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 | Vo2 | 2g |
For an outward flow turbine,
| vi = cv √ [ 2g { H − ɧ − | Vi2 | ( 1 + | uo2 | ) + | ui2 | } ]. |
| 2g | Vi2 | 2g |
For an inward flow turbine,
| vi = cv √ [ 2g { H − | Vi2 | ( 1 + | uo2 | ) + | ui2 | } ]. |
| 2g | Vi2 | 2g |