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 The pressure at the bottom of the pool is given by the density of water, G times height of the o

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 exerted by the water on
(a) the bottom? (b) On each end? (c) On each side?

Key Concepts

Hydrostatic Pressure

This concept explains that in a fluid at rest, the pressure increases with depth due to the weight of the overlying fluid. It is generally given by the relation P = ?gh, where ? is the fluid density, g is the acceleration due to gravity, and h is the depth below the fluid surface. This relationship is fundamental in calculating the forces exerted by a fluid on submerged surfaces.

Force from Pressure Integration

The force exerted by a fluid on a submerged surface is determined by integrating the pressure distribution over the area of the surface. For flat surfaces, this requires accounting for the fact that the pressure may vary over the surface (as in vertical surfaces) or may be constant (as in horizontal surfaces at a uniform depth). The integration process yields the total force acting on that area.

Surface Orientation in Fluid Statics

When calculating forces on submerged surfaces, the orientation of the surface (whether horizontal, vertical, or inclined) is crucial. A horizontal surface experiences a uniform pressure across its area at a given depth, whereas a vertical or inclined surface experiences a pressure that varies linearly with depth. Understanding how the surface's alignment affects the pressure distribution is key to correctly determining the resultant force.

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