282 WORK OF WATER WHEELS. 



supply in the reservoir be maintained. (See Besant's 

 Hydrostatics, p. 112.) 



153. Work of Water Wheels. To utilize ahead of 

 water, consisting of an actual elevation above a datum level 

 at which the water can be delivered and disposed of, a 

 machine may be employed in which the direct action of 

 the weight of the water, while falling through the given 

 height is the principal moving force. 



When a stream of water strikes the paddles of a wheel 

 which has a certain velocity, the energy imparted to the 

 wheel by the water, from (4) of Art, 98, 



W 

 = [*_(_ 7)^ (i) 



where V is the velocity of the periphery of the wheel, v the 

 original velocity of the water, and W the weight of water 

 acting on the wheel per second ; but if the water descends 

 with the paddle there is an additional amount of work done 

 on the wheel due to the mean height h through which the 

 water falls. Hence we have, for the whole work done on 

 the wheel per second, 



W 

 = [> 2 _ ( _ r)J ^ + Wh. (2) 



Now if the water leaves the paddles the work remaining 

 in the water will be lost ; hence, calling v t the velocity of 

 the water after it has left the paddles, we have for the use- 

 ful work U done on the wheel 



U = [v* (v V) - V] r + Wk 



*9 

 w 



= [2vVV* vJ\- + Wh, (3) 



ty 



which is the general expression for the work done by a 

 water wheel when the water impinges upon the paddlec 

 perpendicularly. 



