DELIVEKY AIE VESSELS 621 



*-*+*.-** (30 



(neglecting frictional losses in air vessel as being comparatively small). 



On substituting for a v in (3 ; ) in terms of a s from (1), as before, we have, 

 equation (4) : 



A *- a '*.\ (4 / } 



, ) 

 and substituting in this equation for hj from (2'), on reduction : 



sn 





By substituting in (4') for a s from (2') we get, on reduction : 



X+*.-- ^ 



sin 

 cos 



from which, on assuming values for h v , a curve similar to Fig. 290, 

 showing the pressure on the piston for a series of values of 9 may 

 be plotted. 



In practice, with single- barrel double-acting pumps, suction air vessels 

 of from I/O to 3'0 times the capacity of the pump per revolution are 

 found to give good results, the necessary volume increasing with the 

 rotative speed of the pump and with the length of suction pipe. 



ART. 167. AIR VESSEL ON DELIVERY SIDE OF PUMP. 



Here exactly the same reasoning applies, except that now flow into the 

 air vessel will take place during the first half of the delivery stroke, and 

 flow out of the vessel during the second half when the water column in 

 the delivery pipe is being retarded. 



Considering the latter part of the stroke, for continuity of flow : 



d v d a v v v = A V 

 '- a d a d a v a v A a. 



Also h d now corresponds to (h s TT) in the case of the suction vessel. 

 /. Equation (2) becomes : 



h = h d + -4-^ (neglecting friction) ; 

 9 



