481 



HYDRAULICS AND ITS APPLICATIONS 



causing a diminution in speed, reduces the flow through the wheel, and 

 thus reduces the energy supply when it is most needed. Its peripheral 

 velocity is low, and on that account it is well adapted for driving a 

 pumping plant or milling machinery where the load is uniform and where 

 high velocities are not required. 



The chief losses occur during the emergence of the vanes from the tail- 

 race. Owing, however, to the slow speed of the wheel, all hydraulic losses 

 are low and an efficiency of up to 80 per cent, may be obtained under 

 favourable circumstances, though the large size of the wheel and its 

 comparatively costly construction very largely counterbalance the 

 advantages of high efficiency. 



ART. 123. THE UNDERSHOT WHEEL. 



For heads below 3 feet the undershot wheel is preferable. In its 



simplest form this consists of a 

 wheel carrying a series of flat 

 radial vanes around its circum- 

 ference (Fig. 191). These dip 

 into the water flowing either 

 through an open channel or 

 through a penstock of slightly 

 greater width than the wheel, 

 and are arranged so as to clear 

 the bottom of the penstock by 

 about J inch. In some cases 

 the penstock itself is curved to 

 fit the wheel, and leakage past 

 the buckets, in the interval be- 

 tween successive buckets arriv 



ing at the lowest point of their path, is then largely prevented. 



In this wheel, work is done solely in virtue of the kinetic energy of th. 



moving stream, the force on the moving vanes being due to the change of 



momentum produced in the stream by their presence. 



For maximum work the peripheral velocity should be one half the 



velocity of flow of the stream, in which case the theoretical efficiency 



is '5. 



Owing to mechanical friction and hydraulic losses this efficiency is, 



however, reduced to about 35 per cent., and the maximum efficiency is 



obtained with a value of v ft slightly less than \ v (Fig. 191). 



FIG. 191. The Undershot Wheel. 



