Question $1$: Total Hydrostatic Pressure

Figure below shows a masonry Dam with a water pipe passing through the Dam. To control

the passage of water in the pipe, a cast$-$iron rectangular gate $AB$ is installed at point $A.$ if the

density of water is $1,000k\frac{g}{m^3}$ and the plane of the rectangular gate makes an angle of $45$ with

the vertical, determine the following:

$($i$).$ Total hydrostatic pressure $P$ and the distance of the center of pressure from the hinge at

A$.$ depth $($h$)$ from the hinge $\text{'}A\text{'}$ up to the water level is $3m.$

Your answers must be in $kN$ for $P$ and meters for distance of center of pressure.

$($ii$).$If the weight of the gate is $2\mathrm{.}5kN,$ compute the magnitude of force $F,$ required to open

the gate.

Your answer must be in $kN$