
Apply the Pithagorean theorem and find $c$ (see sketch). The width $w(h)$ of a rectangular strip drawn on the triangle at a distance $h$ from the top varies linearly with $h$ from $l$ to $0$ as $h$ goes from $0$ to $c$. Deduce the following formula $ w(h)=l\left( 1-\frac{h}{c}\right).\tag{1} $ Since the hydrostatic pressure is given by
$P(h)=\rho gh,\tag{2}$ the hydrostatic force exerted on the triangle is the definite integral $ F=\int_{0}^{c}\rho ghw(h)\; dh=l\rho g\int_{0}^{c}h\left( 1-\frac{h}{c}\right) dh=\ldots =l\rho g\times \frac{1}{6}c^{2}\tag{3} $
As for the meaning, numeric values and units of the symbols they are as follows:
- $P$ is the hydrostatic pressure at a generic point $H(\text{measured in }\textrm{Pa } \equiv $ Pascal above the atmospheric pressure)
- $\rho $ is the water density ($\approx 1000 \textrm{kg/m}^{3}$),
- $g$ is the gravitational acceleration ($9.81 \textrm{m/s}^{2}$),
- $h$ is the height of the fluid column above $H\; (\textrm{m}).$ $^1$
- $F$ is the hydrostatic force $(\text{ }\mathrm{N})$
$^1$ $1\text{ }\mathrm{ft\ }=0.3048\text{ }\mathrm{m}$
(See this answer.)