652 HYDRAULICS AND ITS APPLICATIONS 



the pump. From this result it appears that as the discharge Q is 

 diminished the actual efficiency diminishes more rapidly than the mano- 



metric efficiency - - which indeed has a value usually about '5 when 

 J w 3 u 3 



the discharge Q and therefore the actual efficiency is zero. Under normal 

 conditions as to head, speed, and discharge, the calculated manometric 

 efficiency is, however, not widely different from the true working efficiency, 

 the ratio of the latter to the former ranging from about '85 in a pump 

 with recurved vanes and an inefficient collecting chamber, to about I/O 

 in a pump with radial vanes and an efficient vortex chamber or 

 diffuser, so that a knowledge of the probable manometric efficiency 

 guided by a knowledge of the performance of somewhat similar pumps, 

 enables the working efficiency to be predetermined with a fair degree of 

 accuracy. 



Change of Pressure in Passing through Pump. As will be clear from 

 what has already been said, the increase in pressure during the passage of 

 the water through the pump must be such as to balance the statical head 

 together with the head necessary to overcome frictional resistances and- 

 that equivalent to the kinetic energy of flow along the suction or discharge 

 pipes. 



Where the water, on leaving the wheel, is allowed to make the best of 

 its way to the discharge pipe without the provision of a volute, vortex 

 chamber, or guide vanes, the K.E. of discharge is entirely dissipated in 

 shock, and the full pressure change takes place in the impeller. Where-J 

 provision is made for gradually reducing the velocity of the discharging 

 water by one of these devices, a further increase in pressure takes place 

 after leaving the impeller but before leaving the pump casing, while if a 

 diverging discharge pipe is used, as is often the case a further increase 

 in pressure takes place in this pipe. 



The magnitude of these changes in pressure will now be considered. 



(a) Change of Pressure in Passing through the Wheel. The absolute 

 velocity of a particle of water at any point in the wheel may be resolve! 

 into two components, one of whirl with the wheel with a velocity o> 

 and the second of flow parallel to the vanes with relative velocity 

 This latter velocity is evidently that which the water would have if the 

 same volume were passing with the wheel at rest. The total difference of 

 pressure at any two different radii is thus compounded of the differences 

 due to 



(1) Rotation in a forced vortex with angular velocity co. 



(2) Outward flow parallel to the vanes with velocity v r . 



