Question

The basic equation of flood routing through a reservoir can be modified for discrete successive intervals $\Delta t$ by which one of the following?

• A. $\left[\frac{I_1+I_2}{2}\right]\Delta t+[S_1+\frac{Q_1\Delta t}{2}]=[S_2+\frac{Q_2\Delta t}{2}]$
• B. $\left[\frac{I_1+I_2}{2}\right]\Delta t+[S_1-\frac{Q_1\Delta t}{2}]=[S_2+\frac{Q_2\Delta t}{2}]$
• C. $\left[\frac{I_1+I_2}{2}\right]\Delta t+[S_1+\frac{Q_1\Delta t}{2}]=[S_2-\frac{Q_2\Delta t}{2}]$
• D. $\left[\frac{I_1+I_2}{2}\right]\Delta t+[S_1-\frac{Q_1\Delta t}{2}]=[S_2-\frac{Q_2\Delta t}{2}]$

Answer 1

The correct option is B $\left[\frac{I_1+I_2}{2}\right]\Delta t+[S_1-\frac{Q_1\Delta t}{2}]=[S_2+\frac{Q_2\Delta t}{2}]$

The basic continuity equation for reservoir routing is
$\left(\frac{I_1+I_2}{2}\right)\Delta t-\left(\frac{Q_1+Q_2}{2}\right)\Delta t=S_2-S_1$
$\left(\frac{I_1+I_2}{2}\right)\Delta t+(S_1-\frac{Q_1\Delta t}{2})=S_2+\frac{Q_2\Delta t}{2}$