For minimizing water consumption to produce a given amount
of hydropower, it is necessary that dPþ/dQþ in Eq. (14) is close to
its maximum value (3/2)h. Note in Figs. 3 and 4 that for each
curve between approximately dPþ/dQþ ¼ (3/2)h and dPþ/
dQþ ¼ 0.8h, the increase in dimensionless power (Pþ) is approximately linear with increase in dimensionless discharge (Qþ).
Note also in these Figures that for dPþ/dQþ smaller than about
0.8h, the increase in Pþ is small compared to the increase in Qþ.
Herein, to minimize water consumption, the optimal lower limit
of dPþ/dQþ is set to 0.8h.
Substituting dPþ/dQþ ¼ 0.8h into Eq. (14) gives the following
upper limit for the dimensionless flow discharge,