The tangential velocity of the entering water is
wi = vi cos γ = 0.82 √2g (H − ɧ).
The circumferential velocity of the wheel may be (at mean radius)
Vi = 0.5 √2g (H − ɧ).
Hence the vane angle at inlet surface is given by the equation
cot θ = (wi − Vi) / ui = (0.82 − 0.5) / 0.45 = .71;
θ = 55°.
The relative velocity of the water striking the vane at the inlet edge is vri = ui cosec θ = 1.22ui. This relative velocity remains unchanged during the passage of the water over the vane; consequently the relative velocity at the point of discharge is vro = 1.22ui. Also in an axial flow turbine Vo = Vi.
If the final velocity of the water is axial, then
cos φ = Vo / vro = Vi / vri = 0.5 / (1.22 × 0.45) = cos 24º 23′.