WORK DONE BY THE IMPELLER OR CENTRIFUGAL PUMP ON WATER
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In case of centrifugal pump work is done by impeller on water . The expression for the work done by the impeller on the water is obtained by velocity triangle at inlet & outlet of the impeller . The water enters the impeller radially at inlet of pump. For best efficiency the absolute velocity of water at inlet makes an angle of 90 degree with the direction of motion of the impeller at inlet.
Hence angle =90° & Vw1=o. Let, D1 =diameter of impeller at inlet. N =speed of impeller in r.p.m. =angular velocity. u1 =tangential velocity of impeller at inlet = D1N/60. = 2R1N/60 = R1. D2=diameter of impeller at outlet. y
u2 =tangential velocity of impeller at outlet. =D2N/60 = 2R2N/6o =R2. V1 = absolute velocity of water at inlet, Vw1= velocity of whirl at inlet, Vr1= relative velocity of water at inlet, Vf1= velocity of flow at inlet, = angle made by V1 at inlet with direction of motion of vane, = angle made by Vr1 at inlet with direction of motion of vane.
And V2,Vr2,Vf2, and are corresponding value at outlet. Torque on impeller = rate of change of moment of momentum Moment of momentum at inlet=0 (as Vw1=0) Moment of momentum at outlet=WVw2R2/g Therefore, Torque=WVw2R2/g
Work done per second= torque x angular velocity = WVw2R2 x /g =WVw2u2/g (as u2=R2) Work done per second per unit weight of liquid =Vw2u2/g. If flow is not radial, Work done per second per unit weight of liquid =(Vw2u2-Vw1u1)/g «««««..(1) the equation (1) is known as Euler momentum, equation for centrifugal pumps.
