614 HYDRAULICS AND ITS APPLICATIONS 



^ 

 And since this effective space = x . , this gives 





. . / 2 q (ir a h s h f ht) A 



velocity = V - / - . x feet per second. 



Lg d a 



while the piston velocity = u> r sin 



=. w r A/ 1 cos 2 $ 



w V (2 -J a? r feet per second. 



After impact the mean velocity of the supply column becomes equal to 

 that of the piston multiplied by . 



"' 



J / 2 q (n a //., h f h t ) x A 

 .'. Change of velocity at impact = { ^J - 





= Va, feet per second. 



If this change of velocity be assumed to take place instantaneously, the 

 increase of pressure due to water hammer is given by 63'7 v x Ibs. per 

 square inch (p. 235). In the example previously considered, taking x = 

 '47, we have : 



Change of velocity at impact 



= J 



26 X -86 



DO 



= 4-76 - 1-61 

 = 3'15 feet per second. 



/. Water hammer pressure = 3*15 X 63*7 Ibs. per square inch 



= 201 Ibs. per square inch. 



In addition to this we have the pressure necessary to produce a retarda- 



^4 

 tion o> 2 r cos 6 feet per second per second in the supply column. 



o> 2 r A (l- ~\ X W a s L 



This pressure = - Ibs. per square inch 



a s X g X 144 a s 



(7'33) 2 X '25 X 1-83 X -88 X 62-4 X 63 



32 X 144 



= 18*5 Ibs. per square inch. 

 On taking into account the obliquity of the connecting rod, this becomes 

 23 Ibs. per square inch. 



The total pressure which may be attained at impact (provided this 

 pressure is not sufficiently great to lift the delivery valve), is then given 



