230 HYDRAULICS AND ITS APPLICATIONS 



be explained later. If the indicator drum be rotated uniformly and 

 independently of the valve spindle, a diagram similar to Fig. 105 is 

 obtained. Here A A' marks the pressure in the main before opening the 

 valve, B B' the pressure at the valve with steady flow, so that the 



fl v 2 



distance from A A' to B B' represents^ . C marks the instant 



2 g m 



of closing of the valve and C C' indicates the excess pressure p' due 

 to closure. 



Both theory and practice emphasise the importance of a relatively 

 slow motion of ths valve as it approaches its seat, and particularly at the 

 instant of closing. 



Gradual Opening of Valve. If the valve be gradually opened, so that 

 both valve area and velocity of pipe flow increase with time, equation (6) 



1) V 2 1 f 'V? V f f' c 



becomes - \- -- -{ z = - j d x ^ r 2 d- x -f C (6') 



w 2 g g J d t 2 g m Jo 



If the valve is opening uniformly, on proceeding as before (9) becomes 



d VQ . d O.Q c 



an -^ -f- ?'o -7 r = 



d t d t 



and on making the assumption that ( ) is small, this becomes 



\ Ct / ?? 



dv _ ___ ^ I" At_ 



When t = 0, let V Q = v , the flow being steady, and let o = i, 



^ d Q>Q -rr d O,Q 



Then a = i + t r = i + Kt, where A = -= . 



. | v <> r .^-f g I _ / i 



^'o -h q ' VQ r [ " \i H- K 

 from which we get 



I - 



ft. per second, 



where r, <y, ??i and /v have the meanings attached to them on p. 227, viz., 



This gives the velocity of efflux after an interval of t seconds from the 

 commencement of the motion, in terms of the valve opening and velocity 



i Here I = . ^ ami c = 2 g h. 

 a d t 



