use the equation ∆p = ρg∆h

What is Δp?

In a fluid at rest, the pressure changes with depth. The pressure difference between two points is given by Δp = ρ g Δh.
Where:

• ρ = fluid density (kg m⁻³)
• g = acceleration due to gravity (≈9.81 m s⁻²)
• Δh = vertical height difference (m)

Analogy: Water in a Slinky

Imagine a slinky filled with water. The bottom end feels a stronger pull because the water above it pushes down. That extra push is the pressure difference Δp. The deeper you go, the more water is above you, so the pressure grows linearly with depth.

Using the Equation: Step‑by‑Step

1. Identify the fluid and its density ρ.
2. Measure the vertical distance Δh between the two points.
3. Multiply ρ by g and then by Δh to get Δp.

Example: Water (ρ = 1000 kg m⁻³) at a depth of 5 m.
Δp = 1000 × 9.81 × 5 = 49 050 Pa (≈49 kPa).

Example Problem

A tank holds oil with ρ = 800 kg m⁻³. What is the pressure difference between the surface and a point 3 m below?

Exam Tips 🚀

• Always write the full equation: Δp = ρ g Δh.
• Check units: ρ (kg m⁻³) × g (m s⁻²) × Δh (m) = Pa.
• Remember that Δh is the vertical distance downwards from the reference point.
• Use the symbol ρ for density and avoid confusing it with the Greek letter ρ.
• When given a pressure at a depth, you can rearrange the equation to find ρ or Δh if needed.