H = Vo2 / 2g − uo2 cosec2 φ / 2g
or
Vo = √ (2gH + uo2 cosec2 φ).
(8)
and the efficiency of the pump is, from (7),
η = gH / Vowo = gH / {V (Vo − no cot φ) },
= (Vo2 − uo2 cosec2 φ) / {2Vo (Vo − uo cot φ) },
(9)
For φ = 90°,
η = (Vo2 − uo2) / 2Vo2,
which is necessarily less than 1⁄2. That is, half the work expended in driving the pump is wasted. By recurving the vanes, a plan introduced by Appold, the efficiency is increased, because the velocity vo of discharge from the pump is diminished. If φ is very small,