Problem Description
(Idealized Flow Conditions)

Take the direction of rotation (i.e., into the plane) as positive and apply the moment of momentum equation to the control volume (as shown in the figure) in the direction along the axis of rotation:

Note that according to conservation of mass under steady-state conditions:

The negative sign simply means that the shaft work is in the opposite direction of the rotation.

The power generated by the shaft is then given by

     

where ω is the rotational speed of the shaft.