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.

$\frac{\pi }{4} (Do^2 - Db^2)$