Hydrostatic pressure

1. Definition

A. Hydrostatic pressure

Hydrostatic pressure is the pressure in a fluid at rest, caused by the weight of the fluid above a point. It increases with depth.

B. Pressure due to a liquid column

The pressure difference between two points in the same fluid separated vertically by Δ h is:

Δ p = ρ g Δ h

If the fluid surface is at pressure p₀, then at depth h:

p = p₀ + ρ gh

In many O Level questions, p = ρ gh refers to the pressure due to the liquid column: the extra pressure compared with the surface. This is also called gauge pressure when the surface is open to the atmosphere.

• p = pressure (Pa)
• ρ = density (kg m⁻³)
• g = gravitational field strength (N kg⁻¹)
• h = vertical depth below the liquid surface (m)

2. Key Ideas

• Hydrostatic pressure depends on:
  • depth h,
  • fluid density ρ,
  • gravitational field strength g.
• For the same liquid and same g:
  • deeper point → larger pressure (because p ∝ h),
  • same depth → same pressure (even if the container shape is different).
• Hydrostatic pressure does not depend on the shape or cross-sectional area of the container.
• Use the vertical depth from the surface:
  • p = ρ gh
  • Δ p = ρ g Δ h
• If asked for total pressure at depth in an open tank:
  • pₜₒₜₐₗ = pₐₜₘ + ρ gh

3. Detailed Explanations

A. Why pressure increases with depth

The deeper you go in a liquid, the more liquid there is above you.

• more water above → larger weight pressing down
• larger weight over the same area → larger pressure

B. Using p = ρ gh (what is h?)

For a point at depth h below the surface in a uniform liquid:

p_column = ρ gh

If the surface is open to the air, the total pressure is:

pₜₒₜₐₗ = pₐₜₘ + ρ gh

Column pressure vs total pressure (open tank)

Two straight lines versus depth: one shows pressure due to the water column only; the other includes atmospheric pressure as a constant offset.

Scroll across the graph to read all labels.

Open full-size graph

View figure data

Values for Column pressure vs total pressure (open tank)

Depth below surface (m)	Column pressure (ρgh) in water	Total pressure (patm + ρgh)
0	0	100
6	60	160

Values for Column pressure vs total pressure (open tank)

Depth below surface (m)	Column pressure (ρgh) in water	Total pressure (patm + ρgh)
0	0	100
6	60	160

C. Same depth means same pressure (shape does not matter)

In a liquid at rest:

• all points at the same depth have the same pressure
• the pressure at the bottom depends on depth h, not on the container’s shape or width

D. Pressure acts in all directions

Pressure at a point in a fluid acts in all directions (not just downward). This is why water pushes:

• downward on the bottom of a tank,
• sideways on the walls of a tank.

4. Common Mistakes

• Using the wrong h (it must be the vertical depth below the surface, not the slanted distance).
• Forgetting to convert cm to m (e.g. 35 cm = 0.35 m).
• Mixing density units (use kg m⁻³ when using SI units in the formula).
• Forgetting to add atmospheric pressure when the question asks for total pressure.

5. Exam Tips

• Write the formula first ( p = ρ gh or Δ p = ρ gΔ h), then substitute with units.
• Quote the correct unit at the end: Pa (or kPa).
• For water, a common value is ρ = 1000 kg m⁻³.
• If two points are at the same depth in the same connected liquid, state: “same h → same pressure”.

6. Worked Examples

7. Mind Stretchers

8. Practice and next step

Use the Pressure and hydraulics explorer to test depth, density, and vessel shape. Then continue to Hydraulic systems.