# Offtake equations

The lateral offtakes correspond to points of outflows. Therefore, they are obligatorily located at the upstream nodes of the reaches. Under steady flow conditions, one cannot compute the real offtake discharge corresponding to a given offtake gate opening, unless the corresponding secondary canal is described as part of the model (looped model). But, knowing the offtake target discharge, the program is able to calculate the corresponding offtake gate opening.

The offtakes are modeled according to the same hydraulic laws as for cross structures. The originality of the approach resides in the consideration of a possible influence of the offtake downstream condition.

For the discharge, we use the equations described above for the undershot gates. If the offtake is circular, one has to calculate the width of the equivalent rectangular opening in order to be able to use the equations referred to above.

One has to then solve an equation of the following type:

fp(Z1, Z2, W) = Qp with:

Qp: target offtake discharge

Z1: upstream water surface elevation in the main canal obtained via the water surface profile computation

Z2: downstream water surface elevation. This is either known, or its value depends on the offtake discharge Qp and the chosen offtake downstream condition. If Z2 is a function of Qp, one then has an equation of the form:

fp(Z1, fs-1(Qp), W) = Qp **[27]**

with fs being the rating curve corresponding to the chosen offtake downstream condition.

Therefore, in all cases the problem is to find the zero of a function with W as the unknown (see paragraph II.5).