Equation at a singular section

The water surface elevation at a singular section is computed using the previous equations. The flow at the section is equal to the sum of the discharges through each device (e.g., gate, weir).

fk(Zi, Zj) = Q [23]

n is the number of devices in the section and Q the flow at the section.

fk(Zi, Zj) is the discharge law of the device number k, for instance for a submerged weir:

fk(Zi, Zj) = µL(Zi-Zj)1/2(Zj-Zd)

If the discharge and the downstream elevation Zj are known, the water surface elevation Zi upstream of the device can then be calculated.

This means that one has to solve an equation of the form f(Zi)=0 (See § II.5.)