PRESSURE VARIATIONS IN PUMP 605 



receive an acceleration at the commencement of the stroke, the magnitude 

 of the acceleration being given by 



A , 



a t.S.S. 

 a s 



where o = piston acceleration in f.s.s. 



A = piston area in square feet. 

 a s = area of suction pipe in square feet. 



The force necessary to give this acceleration can only be produced by a 

 difference in pressure at the two ends of the suction pipe, and varies as 

 the mass of water in the pipe and as its acceleration. Expressed sym- 

 bolically we have 



W A 



Force necessary to produce acceleration = l s a K . a Ibs. 



If the pressure difference at the two ends of the pipe corresponding to 

 this force is p' Ibs. per square foot 



W 



p' a s = l a A a Ibs. 



W . A 

 .-. p - -. l s a Ibs. per square foot. 



If at the same instant the piston velocity is v f.s., for continuity of 

 flow we have v g = v ; and the loss of pressure due to friction in the 

 supply pipe corresponding to this is given by : 



p" = J '* ' = *- s s- v 2 Ibs. per square foot. 

 2 g m 2 g m a? 



.'. Total difference of pressure at the inlet and outlet of the suction 

 pipe is given by : 



W A ( f A } 



p' -f p" = p = - - I J a + TT-- ~ $ \ Ibs. per square foot. 

 g a s * | 2 m a g J 



Or, expressed as a head " h " in feet of water, 



7 A I, ( f A 2 ) 



h = - \ a -f ^ . v 2 I feet, 



g a s ( 2 m a s \ 



where a is positive or negative according as the piston is being accelerated 

 or retarded. 



Now the head actually available to produce this flow is strictly limited, 

 the higher pressure at the pipe inlet being that corresponding to its 

 depth of immersion together with that of the atmosphere, while the lower 

 limit of pressure is theoretically that corresponding to an .absolute 

 vacuum, although in practice it is impossible to obtain this degree 



