WORK OF UNDERSHOT WHEELS. 



285 



In this wheel, as in the case of the overshot wheel, v t = 

 V, therefore (1) and (2) of Art. 154 also apply to breast 

 wheels, h being the height of the point at which the water 

 meets the vanes above the point where it leaves them. The 

 efficiency is found by experience to be as much as 0.75. 



Sen. 1. Theoretically this wheel also works to the best 

 advantage when the speed of its periphery is one-half that 

 of the stream (Art. 154, Cor.). But Morin found, by ex- 

 periments, that the efficiency of the wheel is not much 

 affected by changes in its velocity. This is owing to the 

 circumstance that the useful work is dependent principally 

 upon the term Wh, and not upon the other term in the 

 formula which alone is affected by the velocity of the wheel. 

 Hence the great advantage of this wheel is, that it may be 

 worked, without materially impairing its efficiency, with 

 velocities varying from \v to \ v. 



SCH. 2. As the diameter of this wheel is greater than 

 the fall, a breast wheel can be employed only for moderate 

 falls. 



Overshot and breast wheels work badly in back-water, 

 and hence if the tail-water level varies, it is better to reduce 

 the diameter of the wheel so that its greatest immersion in 

 flood is not more than one foot. 



156. Work of Undershot 

 Wheels. The common un- 

 dershot wheel consists of a 

 wheel provided with vanes, 

 against which the water im- 

 pinges directly. In this case 

 the water is allowed to attain 

 a velocity due to a considera- 

 ble part of the head immediately before entering the ma- 

 chine, so that its energy is nearly all converted into energy 

 of motion ; and as the water has uo fall on the wheel, and 



