$(18$ pts$)$ Circular gate ABC in the figure below is $4m$ in diameter and is hinged at $B.$ Compute the force $P$ just sufficient to keep the gate from opening when $h$ is $8m.$

$=90$ vertical surface

$D=4m$

$h=8m$

top $of$ hatch $=A=6^{\text{'}}$ below

surface

top of hatch $=A=6$ 'below surface

$O_{24}$

top of surface

$F_R=hcA$

$h_c=y_{c}sin=sin90=1=>h_c=$ he would be halfway

$A=\frac{D^2}{4}=\frac{4^2}{4}=12\mathrm{.}57m^2$