HYDEAULIC ENGINES 577 



oss of kinetic energy per stroke ) . v* f , ,, 



,, ,, . , , , , x - = 62*4 L A s foot IDS. 



(assuming all this to be lost) 2 g 



here L = length of stroke of piston 



D = diameter, A = area of piston in square feet 

 v* = mean square of velocity of flow through ports 



A 2 

 = v z ^y, where v* = mean square of piston velocities throughout 



a stroke. In general v may be taken as T25 times the 

 mean piston velocity v m with sufficient accuracy for practical 

 calculations. 1 



Since the losses of head included under the two latter headings serve 

 oth to diminish the effective pressure on the working stroke and to 

 icrease the back pressure on the discharge, we have the total loss of 

 nergy per working stroke 



= 2-31 p la + 195 ^~ .{1 + 1 J footlbs. 

 Substituting for A and a in terms of D and d, and writing m = -^ this 



ecomes 



Differentiating this with respect to d and equating the result to zero, 

 ire have : 



P i 



rom which, by successive approximations, or by graphical solution, we 

 an find d, the diameter of inlet ports for the total loss to be a minimum. 

 f the inlet passages are rectangular in section it is sufficiently near for 

 iractical purposes to make their sectional area equal to that of this 

 ircle. 



1 Here v m = L time to complete one stroke. 



If a curve be plotted having the squares of the piston velocities as ordinates on a displace- 



aent base, the mean height of the curve will equal i* - In the case of an oscillating 



ylinder with a connecting rod equal to three cranks in length, the ratio is approximately 



Vm 



(n \ 2 

 J = 1-61. With a longer connecting rod this will be reduced, 



that in general ( J will approximately equal T56 = (1'25) 2 . 



