550 HYDKAULICS AND ITS APPLICATIONS 



This loss becomes a minimum when w 3 , i.e., the velocity of whirl at 



f 2 

 exit = 0, and then has the value ^- . 



* 9 



Practically the whole of this energy is lost where the turbine discharges 

 either directly into the tail-race or into a parallel suction tube whose 

 area is equal to that of the vanes at discharge. If, however, the suction 

 tube has an area which gradually increases towards its outlet, a portion, 

 up to about 25 per cent., of this may be converted into pressure energy, 

 with a consequent gain of efficiency by the wheel. 



In general this source of loss accounts for between 3 and 8 per cent, of 

 the total energy supplied, being greatest in turbines of the outward flow 

 type and least in those of the axial flow type. 



(8) Mechanical Friction, H B . This generally accounts for between 

 2 and 4 per cent, of the total energy, its magnitude depending largely on 

 the type of machine (whether hydra ulically balanced or not). 



Taking these losses into account, if H is the total supply head, 

 H = H' -\- loss in pipe friction. 



The hydraulic efficiency 17 N - U _ U 



of the turbine is given by j H loss in pipe friction ~~ EP 



The work done on the i TT rr t4 . iu 



turbine shaft - ff w ^ e ft. Ibe. per sec. 



.'. Gross efficiency of) U H L + E + F+G 



turbine wheel j " H' 



Useful work delivered at ) 



turbine shaft - B*.*.,*.,*. . per sec. 



/. Nett efficiency of; U H L+E+F+G + B 



turbine 1 " H' 



While the gross efficiency ] 



of the plant, including I U - 



supply and discharge | H 



pipes 



ART. 144. THICKNESS OF VANES. 



So far no account has been taken of the fact that the vanes must be 

 made of a certain thickness, and therefore reduce the effective area 

 of the guide and wheel passages. The necessary corrections for this 

 in the case of an inward flow turbine may be made as follows : 



Let t be the vane thickness, and n the number of vanes which cut the 

 circumference under consideration. 



At inlet, the area of guide vane circle occupied by these vanes = b\ 



