Not given in the exam, recall it.
What it is for
Pressure in a liquid column is used in Pressure (SPM Physics Form 5). Keep the SI units in every line of working. Pressure
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| P | liquid pressure | Pa |
| h | depth | m |
| ρ | density | kg m⁻³ |
| g | gravitational acceleration | m s⁻² |
Rearrangements
h = P / (ρg)ρ = P / (hg)
Worked example
Common trap
Understanding pressure in a liquid column
P is the liquid pressure in pascals (Pa), h is the vertical depth below the surface in metres (m), ρ (rho) is the density of the liquid in kilograms per cubic metre (kg m⁻³), and g is the gravitational acceleration in metres per second squared (m s⁻²). The pressure comes from the weight of liquid above a point, so it grows with depth and with density but does not depend on the shape or cross-section of the container.
Because P = hρg, you can find the depth with h = P / (ρg) or the density with ρ = P / (hg). Use h as the vertical depth measured straight down from the surface, not the slant distance.
This gives the pressure due to the liquid alone.
A worked example, step by step
A diver is at a depth h = 15 m in sea water of density ρ = 1025 kg m⁻³ (take g = 9.81 m s⁻²). Find the pressure due to the water.
- Write the formula: P = hρg.
- Substitute with units: P = 15 m × 1025 kg m⁻³ × 9.81 m s⁻² = 150 828 Pa.
- Round sensibly: P = 1.5 × 10⁵ Pa to two significant figures.
The unit check works: m × kg m⁻³ × m s⁻² = kg m⁻¹ s⁻² = Pa. This is the pressure from the water only; to get the total pressure on the diver you would add the atmospheric pressure of about 1.0 × 10⁵ Pa pushing on the surface.
Common mistakes and how this is tested
The classic trap is using a slant or along-the-tube distance for h instead of the vertical depth, pressure depends only on how far straight down you are. Another mistake is quoting the liquid pressure as the total pressure; unless the question says gauge pressure, add atmospheric pressure for the true total.
- Mixing up density units, use kg m⁻³, not g cm⁻³.
- Thinking a wider or oddly shaped container changes the pressure, when it does not.
Questions ask you to calculate the pressure at the bottom of a dam, explain why dam walls are thicker at the base, or compare pressures at two depths. For the explanation, link greater depth to greater pressure through P = hρg.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)