger 
multiplied by the length of its Fic. 801. 
stroke. 
A duplex pump, consisting of two plunger pumps side by side and 
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Fig. 802. 
delivering into the same pipe, is shown in Fig. 802. The two plungers 
