286 WORK OF THE PONCE LET WATER WHEEL. 



its velocity on leaving the vanes is the same as the velocity 

 of the vane itself, we have Jt = 0, v v = F; therefore (3) 

 of Art. 153 becomes 



W 

 U = (v- F) F , 



9 



or U= m(v F) F , 



where m, as before, is the efficiency of the machine. 



Sen. The wheel works to the best advantage when the 

 speed of the periphery is one-half that of the stream (Art. 

 154, Cor.), but the efficiency is low, never exceeding 0.5. 



Wheels of this kind are cumbrous. In the early days of 

 hydraulic machines, they were often used for the sake of 

 simplicity. In mountain ceuntries, where unlimited power 

 is available, they are still found. The water is then con- 

 ducted by ah artificial channel to the wheel, which some- 

 times revolves in a horizontal plane. When of small 

 diameter, their efficiency is still further diminished.* 



157. Work of the Poncelet Water Wheel. When 



the fall does not exceed G feet, the best water motor to adopt 

 in many cases is the Poncelet undershot water wheel. In 

 the common undershot water wheel, the paddles are flat, 

 whereas in the Poncelet wheel they are curved, so that the 

 direction of the curve at the lower edge, where the water 

 first meets the paddle, is the same as the direction of the 

 stream. By this arrangement, the water, which is allowed 

 to flow to the wheel with a velocity nearly equal to the 

 velocity due to the whole fall, glides up the curved floats 

 without meeting with any sudden obstruction, comes to 

 relative rest, then descends along the float, and acquires at 

 the point of discharge from the float a backward velocity 

 relative to the wheel nearly equal to the forward velocity of 



* See Cotterill'i App. Mocha. ; also, Fairbairn's Millwork and Machinery. 



