Let us examine how to consider an offtake which is only described in the form of a time varying outflow relationship, Qp(t).

Figure 28

first sweep:

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DQn = DQ1 + DQp + Q1n + Qpn - Qnn

• DZn = DQ1 + - DZn + Q1n + Qpn - Qnn

DQ1 + ( - ) DZ1 = Qnn - Q1n - Qpn + -

Remark : n is used both in subscript to indicate the cross section index, and in superscript to indicate the current time step.

Then:

We can then go down the first sweep. The second sweep does not pose any particular problems and one calculates W(t) in order to satisfy the offtake discharge for the given water surface elevation at the node.