At each singular section, one particular gate can be chosen to play the role of a regulator (this means that the opening of this gate is not fixed a-priori. instead, the model will compute the opening required to maintain a target water level immediately upstream. the openings of all other gates are imposed a-priori). The opening of this gate is unknown. The maximum possible opening and the target water elevation (e.g. Full Supply Depth) upstream of the gate are known. This results in an equation at the singular section similar to the previous one, but in this case, the unknown is no longer the upstream water surface elevation, but the opening of the gate working as a regulator. One ends up with an equation of the following type:

Q - fk(Zi, Zj) = fr(Zi, Zj, W) [24]

with:

k = 1 to n : for gates with fixed openings.

W : the regulator opening to be calculated.

Zi : known value (target upstream water elevation).

fk(Zi, Zj) : the discharge going through the fixed gate number k for the target upstream water elevation Zi and the downstream water elevation Zj. The equations considered are those described for the weirs and the gates.

fr(Zi, Zj, W) : the discharge going through the regulator type gate for an opening W and the target upstream water elevation Zi.

The fk(Zi, Zj) are known values. Then equation [24] is reduced to fr(Zi, Zj, W) = constant. One then has to look for the zero of a function, but this time, the unknown is W.