A backyard swimming pool with a circular base of diameter 6.00 m is filled to depth 1.50 m. (a)

step 1 The absolute pressure at the bottom of the pool is given by atmospheric pressure plus Rho G H eq

A backyard swimming pool with a circular base of diameter...

A backyard swimming pool with a circular base of diameter $6.00 \mathrm{m}$ is filled to depth $1.50 \mathrm{m}$. (a) Find the absolute pressure at the bottom of the pool. (b) Two persons with combined mass $150 \mathrm{kg}$ enter the pool and float quietly there. No water overflows. Find the pressure increase at the bottom of the pool after they enter the pool and float.

Key Concepts

Fluid Statics

Fluid statics, or hydrostatics, is the branch of physics that studies fluids at rest and the forces exerted by them. It encompasses principles such as the transmission of pressure in a fluid and the concept of equilibrium of forces, which underpin the analysis of pressure distribution in any stationary fluid system.

Buoyancy and Displacement

Buoyancy is the upward force experienced by an object immersed in a fluid, which is equal to the weight of the fluid displaced, as stated in Archimedes’ principle. This concept explains why objects float or sink and how the displacement of fluid by an object alters the pressure distribution within the container.

Absolute Pressure

Absolute pressure is the total pressure at a point in the fluid measured relative to a perfect vacuum. It includes both the atmospheric pressure and the additional pressure due to the fluid’s depth. Recognizing the distinction between absolute and gauge pressure is crucial in many problems involving pressure measurements in fluids.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the gravitational force acting on it. It increases linearly with depth and is calculated using the formula ?gh, where ? is the density of the fluid, g is the gravitational acceleration, and h is the depth below the surface. This concept is central to understanding how pressure varies in a stationary fluid.

Load-Induced Pressure Variation

When an additional load is placed on a fluid, it displaces a certain volume, causing the fluid level to rise. This increase in depth results in an increased hydrostatic pressure at the bottom of the container. Understanding how added weight affects pressure is important in analyzing systems where external loads interact with fluid surfaces.

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