In practice, the ratios AN/A2 and Ad/A2 in Eq. (13) are typically
kept constant, which means thatbvaries as a function off, L,D2, and
the coefficients of local head losses (Pk). In many applications,
friction losses are more important than local head losses, that is
fL=D2[Pk. Also, L is typically constant as it is restricted by
topographic conditions. In addition, f does not show significant
variation as a function of discharge or penstock diameter. Let's
recall that for a given penstock diameter, f is independent of the
Reynolds number for fully developed turbulent flows, which is the
case of most penstock flows. Hence, b is more or less inversely
proportional to the penstock diameter, D2 f 1/b.
The variation of Pþ with respect to Qþ for a fixed b can be obtained by differentiating Pþ with respect to Qþ in Eq. (12), which
gives