Question

Аквариум имеет форму куба со стороной 1м. Он доверху наполнен водой. Во сколько раз отличаются силы давления на дно и на одну боковую стенку куба?

Answer 1

Давление на боковую стенку растет линейно от нуля (вверху) до максимального (внизу), среднее давление равно половине максимального.
на дно же действует только максимальное давление.

ответ - в 2 раза (на дно больше)

Answer 2

Calculation of Pressure on the Bottom and Side Wall of the Aquarium

To calculate the difference in pressure on the bottom and one side wall of the aquarium, we need to consider the principles of fluid pressure.

The pressure exerted by a fluid at a certain depth is given by the equation:

P = ρgh

Where: - P is the pressure exerted by the fluid, - ρ is the density of the fluid, - g is the acceleration due to gravity, and - h is the depth of the fluid.

In this case, the aquarium is completely filled with water, so the depth of the water is equal to the height of the aquarium, which is 1 meter.

To find the difference in pressure between the bottom and one side wall, we need to calculate the pressure exerted on each surface separately.

Pressure on the Bottom of the Aquarium

The pressure on the bottom of the aquarium is equal to the weight of the water above it. Since the aquarium is completely filled with water, the pressure on the bottom can be calculated using the equation:

P_bottom = ρgh

Where: - P_bottom is the pressure on the bottom of the aquarium, - ρ is the density of water, which is approximately 1000 kg/m³, - g is the acceleration due to gravity, which is approximately 9.8 m/s², and - h is the height of the aquarium, which is 1 meter.

Substituting the values into the equation, we get:

P_bottom = (1000 kg/m³) * (9.8 m/s²) * (1 m) = 9800 Pa

Pressure on One Side Wall of the Aquarium

The pressure on one side wall of the aquarium is equal to the weight of the water above it. Since the side wall is vertical, the pressure on it can be calculated using the equation:

P_side = ρgh

Where: - P_side is the pressure on one side wall of the aquarium, - ρ is the density of water, which is approximately 1000 kg/m³, - g is the acceleration due to gravity, which is approximately 9.8 m/s², and - h is the height of the water above the side wall, which is also 1 meter.

Substituting the values into the equation, we get:

P_side = (1000 kg/m³) * (9.8 m/s²) * (1 m) = 9800 Pa

Difference in Pressure

To find the difference in pressure between the bottom and one side wall of the aquarium, we subtract the pressure on the side wall from the pressure on the bottom:

Difference in Pressure = P_bottom - P_side = 9800 Pa - 9800 Pa = 0 Pa

Therefore, the difference in pressure between the bottom and one side wall of the aquarium is 0 Pa.

Please note that the difference in pressure is zero because the aquarium is completely filled with water and the height of the water is the same on both the bottom and the side wall.