30 per cent., the maximum theoretical efficiency 
“being only 50 per cent., the velocity of the 
vanes being then half that of the impinging : 
“stream (see Art. 415, p. 477). 
by Poncelet, who curved the vanes, as shown 
in Fig. 784. In the Poncelet wheel the water 
_ 419, pp. 480-483, and the obser- 
vations there made apply to Fig. 
_ parallelograms of velocities as the 
water enters the wheel at B and 
WATER WHEELS AND TURBINES 487 
_ 423, Undershot Wheels.—The undershot wheel acts entirely by the 
of the water on its vanes. The older undershot wheels had 
vanes, as shown in Fig. 783, and on 
account of the loss of energy, due to shock, the 
efficiency of these wheels was only from 20 to 
The undershot wheel was greatly improved : 
enters without shock, leaves it with a small Ba 788. 
_ velocity in a nearly vertical direction, and during the whole time that 
_ the water is in the wheel it exerts an impulse on the vanes. The 
supply of water is regulated by a 
eurved sluice A. The theory of 
the form of the vanes has ~been 
discussed in Articles 418 and 
785, which shcws the vanes of a 
Poncelet wheel in action, with the 
Fig. 784. 
leaves it at C. BD=v is the direction and magnitude of the velocity 
_ of the water in the impinging stream. BE is tangential to the wheel at 
B, and equal to v,, the velocity of the 
outer circumference of the wheel. est 
Completing the parallelogram BEDH, 
the vane at B must be tangential to 
BH. The water glides up the vane 
with the relative velocity v,, and re- 
turns, gliding down the vane, leaving Fic. 785 
it at C. At C the water has a velo- aoe 
city v, in the direction CL tangential to the wheel at C; it also has a 
velocity in the direction CK tangential to the vane at C, and slightly less 
than ¥,, on account of loss by friction. Neglecting this loss, if CL be 
made equal to v,=BE, and CK=»,=BH, and if the parallelogram 
CKNL be completed, then CN is the absolute velocity of the water as 
it leaves the wheel at C. 
The efficiency of the Poncelet wheel is about 60 per cent. 
Common undershot wheels with radial vanes should not be used 
a greater than 5 feet. Poncelet wheels are suitable for falls up 
to 7 feet. 
A suitable diameter for undershot wheels is from two to four times 
the head due to the velocity of the impinging stream, and the linear 
velocity of the tips of the vanes should be about half that of the 
impinging stream. 
424, Pelton Wheel.—The Pelton wheel is a development of the old 
hurdy-gurdy, which was introduced into the mining districts of California 
