Pressure
Pressure in liquids
Pressure in liquids
| Symbol | Quantity | Unit |
|---|---|---|
| \( P \) | Pressure at depth \( h \) | pascal, Pa |
| \( h \) | Depth below the liquid surface | metre, m |
| \( \rho \) | Density of the liquid | kg/m³ |
| \( g \) | Gravitational field strength | N/kg (= 10 N/kg near Earth's surface) |
- Pressure increases with depth — the greater the depth, the greater the weight of liquid above.
- Pressure depends on the liquid's density — mercury (13 600 kg/m³) produces far greater pressure at a given depth than water (1000 kg/m³).
- Pressure is independent of the shape of the container — only the vertical depth matters.
- Pressure at a given depth acts equally in all directions — upward, downward, and sideways.
Worked examples
Example 1 — pressure at depth in water
Calculate the pressure due to the water at a depth of 5.0 m in a swimming pool. (ρ_water = 1000 kg/m³, g = 10 N/kg)
\( P = h\rho g = 5.0 \times 1000 \times 10 = 50\,000\,\text{Pa} = 50\,\text{kPa} \)
Example 2 — find depth from pressure
The pressure at the bottom of a tank of mercury is 65 000 Pa. Find the depth of the mercury. (ρ_mercury = 13 600 kg/m³, g = 10 N/kg)
\( h = \dfrac{P}{\rho g} = \dfrac{65\,000}{13\,600 \times 10} = \dfrac{65\,000}{136\,000} = 0.478\,\text{m} \approx 0.48\,\text{m} \)
Example 3 — compare two liquids at the same depth
A diver is at a depth of 10 m in fresh water (ρ = 1000 kg/m³) and in sea water (ρ = 1025 kg/m³). Compare the pressures from each liquid alone.
Fresh water: \( P = 10 \times 1000 \times 10 = 100\,000\,\text{Pa} \)
Sea water: \( P = 10 \times 1025 \times 10 = 102\,500\,\text{Pa} \)
Sea water exerts 2500 Pa more pressure at the same depth due to its higher density.
Applications
- Dams — built thicker at the base because pressure increases with depth; the base must withstand greater force.
- Submarines — designed with reinforced hulls to withstand increasing pressure at depth.
- Hydraulic systems — liquid transmits pressure equally in all directions (Pascal's principle), used in car brakes and hydraulic presses.
- U-tube manometer — liquid levels show relative pressure; the side with higher pressure is lower.