HYDRAULIC ENGINES 575 



ART. 155. THEORY OF THE HYDRAULIC ENGINE. HORSE 

 POWER. 



If K = number of cylinders supposed single acting. 



p = mean effective pressure in Ibs. per square inch in each 



cylinder. 

 N = number of revolutions per minute. 



I = length of stroke in feet. 

 A = ram area in square inches. 



Then I.H.P. = K . P -^. 



The mechanical efficiency varies with the size and type of engine, and 

 with its condition, but will be generally about 85 per cent. 

 If Q = volume of water used per minute in cubic feet. 



H = supply head in feet. 

 The hydraulic efficiency 



_ indicated work on piston _ K . p I A N 

 energy in supply water " 62*4 Q H ' 

 or writing Q = K I A N -=- 144, 



144 p 2-31 p 



we have the hydraulic efficiency = = 2 . 



33,000 (B.H.P.) 



The total efficiency of the system = \- 



oz'4 (/ ri 



= hydraulic efficiency X mechanical efficiency. 



Pressure on Piston. As in the reciprocating pump, the pressure on the 

 piston at any point of the stroke is affected by the inertia of the supply 

 column. The engine may in fact be considered as a reversed pump with 

 mechanically operated valves, and the investigation into pressure condi- 

 tions in the cylinder proceeds on exactly similar lines to that in the case 

 of the pump. For a further investigation of these pressure effects the 

 reader is referred to Art. 163. It may be noted, however, that at any 

 point of the stroke, where a is the piston acceleration and v its velocity,, 

 if a, is the area and l s the length of the supply pipe, in being its hydraulic' 

 mean depth, we have : 



Head on piston ) [~ supply head A l^ ( f ?? 2 A ) , "I 

 in feet } = [_ ^ feet ~ V ' \ a h ^n~a s \ ft< J ' 



Here a is positive during the first, and negative during the last part of 

 the stroke. 



A weighted accumulator feeding the supply pipe line has the effect of 

 increasing acceleration pressures as explained in Art. 193. The provision 



