k = ro / rw.
The lift is then, adding this to the lift in the last case,
H = {Vo2 − uo2 cosec2 φ + vo2 (1 − k2)} / 2g.
But
vo2 = Vo2 − 2Vouo cot φ + uo2 cosec2 φ;
∴ H = {(2 − k2) Vo2 − 2kVouo cot φ − k2uo2 cosec2 φ} / 2g.
(10)
Putting this in the expression for the efficiency, we find a considerable increase of efficiency. Thus with
| φ = 90° and | k = 1⁄2, | η = 7⁄8 nearly, |
| φ a small angle and | k = 1⁄2, | η = 1 nearly. |
With this arrangement of pump, therefore, the angle at the outer ends of the vanes is of comparatively little importance. A moderate angle of 30° or 40° may very well be adopted. The following numerical values of the velocity of the circumference of the pump have been obtained by taking k = 1⁄2, and uo = 0.25√(2gH).