Fluid Pressure and Upthrust

When you dive to the bottom of a swimming pool, you feel a squeezing sensation in your ears. The deeper you go, the greater the pressure. This everyday experience is rooted in one of the most important principles in fluid physics: pressure in a fluid increases with depth.

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Pressure in Fluids

Pressure at a point in a fluid is caused by the weight of the fluid above that point pressing down. The equation for the pressure at depth h in a fluid of density ρ is:

$p = \rho g h$p=ρgh

where:

• p is pressure in Pa (pascals), where 1 Pa = 1 N m⁻²
• ρ is the density of the fluid in kg m⁻³
• g is the gravitational field strength (9.81 m s⁻² on Earth)
• h is the depth below the surface of the fluid in metres

This equation tells us three things:

1. Pressure increases linearly with depth.
2. Pressure is greater in denser fluids (mercury exerts more pressure at a given depth than water).
3. Pressure does not depend on the shape of the container — only on the depth.