Pressure and pressure differences in fluids
Pressure is the force per unit area exerted by a fluid (or solid) on a surface.
$p = \dfrac{F}{A}$
- $p$ — pressure (pascal, Pa = N/m²).
- $F$ — force (N).
- $A$ — area (m²).
Pressure with depth in a liquid
In a static liquid, pressure increases with depth:
$p = h\rho g$
- $h$ — depth below surface (m).
- $\rho$ — density of liquid (kg/m³).
- $g$ — gravitational field strength.
This is "extra" pressure on top of any atmospheric pressure at the surface.
✦Worked example
What is the pressure at 5 m depth in fresh water? $\rho = 1000$ kg/m³, $g = 9.8$.
- $p = h\rho g = 5 \times 1000 \times 9.8 = 49,000$ Pa = 49 kPa.
Atmospheric pressure
The weight of the air column above us creates atmospheric pressure ≈ 101 kPa at sea level. It decreases with altitude (the column of air above is thinner).
Floating and sinking
When an object is in a fluid, pressure on its bottom is greater than on its top. This pressure difference creates an upthrust (buoyancy).
- If upthrust = weight → object floats.
- If upthrust < weight → object sinks.
- If upthrust > weight → object rises.
For a floating object: weight = upthrust = weight of fluid displaced (Archimedes).
Why ships float
A steel ship has overall density much less than water (most of its volume is air). When in water, it displaces enough water that the displaced water's weight equals the ship's weight. So upthrust = weight → floats.
Higher Tier — atmospheric pressure variation
- At 5 km altitude, pressure is roughly half sea-level.
- High mountains: low pressure → boiling point of water lowers.
- Aircraft cabin pressurised to ~80 kPa for comfort.
⚠Common mistakes
- Forgetting to convert area to m². 1 cm² = 1 × 10⁻⁴ m².
- Saying pressure is the same at every depth.
- Treating upthrust like a fixed quantity — it depends on volume submerged.
- Confusing floating density with sinking density. Compare to fluid's density.
AI-generated · claude-opus-4-7 · v3-deep-physics