618 HYDRAULICS AND ITS APPLICATIONS 



substantially equal to that in the suction chamber we have, denoting this 

 pressure by hj feet of water, neglecting frictional losses in the supply 

 pipe, and simply considering the acceleration effect : 



7 T \ TT" a * W I <! 



(77 - h, - hj) a, II = ------- '- 



Also, considering the flow down the air vessel : - 



Substituting for a v in terms of a s from (1) we get : 

 7 //,. (A a a, a,) 



^ = * + *- 7 J r } 



Substituting for hj from (2), this becomes : 



(3) 



a. = 9 * - (h, + A.) + h, - 1 



s k. , , 



I fc S 



a v 

 as compared with its value -- , without air vessel. 



Neglecting, for the time being, the variation in h a and h v with a varia- 

 tion in the piston acceleration a, it is evident from (6) that for a s to be 

 affected as little as possible by a variation in a, the term involving a must 

 be as small as possible. This indicates that a w the sectional area of the 

 vessel, should be as large, and h v as small as possible a deduction which 

 is verified in practice. 



When the pump is working, the water surface h v undergoes cyclical 

 variations in height, h a assuming corresponding values. The connectic 

 between the two may be obtained on the assumption that the air folkn 



1 This assumes the air vessel to be of uniform diameter to its junction with the suction pij 

 If, as is more usual, the junction is made through a smaller pipe of area a\, this formi 



becomes h a + h v hj = - iv ai . where 01 = a^ . 



