Density and Pressure

Overview

This lesson links two familiar quantities, density and pressure, to a more powerful model for fluids. You should be able to explain why pressure increases with depth and use that idea in calculations.

What You Need to Know

• Use density to compare how much mass is packed into a given volume.
• Use pressure to compare how a force is spread over an area.
• In a liquid, pressure increases with depth because a deeper point has more fluid above it.
• The pressure difference in a liquid is delta p = rho g delta h.
• Hydrostatic pressure depends on density, gravitational field strength, and vertical depth, not on the shape of the container.

How to Work Through It

1. Start by reviewing density and pressure calculations from IGCSE.
2. Derive the hydrostatic pressure equation from the weight of a column of liquid.
3. Practise choosing the correct area, depth, and pressure difference in fluid questions.
4. Use diagrams to compare points at different depths in the same liquid.

Check Your Understanding

• Why does pressure increase with depth in a liquid?
• Which variables affect hydrostatic pressure difference?
• Why does container shape not appear in delta p = rho g delta h?
• How would doubling the liquid density change the pressure difference?

Common Mistakes

• Using total distance through the liquid instead of vertical depth.
• Confusing pressure with force.
• Forgetting that delta p is a pressure difference between two levels.
• Leaving density in g cm-3 when the rest of the calculation needs SI units.

Next Steps

• Practise unit conversions for density and pressure.
• Bring hydrostatic pressure into the next lesson, where pressure differences explain upthrust.