Q$1($a$)$ For a plane surface, prove the equation $D=si{n}^2()*(\frac{k_{GG}^2}{(ybar)})+(ybar)$

$($b$)$ For the Gate in figure Q$1($b$)$ below, find the following

$($i$)$ The Horizontal Force

$($ii$)$ The vertical Force

$($iii$)$ The Force P required to keep the Gate closed

Surface open to atmosphere