CENTRIFUGAL PUMPS 669 



proportional to the radius and has a value ranging from J r 3 to T X Q r 3 , the 

 former value applying to low-lift, and the latter to high-lift pumps. 

 Putting b 3 x r 3 , we have Q x o> r 3 3 



TJt Q 



1 O) 1(3 11 3 

 7=r X X o X o 



Q r 3 r 3 2 r 3 2 u 3 



While this is not strictly true in the case of an actual pump, yet it 

 shows that in every case for a given value of H' and of Q, there is 

 a definite value of r for maximum efficiency, this value, however, 

 depending on the relative magnitude of the frictional losses. 



Since, in a perfect pump, with radial vane tips, we have g H r = ?/ 3 2 , 



while Q x u a r 3 2 , if the ratios - 5- , and ^-^ be plotted this enables a 



comparison to be made between the performances of different pumps. 

 Professor Rateau terms the ratio ^ the manometric efficiency; the 



ratio -^-2 ^ ne volumetric efficiency; and the ratio of the product of 



these, viz., '^-^ . 2 to the mechanical efficiency ~ , the 



co-efficient of transmission to the pump shaft. The latter thus 

 equals 



g H' Q U 



The three curves showing the mechanical efficiency, the manometric 

 efficiency, and the co-efficient of transmission, on a base of volumetric 

 efficiencies, are then termed the characteristics of the pump, and if drawn 

 for a given pump apply to any similar pump of different size, so long as 

 the previous relationships hold, and therefore so long as 



(1) The peripheral speeds are proportional to .*/ H' ; 



(2) The revolutions are proportional to 



^ 



(3) The quantity discharged is proportional to $ 2 



where S is the ratio of similar linear dimensions of the two pumps. 



The same conditions hold for identical results to be obtained from two 

 similar pressure turbines. 



ART. 182. REMARKS ON THEORY OF PUMP DESIGN. 



None of the fundamental assumptions made in the foregoing discussion, 

 are accurately true. Thus the assumption of radial motion immediately 

 before entering the impeller is certainly incorrect since viscositv must 



