The aquarium has the shape of a cube from the side a = 60 cm. To what height should water be poured so that the force

The aquarium has the shape of a cube from the side a = 60 cm. To what height should water be poured so that the force of hydrostatic pressure on the side wall is n = 6 times less than an hour at the bottom.

The hydrostatic bottom pressure is defined as
p = ro * h * g,
where ro is the density of the liquid, h is the height of the liquid g is the acceleration of gravity
Bottom pressure:
F1 = p * S1, where
S1 = a ^ 2 – bottom area
F1 = p * a ^ 2 = ro * h * g * a ^ 2
The force of pressure on the side wall is determined by half the pressure on the lowest point, since the pressure changes linearly with height:
F2 = (p / 2) * S2
S2 = a * h – the area of that part of the wall that is in the water.
F2 = (p / 2) * a * h = 0.5 * ro * h * g * a * h = 0.5 * ro * a * g * h ^ 2
By the condition of the problem
F1 / F2 = 6
Substitute values for F1 and F2
(ro * h * g * a ^ 2) / (0.5 * ro * a * g * h ^ 2) = a / (0.5 * h) = 6
h = a / 3 = 20 cm



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