Pressure is the force exerted per unit area. It is expressed as
\$P = \frac{F}{A}\$
where F is the normal force acting on a surface of area A.
Pressure in a fluid at rest
In a fluid that is not moving, the pressure at any point is the same in all directions. This is known as Pascal’s principle.
How pressure varies with depth
When you go deeper beneath the surface of a liquid, the weight of the liquid above you adds to the atmospheric pressure acting on the surface. The deeper you go, the more liquid there is above, so the pressure increases.
The increase in pressure with depth is given by the relation
\$\Delta P = \rho g h\$
where
\(\rho\) = density of the liquid (kg m⁻³)
\(g\) = acceleration due to gravity (≈ 9.81 m s⁻²)
\(h\) = vertical depth below the surface (m)
The total pressure at depth \(h\) is therefore
\$P{\text{total}} = P{\text{atm}} + \rho g h\$
Qualitative description of the effects
Depth (\(h\)): As depth increases, the column of liquid above the point becomes taller, so the weight of that column increases. Consequently, pressure increases linearly with depth.
Density (\(\rho\)): A denser liquid has more mass per unit volume. For the same depth, a denser liquid exerts a larger weight per unit area, giving a greater pressure increase. Thus, pressure increases with density.
Atmospheric pressure (\(P_{\text{atm}}\)): This is the pressure at the surface of the liquid. It adds a constant offset to the pressure at all depths, but does not affect how pressure changes with depth.
Examples
Comparing water (\(\rho \approx 1000\) kg m⁻³) and oil (\(\rho \approx 800\) kg m⁻³) at the same depth: the pressure in water is larger because of its higher density.
At a depth of 5 m in fresh water, the pressure increase is \(\Delta P = 1000 \times 9.81 \times 5 \approx 49\,050\) Pa (≈ 0.49 atm). Adding atmospheric pressure (\overline{101} kPa) gives a total pressure of about 150 kPa.
Summary Table
Parameter
Effect on pressure beneath the surface
Depth (\(h\))
Pressure increases linearly with depth; deeper → higher pressure.
Density (\(\rho\))
For a given depth, higher density → greater pressure increase.
Atmospheric pressure (\(P_{\text{atm}}\))
Provides a constant base pressure at the surface; adds to pressure at all depths.
Suggested diagram: A vertical column of liquid showing depth \(h\), atmospheric pressure at the surface, and the increasing pressure with depth. Label \(\rho\), \(g\), and \(h\).