428 



HYDRAULICS AND ITS APPLICATIONS 



Efficiency of Wheel. Soon after the buckets pass the centre line of the 

 wheel they begin to empty, at A (Fig. 185), while they are completely 

 emptied by the time they reach the position B, where the outer part of 

 the bucket is horizontal. If then h is the mean vertical distance through 

 which the water is carried before being discharged, the work done in virtue 

 of its weight = W Q h fooHbs. per second. 



It may readily be shown that the efficiency is a maximum when the 

 peripheral velocity is one half that of the inflowing stream. A consider- 

 able increase in speed has, however, very little effect on the efficiency. 

 The most important effect of such an increase is due to the tendency to a 

 premature emptying of the buckets by increased centrifugal action. 



To prevent loss by splash and shock at entrance to the buckets, the 



vane angles should be so 

 arranged that the rela- 

 tive motion of water and 

 vane at entrance is 

 parallel to the tip of the 

 vane. Thus if a b (Fig. 

 185) represents the ve- 

 locity v in direction and 

 magnitude, and if c b re- 

 presents the linear velo- 

 city, R of the vane, 

 then a c represents the 

 velocity of the water 

 relative to the vane, and for the water to enter by sliding along the vane 

 this should be parallel to a c at entrance. 



The general practice is to form the bucket tips so as to make an angle of 

 25 to 30 with the tangent to the circumference at the tip. This gives a 

 bucket which retains the water for a vertical distance equal to about *8 of 

 the wheel diameter. 



If this angle be 0, the bucket is not completely emptied until the wheel 

 has turned through 180 /3. 



Having drawn in the profile of the buckets, if a straight line d c (Fig. 

 185) be drawn through the bucket tip so as to enclose an area d e f = 

 (x X bucket area), the water will begin to escape from the bucket when 

 e d becomes horizontal. When / e becomes horizontal the bucket is 

 completely emptied. Thus with radial vanes the water is entirely emptied 

 from a bucket by the time it has fallen to the level of the wheel axle. 

 Water may be retained in the buckets until these are near the lowest 



FIG. 185 A. 



