Question

Water stands at a depth H behind the vertical upstream face of a dam. The total width of the dam is L. The horizontal force acting on the dam is (density of water =$\rho$ )

• A. $\frac{1}{3}\rho gL{H}^2$
• B. $\frac{1}{2}\rho gL{H}^2$
• C. $\rho gL{H}^2$
• D. $3\rho gL{H}^2$

Answer 1

The correct option is B $\frac{1}{2}\rho gL{H}^2$

Consider an area (Ldy) on the wall at a depth y below the surface, where is the width of the dam.

$dF=\rho bdy$
$=\rho gybdy$
$F=\rho gL{\int }_0^{H}ydy$
$=\frac{1}{2}\rho gL{H}^2$