668 HYDRAULICS AND ITS APPLICATIONS 



Owing to viscosity moreover, even though the pump be not actually 

 discharging, the water in the vortex chamber will be affected by the 

 rotation of the impeller, and will, to a certain extent, form a free vortex 

 with the pressure greatest and the velocity least at the outside. This 

 reduces the speed for impending delivery by an amount which depends 

 on the design and construction of the vortex chamber, and for the calcula- 

 tion of which insufficient experimental evidence is available. Experi- 

 ments 1 on a series of pumps having radial vanes with impellers 8'813" 

 outside and 5*375" inside diameter, and with a vortex chamber 1T375" 

 diameter, showed that when on the point of impending delivery this 

 served as a true vortex chamber, the value of K (p. 654) being 

 about *5. 



In all probability this effect would not be so pronounced in a pump 

 having a proportionately larger vortex chamber. 



ART. 181. SIZE OF PUMP FOR A GIVEN DISCHARGE SIMILAR PUMPS 

 PROPORTIONS OF PUMPS. 



For a given speed of rotation and a given radius r 3 , the difference in 

 pressure between inlet and outlet, and therefore the head pumped against, 

 increases with the difference between the inner and outer radii of the 

 impeller r 2 and r a . Since, too, the proportional effect of disc friction ( ex j- 5 , 

 see p. 180), diminishes rapidly as the radius diminishes, the inner radius 

 should, for efficiency, be made small. This may be accomplished, keep- 

 ing the discharge constant, by increasing the velocity of flow / 2 , but with 

 a large suction head a limit to this maximum velocity is soon reached, and 

 in practice it is usual to make the inner radius from J to \ the outer 

 (r 3 = 3 ?a to 2 ?*a), the former value being preferable. 



Again, since the head pumped against is approximately proportional to 

 u 3 , i.e., to co 2 r 3 2 , a given head may be obtained either by an increase 

 in co or in r. But Q x / 3 r 3 b 3 , and assuming / 3 to be proportional to u 3 , 



we have : 



Q oc u 3 r 3 b 3 , 

 x co r 3 2 b 3 , 

 IT co 



It follows that for large values of H', in order to avoid excessive value 

 of co, the value of b 3 should be comparatively small. This is borne out 

 in practice, where the breadth b 3 of the impeller at the rim is usually 



1 "Bulletin of the University of Wisconsin," No. 173. Vol. III. No. 6, p. 447. J'.y 

 C. B. Stewart. 



