446 HYDRAULICS AND ITS APPLICATIONS 



then gc, the bisector of the angle bed, be a normal to the surface of 

 impact at c, the required conditions will be fulfilled, the jet striking the 

 vane in the direction d c and leaving (relatively to the wheel) in the 

 direction of c b. The direction and magnitude of ac, and the direction 

 of b < being fixed, if the final relative velocity be approximately known, 

 the magnitude of be and therefore the most efficient speed of rotation 

 may be determined. In a well-designed bucket the final relative velocity 

 may be taken as *75 of the initial. If c and k be the first and last points 

 at which the jet impinges on the ridge and if a third point I be taken 

 midway between c and k, the directions of such normals as c g may be 

 determined for these three points, and a smooth curve drawn through 

 these points and having the required normals will give the correct curve 

 for a longitudinal section of the receiving edge of the bucket. In general, 

 a circular arc with centre at p, the intersection of the normals through 

 c and k will give a very close approximation to the curve. 



Strictly, since the path of the mid particles of the jet relative to the 

 bucket is given by c q s, the normal at q should bisect this angle. If, 

 however, the curve through q be made parallel to elk, the approximation 

 to the correct curve will be sufficiently near. 



A close approximation may also be obtained by determining graphically 

 the points of intersection of the bucket with the axis of the jet for 

 different positions of the bucket, and by drawing a smooth curve such 

 that the axis of the jet is normal to the curve in every position of the 

 bucket. 



To prevent the jet striking the back of the bucket, this should be 

 everywhere above the line d c, while to reduce splash on passing through 

 the jet the edge at c should be as sharp as possible. 



In modern practice the width of the buckets is between three and five 

 times the diameter of the jet, the ratio diminishing as the size of jet 

 increases, while the wheel diameter should not be less than about 

 ten times the jet diameter. If, on settling the number of revolutions and 

 peripheral speed, and hence the diameter of a wheel, this is less than the 

 required multiple of the diameter of a single jet to give the required 

 power, duplicate jets should be used. 



Number of Buckets. For minimum loss these must be as few as is 

 consistent with the jet being wholly intercepted for all bucket positions, 

 so that the entering bucket may entirely intercept the jet before the 

 leaving bucket begins to free itself. From this consideration, a simple 

 geometrical construction shows that if n be the minimum possible 

 number of buckets, R the extreme outer radius over the receiving edges 



