A swimming pool has dimensions 30.0 m ×10.0 m and a flat bottom. When the pool is filled to a de

step 1 Question number 12. First of all, we will find the hydrostatic pressure at a depth of 2 meters.

A swimming pool has dimensions 30.0 m ×10.0 m and a flat...

A swimming pool has dimensions $30.0 \mathrm{m} \times 10.0 \mathrm{m}$ and a flat bottom. When the pool is filled to a depth of 2.00 $\mathrm{m}$ with fresh water, what is the force caused by the water on the bottom? On each end? On each side?

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Key Concepts

Force on Submerged Surfaces

The force exerted by a fluid on a surface is the result of pressure acting over that area. When the pressure is constant, as on a flat, horizontal bottom, the force is simply the product of pressure and area. For surfaces where pressure varies, such as vertical walls of a pool, the total force must be calculated by integrating the pressure over the area of the surface.

Pressure Distribution on Vertical Surfaces

Vertical surfaces in a fluid experience a non-uniform pressure that increases from zero at the fluid surface to a maximum at the bottom. The integration of this linearly varying pressure across the area yields the total force on the wall. Additionally, the center of pressure, where the resultant force is considered to act, is located lower than the geometric center because of the increasing pressure with depth.

Hydrostatic Pressure

This concept explains that in a fluid at rest, the pressure increases linearly with depth due to the weight of the fluid above. The relationship is given by P = ?gh (ignoring atmospheric pressure), where ? is the density of the fluid, g is the acceleration due to gravity, and h is the depth. Understanding this allows us to determine how pressure is distributed over submerged surfaces.

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