WORK OF OVERSHOT WHEELS. 



283 



154. Work of Overshot Wheels. When a waterfall 

 ranges between 10 and 70 feet, and the water supply is from 

 3 to 25 cubic feet per second, it is 

 possible to construct a bucket 

 wheel on Avhich the water acts 

 chiefly by its weight. If the varia- 

 tion of the head-water level does 

 not exceed 2 feet, an overshot 

 wheel may be used. The Avater is 

 then projected over the summit of 

 the wheel, and falls in a parabolic 

 path into the bucket. If v be the 

 velocity of delivery to the wheel, 



the part is converted into energy of motion before reach- 

 ing the buckets and operates by impulse ; hence in a wheel 

 of this class the Avater does not operate entirely by weight. 



The height li through Avhich the Avater falls is the vertical 

 height of the point at which the water meets the buckets 

 above the point Avhere it leaves them, Avhich in this wheel 

 is nearly equal to the diameter of the wheel ; and as the 

 A'elocity of the water on leaving the bucket is the same as 

 the velocity of the bucket itself, we have v l = F; hence 

 (3) of Art. 153 becomes 



= ( V -V) V + Wh. 



(1) 



Calling m the efficiency* of these Avheels, we have from (1) 

 U=m\ -(v-V)V+h \W. (2) 



COB. To find the relation of v and F so that the useful 

 work U of the wheel may be a maximum, we must equate 

 to zero the derivative of U with respect to F, which gives 



. Jleche., Art. 6. 



