536 



HYDRAULICS AND ITS APPLICATIONS 



efficiency of the machine is the ratio of the useful work delivered at the 

 turbine shaft to the energy supplied at the wheel inlet, and is given by the 

 ratio 



2 TT N M where N revolutions per second 



W Q H ' M = turning moment on shaft in foot Ibs. 



Here M is less than the hydraulic turning moment 



WQ 



' 2 r a w a r a ) 



foot Ibs. by an amount depending on the frictional resistances of the 



turbine bearings and on the hydraulic frictional losses in the wheel itself. 



From (10) it appears that the efficiency should theoretically increase as 



the ratio r ~ diminishes, i.e., as the breadth of the turbine is more 



3 ?*3 



rapidly increased towards the centre. Even theoretically, however, this 

 possible increase is only small because of the smallness of tan 2 a, while 

 such a construction, by giving wheel passages which have a sectional area 

 increasing in the direction of flow, tends to produce unsteady motion with 

 a consequent loss of energy in eddy production. 



Again from equation (10) it appears that the efficiency increases as /3 

 increases, and diminishes with an increase in a, the following table giving 

 values of rj corresponding to different values of these angles, in the case 



where ^ ^ = 1, and where in consequence / 2 = /a- 



Values of a. 



