This topic accounts for approximately 8% of your exam marks.
stable
Low
Stable8%
ρ = m/V and pressure calculations (P = F/A, P = hρg) appear as standard calculation questions.
What changes with depth
A 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 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 exam questions only ask for the hydrostatic term
Worked example
Calculate pressure at depth in a liquid
A diver descends to a depth of 25 m in seawater with a density of 1 020 kg/m³ (g = 10 N/kg).
Solution:
State the formula: P = h × ρ × g
Substitute: P = 25 × 1 020 × 10
P = 255 000 Pa (255 kPa)
Note: this is the pressure due to the liquid alone. The total pressure at that depth also includes atmospheric pressure (~100 000 Pa) added on top.
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