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

The answers for the questions should be these values, however the previous expert done it complety wrong. Please redo it again.

Q$1$

$($a$)($i$)$ Proof

$($b$)($i$),R_H=588,600N$

$($ii$),F_V=412,020N$

$($iii$),P=436,447N$