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1] The peripheral velocity at inlet and outlet are equal.
$u_1 = u_2 = \frac{\pi DoN}{60}$ (Do = outer Diameter)
2] Velocity of flow at inlet and outlet are equal.
$vf_1 = vf_2$
3] Area of flow at inlet = Area of flow at outlet.
$\frac{\pi }{4} (Do^2 - Db^2)$