586 



HYDEAULICS AND ITS APPLICATIONS 



But if h s and h d are the mean suction and delivery heads, we have : 

 Work on up stroke = W { (A a) li d + A h s } L foot Ibs. 

 Work on down stroke = W {a h d ] L foot Ibs. 

 /. For equality : 



(/I a] li d -J- A h = a h d 



which approximates to -^ as li d becomes large compared with h g . 



Where the pump is vertical, and the weight of plunger line great, this 

 requires modification if the forces acting at the upper end of the plunger are 





FIG. 273. Piston and Plunger Pump. 



to be equal on both strokes. In this case, if W P = weight of plunger line : 

 Force to be exerted on 



up stroke 

 Force to be 



= W { (A - a) h d + A h, } + W P Ibs. 



exerted on | 



TT . , 7 



W \ a h* \ 



Ibs. 



down stroke 



.'. For equality, 2 W P W { (2 a A) h d - 

 = W { 2 a h d A (h d 

 . W P .Afa + li,) 

 'Wh^ <2h d 



The bucket valves may be eliminated while retaining the advantage of 

 uniform delivery or uniform work on both strokes, by the type of 

 construction indicated in Fig. 273 and known as the Piston and Pluni/er 

 pump. Here a solid piston is used instead of the hollow bucket. Suction 

 takes place on the out-stroke, while at the same time a volume (A a) 

 L is delivered. On the in-stroke, a volume L A is discharged through 



