552 HYDRAULICS AND ITS APPLICATIONS 



In general, with swivelling vanes, the number of guide vanes is made 

 slightly less than the number of wheel vanes, while with stationary 

 guides the number is usually slightly greater. The thickness t varies 

 from J inch in a small turbine with steel plate vanes to about \ inch in a 

 large turbine with cast vanes. In high-class turbines the vanes have 

 rounded edges at entrance and exit, so that the effective value of t 

 generally varies from about j 1 ^ inch to T 5 ^ inch. 



ART. 145. CURVATURE OF VANES. 



So long as the inlet and outlet angles of the vanes are correctly pro- 

 portioned, the shape of the vane between these points only affects the 

 efficiency in so far as it tends to give steady or unsteady motion in the 

 stream. To this end the design should be such that the passages are 

 nowhere divergent, and that any changes of curvature are as gradual as 

 possible. The first of these requirements is more easily satisfied in the 

 inward flow than in the outward flow turbine. With this requirement 

 fulfilled, the most efficient vane curve will be that with which the change 

 in curvature of the path of the stream is most gradual, and to determine 

 this it is advisable to set out a diagram showing for any proposed vane 

 the true path of the particles of water in passing through the wheel. 

 Two such diagrams are shown in Fig. 259, in which (a) shows the true 

 path where the velocity of flow is uniform, and (b) where the velocity of 

 flow varies inversely as the radius. To construct diagram (a), a series 

 of equidistant circles are set out between the inner and outer vane 

 circles. If s be the radial distance between each pair of these, the 



o 



time for a particle to pass from one to the other = -r seconds. Next set 

 out the same number of equidistant vanes, the distance apart on the outer 

 vane circle being o> r 2 -^ feet. A particle leaving the intersection of the 

 first circle and first vane will then be at the intersection of the second 

 circle and vane after an interval of time -j seconds and so on, so that 



the path of the particle can be sketched in, as at I m. 



Where the velocity of flow is not uniform, the only difference in the 

 construction is that the intermediate circles are not equidistant but are 

 so spaced that the particle travels radially from one to the other in equal! 

 intervals of time. Thus in case (b) a radius o a being drawn, a right- 

 angled triangle o a b is constructed on this and lines c d, ci di, etc., drawn, 



