EXAMPLES 569 



EXAMPLES. 



(1) Show that in a reaction turbine working under conditions of 

 maximum efficiency, the efficiency is given by 



where e measures the proportion of energy existing in the form of 

 pressure energy, in the water at entrance to the wheel. 



(2) The angle of the guide blades in an LF. reaction turbine is 12, the 

 peripheral speed is 32 feet per second, and the velocity of the water at 

 inlet is 36 feet per second. Determine theoretical vane angles at inlet 

 and outlet, the inner being the outer diameter and the velocity of flow 

 constant. 



( Inlet angle = 67. 

 Answer. _ 1?0 2(y< 



(3) If in the previous example the head is 36 feet, the B.H.P. 50, the 

 gross efficiency 82 per cent., what must be the effective area of the wheel 

 inlet, assuming a coefficient of contraction of *95. 



Answer. 2*10 square feet. 



(4) The external and internal diameters of an LF. reaction turbine are 

 4 feet and 2 feet 3 inches, the vanes are radial at inlet, the velocity of 

 flow through the wheel is = J *J 2 g H f , and the peripheral velocity is 



TTf 



that due to a fall through -=-. Determine the vane angle at outlet for 



a 



the water to be discharged without any tangential velocity. 



Answer. 17 27'. 



(5) If in the turbine of the preceding question the vanes at outlet make 

 an angle of 20 with the circumference, determine the speed at which 

 the wheel should run ; the velocity of flow ; and the pressure and kinetic 

 heads in the supply chamber, in terms of the available head H 1 ', 

 and also determine the angle which the guide blades make with the 

 circumference. 



Answer. 



^Revolutions per minute = 4'71 >J g H' a = 10 11'. 

 Velocity of flow, / = '7 ^/~g~H' 

 Pressure head = '492 H' 



Kinetic head = '508 H'. 



