For the moving vane of Sample Problem 4/6, determine the optimum speed \(u\) of the vane for the generation of maximum power by the action of the fluid on the vane.

Problem 4/6,

The smooth vane shown diverts the open stream of fluid of crosssectional area \(A\), mass density \(ho\), and velocity \(v\).

(a) Determine the force components \(R\) and \(F\) required to hold the vane in a fixed position.

(b) Find the forces when the vane is given a constant velocity \(u\) less than \(v\) and in the direction of \(v\).

y R Fixed vane F x