620 HYDRAULICS AND ITS APPLICATIONS 



It only remains to substitute for h vt and if, as indicator diagrams show 

 to be usually the case, we assume that this has its minimum value shortly 

 after the piston begins its suction stroke, we may obtain the acceleration, 

 at this point by putting h v = ['5 '28] = '22 feet in the above expression, 

 and by writing 



4 Tr 2 X 100 2 v 



The " "> = 30-055 



= 2-62 f.s.s. 

 as compared with its value co 2 r X 4 = 219*3 f.s.s. without air vessel. 



The maximum acceleration will in general be found to occur at about '2 

 of the suction stroke. 



Evidently a further increase in the size of air vessel, or an increase in 

 the length of suction pipe will reduce the value of a s still further, and 

 with a suction pipe of any considerable length its value approximates 

 very sensibly to zero. In such a case the flow along the pipe is sensibly 

 constant, and the velocity is equal to the discharge in cubic feet per 

 second divided by the area of the pipe. If this assumption be made, 

 calculations relating to the necessary size, etc., of the air vessel are 

 considerably simplified, as will be shown later. 



Modifying Effect of Friction and Kinetic Losses in Suction Pipe. Taking 

 the total difference of head between supply reservoir and piston as being 

 given by 



2 g \ m / y 



this may be written as : 



Since a, = a> 2 r cos 

 a s 



99- 2/1 A 2 sin 2 ^4 



and v, J = o> 2 r 1 sin *n ^ = a, ? - - . - 

 a s 2 cos 6^ a, 



... ,_,,-,, = ^|, + fl ^| feet . 



The preceding equations now become : 



