The aquarium is filled to the brim with water. With what force does the water press

The aquarium is filled to the brim with water. With what force does the water press on the wall of the aquarium 50 cm long and 30 cm wide?

1. Let’s translate the given value into the SI system:
l = 50 cm = 0.5 m
h = 30 cm = 0.3 m
2. The average pressure on the side face is equal to the half-sum of the pressures at the surface and at the bottom:
P = (P1 + P2) / 2, where P1 is the surface pressure, P2 is the bottom pressure.
3. Hydrostatic pressure at depth:
P = ρ * g * h, where ρ is the density of water ρ = 1000 kg / m3, g is the acceleration of gravity g = 9.8 m / s2, h is the depth.
At bottom level pressure:
P2 = ρ * g * h
Surface pressure:
P1 = ρ * g * h, because the depth on the surface is 0, hence the pressure, respectively, P1 = 0
4. It turns out:
P = P2 / 2
5. Force of pressure on the wall:
F = P * S = P2 * S / 2 = ρ * g * h * S / 2, where S is the wall area
S = l * h
6. Substitute the area expression into the force expression:
F = ρ * g * h * l * h / 2 = 1000 * 9.8 * 0.3 * 0.5 * 0.3 / 2 = 220.5 N
Answer: The force of pressure on the wall F = 220.5 N