In axial flow turbines, the circumferential velocities at the mean radius of the wheel may be taken
Vo = Vi = 0.6 √2gH to 0.66 √2gH.
In a radial outward flow turbine,
Vi = 0.56 √2g(H − ɧ)
Vo = Viro / ri,
where ro, ri are the radii of the outlet and inlet surfaces.
In a radial inward flow turbine,
Vi = 0.66 √2gH,
Vo = Viro / ri.
If the wheel were stationary and the water flowed through it, the water would follow paths parallel to the wheel vane curves, at least when the vanes were so close that irregular motion was prevented. Similarly, when the wheel is in motion, the water follows paths relatively to the wheel, which are curves parallel to the wheel vanes. Hence the relative component, vr, of the water’s motion at c is tangential to a wheel vane curve drawn through the point c. Let vo, Vo, vro be the velocity of the water and its common and relative components at the outlet surface of the wheel, and vi, Vi, vri be the same quantities at the inlet surface; and let θ and φ be the angles the wheel vanes make with the inlet and outlet surfaces; then