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Fluids

Pressure, Bernoulli, viscosity and surface tension. It has grown since the early papers, and most of its questions are calculations.

Questions in the bank
113
q/paper in 2025–26
1.07
Numeric answer
33%
Notes pages
6

Tier: Core

When you’ll see it

Pressure at a depth, a floating body, flow through a narrowing pipe, a jet from a tank, a sphere falling through a liquid, or a drop, bubble or capillary.

How this chapter is tested

The chapter has two halves. Liquids at rest or in motion are nearly always a balance: of pressures at one level, of energy per unit volume along a pipe, or of weight against buoyancy and drag. Surface tension is the other half, where the energy or the extra pressure of a curved surface does the work.

This is a core chapter, and it has grown in recent papers. The physics is short, and many questions ask for a number rather than an option.

Marks are lost on a factor. A soap bubble has two surfaces and an air bubble in water has one, a stem gives a diameter where the formula wants a radius, and the atmosphere is added where it cancels or left out where the stem gives it.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Pressure, Pascal's law and buoyancy

    P = P₀ + ρgh; a pressure added to an enclosed liquid reaches every point; a floating body displaces its own weight of liquid.

  • Continuity, Bernoulli and efflux

    A₁v₁ = A₂v₂; P + ρgh + ½ρv² is constant, so pressure falls where the pipe narrows; a jet leaves a tank at √(2gh).

  • Viscosity, Stokes' law and Reynolds number

    Viscous force is ηA times the velocity gradient; a slow sphere feels 6πηrv; ρvd/η says whether a flow stays smooth.

  • Terminal velocity

    Drag plus buoyancy equals weight at v = 2r²(ρ − σ)g/9η, so for one material v grows as r².

  • Surface energy of drops and bubbles

    New surface costs T × ΔA: splitting a drop needs work, merging releases energy, and a soap bubble pays for two surfaces.

  • Excess pressure and capillary rise

    Excess pressure is 2T/r for one surface and 4T/r for a soap bubble; liquid rises in a narrow tube to h = 2T cos θ/ρgr.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Two surfaces for an air bubble

    Only a soap bubble in air has two faces. An air bubble under water has one, so its excess pressure is 2T/r, not 4T/r.

  • A diameter used as a radius

    Bores, drops and spheres are often given by diameter. Halve it before squaring, or the energy or terminal speed is four times too big.

  • The atmosphere where it cancels

    Air presses on the free surface and on the jet alike, so P₀ cancels in efflux and across a partition. Keep it only where the stem asks for an absolute pressure or gives P₀ for a force.

  • Buoyancy added to the drag

    At terminal speed the drag is the weight minus the buoyancy. Adding them gives a force bigger than the weight.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Fluids notes

Drill every Fluids question

113 questions from the bank, across 6 subtopics.

Drill the 113 questions

Drill one subtopic at a time

The 6 subtopics, in teaching order.

Related playbooks

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