$\"\"$

\

Observe the figure:

\

The Depth is $\"\"$ .

\

The length is $\"\"$ .

\

Redraw the figure:

\

$\"\"$

\

The semicircle is $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Length of the semicircle is $\"\"$ .

\

The weight density of water is $\"\"$ .

\

The limits range from $\"\"$ to $\"\"$ .

\

$\"\"$

\

The fluid force is : $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ and $\"\"$ .

\

$\"\"$

\

Consider $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

If $\"\"$ then $\"\"$ .

\

if $\"\"$ then $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Therefore, the fluid force is $\"\"$ .

\

$\"\"$

\

The fluid force is $\"\"$ .