Chapter 6.8, Problem 16ES

Formula $\left(8\right)$ gives the fluid force on a flat surface immersed vertically in a fluid. More generally, if a flat surface is immersed so that it makes an angle of $0<\theta <\pi /2$ with the vertical, then the fluid force on the surface is given by

$F={\displaystyle {\int }_a^b\rho h\left(x\right)\omega \left(x\right)\sec \theta dx}$

Use this formula in these exercises.

Derive the formula given above for the fluid force on a flat surface immersed at an angle in a fluid.