THEORY OF TURBINE DESIGN 



561 



The actual path, k d, of a particle through the wheel may be drawn 

 is in the case of the pressure turbine, except that now, in the case of an 

 ixial flow turbine, the relative velocity of water and vane is fixed, 1 while 

 ,he velocity of flow varies. In this case, then, a series of equidistant 

 )oints on the curve of the vane being taken from entrance to exit, the 

 )oints in which concentric circles through these points cut corresponding 

 equidistant vane positions will give points on the true path of the 

 article, the time required for the particle to travel from point to point 

 ilong the vane being equal to the time required for the vane to travel 

 rom one position to the next. 



Once a and y have been determined, the peripheral speed for maximum 

 efficiency may readily be obtained graphically. 



Thus, with the usual notation, a b c and d ef (Fig. 2G3) represent the 

 iriangles of velocity for the inlet and outlet edges of an impulse turbine. 

 !n an axial flow turbine the relative velocity d f at exit will be equal to 

 ihat of a c at inlet. In an outward flow turbine d f will be greater, but, 

 is previously explained, may be determined graphically. 



Also for maximum efficiency the velocity of the water on leaving the 



1 Except as modified by the influence of gravity. Neglecting f Fictional resistances and 

 yindage, this is true so long as every portion of the vane over which a given filament passes 

 s moving at the same speed, as is the case in an axial flow machine where the path of each 

 ^article is presumably parallel to the axis. If, how- 

 jver, different portions of the surface with which a 

 ^article comes in contact have different velocities 

 is in the case of a radial flow turbine, the relative 

 velocity is no longer constant. It may, however, be 

 ietermined graphically, since it will be the resultant 

 jf the relative velocity at inlet, and of the com- 

 ponent in the direction of the vane at the required 

 point, of the relative velocity of the vane at that 

 point and at inlet. Thus, if in Fig. 262, 



, n a = relative velocity at inlet 

 a b = velocity of vane at inlet 

 i c d = velocity of vane at outlet 



\ m c p = y. 



rhen d e = relative velocity of vane at outlet and 

 it inlet, and ef, drawn parallel to c m, represents 

 the component of this in the direction of the vane 

 at outlet. If then c U = n a, and if c k be produced 

 to m where k m = ef, the relative velocity at out- 

 let is represented by e m. Where, in the case of a Girard turbine, the ratio of outer and inner 

 radii = 1-25 with a value of 7 = 21 the actual relative velocity at outlet is approximately 

 1-23 times that at inlet. Frictional resistance will, however, reduce this by some unknown 

 amount, and will probably bring the ratio down to about 1-10. In any case, the effect on the 

 value of 7 for maximum efficiency will be slight, the effect being to reduce this value, and this 

 should be taken into account in arranging the design (see Fig. 261). 



H.A. O O 



FIG. 262. 



