A tank has a fixed vertical retaining wall. On one side of the wall, the tank is filled with a liquid of density $\rho$, to a height of $1$ m. On the other side of the wall, the tank is filled with a different liquid of density $0.5\rho$, to a height $h$ m. Let $p_A$ be the atmospheric pressure.
(a) For each liquid, determine the pressure at a height $d$ below the surface.
(b) If the liquids exert forces of equal magnitude on the retaining wall, find the value of $h$.
(a) For the first liquid, we have $p_1 = p_A + dg\rho$, where $g$ is the gravitational acceleration. Similarly, for the second $p_2 = p_A + 0.5dg\rho$.
(b) How would I go about answering this one? Would I have to integrate the equations for pressure with respect to the area of the wall in contact with the liquids?