# Force on a retaining wall in a tank of liquid and pressure calculations [closed]

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 $h$.

My attempt:

(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?

## closed as off-topic by John Rennie, Jon Custer, Kyle Kanos, heather, David Z♦Jan 31 '17 at 21:18

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• So would it be as simple as drawing a graph of pressure minus atmospheric pressure on the $y$-axis of each graph against vertical distance below the surface on the $x$-axis, then calculating the area of the triangle for each? – user143811 Jan 30 '17 at 22:01