**Work Done:**

In case of centrifugal pump, work is done by impeller on the water.

Velocity triangles are drawn at inlet and outlet of the impeller in the same way as that of turbine, so as to obtain an expression for the work done by impeller on water.

The water enters the impeller radically at inlet for bet efficiency of the pump, which means the absolute velocity of water at inlet makes an angle of 90 degree with the direction of motion of the impeller at inlet.

Hence a = 90 degree and vw1 = 0

$= \frac{\pi D_1 N}{60}$

$D_2$ = Diameter of impeller at outlet,

$u_2$ = Tangential velocity of impeller at outlet.

$= \frac{\pi D_2 N}{60}$

$v_1$ = Absolute velocity of water at inlet.

$vr_1$ = Relative velocity of water at inlet.

a = Angle made by (v1) at inlet with direction of motion of wave.

o = Angle made by relative velocity (vr1) at inlet.

As mentioned above, a = 90 degree, Vw1 = 0.

$\therefore$ work done by water on the runner per second per unit weight of the water striking per second is given by,

$\frac{1}{9}$ $[vw_1 u_1 - vw_2 u_2]$

$\therefore$ work done by the impeller on the water per second per unit weight of water striking per second.

$= [\frac{1}{9} (vw_1 u_1 - vw_1 u_2)]$

$= \frac{1}{9} [vw_1 u_2 - vw_1 u_1]$

$= \frac{1}{9} vw_2 u_2$ ------(1)

work done by impeller on water per second,

$= \frac{w}{g} \times vw_2 u_2$

where, w = weight of water

= p x g x q

Q = volume of water

Q = $\pi D_1 B_1 \times vf_1$

and

$Q = \pi D_2 B_2 \times vf_2$

where B1 and B2 are width of impeller at inlet and outlet and vf1 and vf2 are velocities of flow at inlet and outlet.