Question

Find the force acting on the rectangular plate due to the liquid.

Answer 1

The force acting on the rectangular plate due to the liquid is: $F = \left( \frac{\rho g h_1 + \rho g h_2}{2} \right) A$

Answer 2

The hydrostatic force on a submerged plane surface is given by the product of the pressure at the centroid of the surface and the area of the surface ($F = p_c A$). For a rectangular plate submerged vertically, with its top edge at a depth $h_1$ and its bottom edge at a depth $h_2$ from the liquid surface, the depth of the centroid ($h_c$) is the average of these depths: $h_c = \frac{h_1 + h_2}{2}$. The pressure at the centroid is $p_c = \rho g h_c = \rho g \left(\frac{h_1 + h_2}{2}\right)$, where $\rho$ is the density of the liquid and $g$ is the acceleration due to gravity. Thus, the force $F$ acting on the plate is $F = p_c A = \rho g \left(\frac{h_1 + h_2}{2}\right) A$. This expression can also be written as $F = \left( \frac{\rho g h_1 + \rho g h_2}{2} \right) A$.