Problem # $3[15$ marks$]$ A cylindrical gate of length $l=1m($into the page$)$ and radius $R=0\mathrm{.}50m$ is pivoted

at $A.$ The gate opens by rotating counterclockwise about A when the level in the tank is equal to $h_w=$

$3\mathrm{.}50$ m $.$

Determine the magnitude and direction $($angle$)$ of the pressure force exerted by the water when the

cylindrical gate is about to open. $[10$ marks$]$

If the pressure force is passing through the center of the cylinder, determine the weight of the cylindrical

gate. $[5$ marks$]$

$A=bL$

$I_{}=\frac{b{L}^3}{12}$

$I_{xy}=0$