Hydrostatic Force on a Curved Surface

Consider a curved portion of the swimming pool shown in Fig. 2.23a. We wish to find the resultant fluid force acting on section BC (which has a unit length perpendicular to the plane of the paper) shown in Fig. 2.23b.

We first isolate a volume of fluid that is bounded by the surface of interest, in this instance section $BC$, the horizontal plane surface $AB$, and the vertical plane surface $AC$. Then, we have:

$$\begin{array}{rl}{F}_1& =\gamma h_{1}A\\ F_2& =\text{ pressure prism}\\ F_H& =F_2\\ F_V& =F_1+W\end{array}$$

and the magnitude of the resultant is

$$F_R=\sqrt{F_H^2+F_V^2}$$