What changes with depth
- A fluid is anything that can flow: both liquids and gases qualify
- A stationary fluid exerts pressure on any surface inside it:
- The pressure acts at right angles to the surface, no matter which way the surface is facing
- The pressure increases with depth below the surface of the fluid. The deeper you go, the more fluid is piled above and pressing down
- The pressure is the same at the same depth, regardless of direction or position in the fluid
Why depth raises pressure
- Imagine a column of liquid sitting on top of a small horizontal patch of area at some depth h
- The weight of that column is m × g = (ρ × V) × g = ρ × A × h × g
- That weight presses on the patch, contributing a pressure of:
P = (force) / (area) = (ρ × A × h × g) / A = ρ × g × h
- The area cancels out, so the pressure depends only on the depth, the density of the fluid and the gravitational field strength
The depth-pressure equation
P = h × ρ × g
- where:
- P = pressure at depth h below the surface (Pa)
- h = depth below the surface (m)
- ρ = density of the fluid (kg/m³)
- g = gravitational field strength (10 N/kg on Earth)
- This is the extra pressure caused by the fluid above. Outside the fluid, atmospheric pressure is also present (about 101 000 Pa at sea level), so the total pressure on something deep underwater is atmospheric + the hydrostatic term above. Most IGCSE questions only ask for the hydrostatic term
Example — calculate the hydrostatic pressure at the bottom of a freshwater swimming pool that is 3.5 m deep. Take ρ_water = 1000 kg/m³ and g = 10 N/kg.
- P = h × ρ × g = 3.5 × 1000 × 10 = 35 000 Pa (35 kPa)
Example — a deep-sea diver descends to 15 m below the surface of the sea. Sea water has a density of 1025 kg/m³. Calculate the hydrostatic pressure on the diver. Take g = 10 N/kg.
- P = h × ρ × g = 15 × 1025 × 10 = 153 750 Pa (≈ 154 kPa, or roughly 1.5 times atmospheric pressure on top of the air pressure already pushing down)
Why dams are built thicker at the base
- The water inside a reservoir exerts a hydrostatic pressure on the dam wall, and that pressure rises linearly with depth
- The pressure on the wall is therefore small near the surface and largest near the bottom
- Engineers make the dam wall much thicker at the base than at the top so that the thicker section can resist the much larger force from the deeper water. The wall's cross-section is roughly triangular, with the wide end at the bottom and the narrow end at the surface
- The same logic explains why submarines have a maximum operating depth: at some depth, the hydrostatic pressure exceeds the design strength of the hull