654 



HYDRAULICS AND ITS APPLICATIONS 



designed volute chamber, however, experiments show that K may 

 increased to about "60 (see p. 633, footnote). 



(c) Volute provided with Divergent Discharge Pipe. If the discharge 

 from the volute take place into a pipe of gradually increasing sectional 

 area, the gain of pressure in this pipe may be readily estimated in terms 

 of the velocities of flow from the data of Art. 34, p. 84, when the angle 

 divergence of the sides is known. 



(d) Change of Pressure in Vortex Chamber. Here the water on 

 leaving the vanes forms approximately a free vortex; the pressure 

 increases as the velocity diminishes towards the outside of the chamber, 

 and part of the kinetic energy of discharge may thus be recovered as 

 pressure energy. 



If the suffix (3') now refers to the outside of the vortex, we have, neglect- 

 ing changes of level between (3) and (3') : 



W 





giving the gain of pressure head in the chamber on the assumption of true 

 vortex motion, with no eddy losses. 



But if ?* 3 and r' 3 are the inner and outer radii of the chamber we 



B 3 

 have = = c (say) 



(1 - 



feet of water. (6) 



Pa 1 Ps _ 



W 



The theoretical efficiency of the vortex chamber may be taken as 

 (1 c 2 ), the following table indicating how this varies with an increase in 

 the radius of the chamber. 



Experiments by Stanton 1 on a pump having a vortex chamber 18 inches 

 in diameter, showed a chamber efficiency of about 39 per cent, with either 

 a 7-inch or an 11 -inch wheel. 



The actual gain in pressure is thus considerably less than that obtained 

 in the ideal case, and is given more nearly by 



(w a +/ 3 ) J feet (7) 



where K varies probably from *4 to '55, depending on the form of the 



1 Proc. Inst. Mech., Eng., 1903 (p. 715). 



