Pressure in fluids and the atmosphere

Physics · Forces. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A fluid is a liquid or a gas. The pressure in a fluid pushes at right angles (normal) to any surface it touches. Pressure is the force on each square metre.

In a liquid, pressure increases with depth, because there is more liquid above and its weight is greater. It also increases with the density of the liquid.

The bottom of a submerged object is deeper than the top, so the pressure on the bottom is larger. This gives a resultant upward force called upthrust. An object floats if the upthrust equals its weight. It sinks if it is denser than the liquid. The atmosphere is a thin layer of air; higher up there is less air above, so atmospheric pressure is lower.

Rules to remember

pressure = force normal to the surface ÷ area (p = F/A); unit pascal, 1 Pa = 1 N/m².
pressure due to a column of liquid = height × density × gravitational field strength (p = hρg).
h in m, ρ in kg/m³, g = 9.8 N/kg, p in Pa.
Floating at rest: upthrust = weight, and the object is less dense than the liquid.
Sinking: the weight is greater than the upthrust; the object is denser than the liquid.
Atmospheric pressure decreases as height increases because the weight of air above each unit area is smaller.

Common mistake

Students forget to work out the area in m² before dividing, or leave a depth in centimetres in p = hρg. Convert every quantity to SI units first.

Worked example

A tank holds oil to a depth of 3.0 m. The density of the oil is 800 kg/m³. What is the pressure due to the oil at the bottom, and the force on a base of area 0.50 m²? (g = 9.8 N/kg)

p = h × ρ × g = 3.0 × 800 × 9.8.
3.0 × 800 = 2400, and 2400 × 9.8 = 23 520 Pa.
F = p × A = 23 520 × 0.50 = 11 760 N.

Answer: Pressure 23 520 Pa (about 24 kPa); force 11 760 N (about 12 kN)

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