674 HYDBAULICS AND ITS APPLICATIONS' 



For example, in the wheel shown in Fig. 305, the pressure in the wheel 

 itself varies at different radii owing, firstly, to the production of a forced 

 vortex, and secondly, to the necessity of maintaining an outward flow. 

 In the clearance space to the right this outward flow is absent, so that 

 the difference of pressure on the two sides of the shrouding at a radius r 

 is given by the pressure necessary to maintain this flow, and if p r repre- 

 sent this pressure intensity in pounds per square foot 



W~~W 





This assumes the law of pressure variation in outward flow to be the 

 same as in inward flow, i.e., neglects losses of energy due to eddy forma- 

 tion, and since this loss varies with the form and number of the blades 

 (i.e., with the rate of their divergence), becoming less as the number and 

 curvature of the vanes is increased, the theory is to this extent unsatis- 

 factory. Allowing for this, we have : 



r- K i 



W W 2g 



where K is a co-efficient, varying probably from about *7 in the case of 

 radial vanes to "85 with vanes having a delivery angle of 30. 



NOW 2 ^r : 



And r v r = f r cosec 0, where = angle made by the vanes at this radius 

 with the tangent to the corresponding circle. 



Pr _ K P* | 2 r 



w" MF 27~P ~^~ 9 ' 



The axial force F may be obtained by dividing the disc into a series 

 of concentric elements, and by obtaining the relative velocity at the 

 mean radius of each element by this method or by the graphical con- 

 struction of p. 553. The unbalanced force on each element may then 

 be calculated by an application of equation (2) above, as shown on p. 554, 

 and the sum of these, taken over, the whole area, gives the resultant 

 axial force. 



Equating this to the unbalanced pressure on the inlet side of the 

 shrouding produced by the axial change of momentum of the water, and 

 to the unbalanced pressure on the remaining annulus of width r a R , 

 on fixing 7?i the required outer radius R may be determined. 



Where balancing vanes are fitted they should not be too deep and 



