vro = Vo √ (1 + uo2 / Vo2).

It will be shown immediately that

vri = ui cosec θ;

or, as this is only a small term, and θ is on the average 90°, we may take, for the present purpose, vri = ui nearly.

Inserting these values, and remembering that for an axial flow turbine Vi = Vo, ɧ = 0, and the fall d in the wheel is to be added,

vi = cv √ { 2g ( H − Vi2( 1 + uo2) + ui2− d ) }.
2g Vo22g

For an outward flow turbine,

vi = cv √ [ 2g { H − ɧ − Vi2( 1 + uo2) + ui2} ].
2g Vi22g

For an inward flow turbine,

vi = cv √ [ 2g { H − Vi2( 1 + uo2) + ui2} ].
2g Vi22g