Question

A vertical gate 6 m $\times$ 6 m holds water on one side with the free surface as its top. The moment about the bottom edge of the gate water force will be (${\gamma }_w$ is the specific weight of water)

• A. 18 ${\gamma }_w$
• B. 36 ${\gamma }_w$
• C. 72 ${\gamma }_w$
• D. 216 ${\gamma }_w$

Answer 1

The correct option is D 216 ${\gamma }_w$

The force on the gate = $\rho g{h}_{c}A=\gamma \times 3\times 36=108\gamma$
The depth of centroid from free surface,
$h_p=\frac{2h}{3}=\frac{2\times 6}{3}=4m$
From bottom edge the centroid will be at a distance of 6-4 =2 m
Therefore moment about the bottom edge of the gate of the water force $=108\times 2\gamma =216\gamma$