Unit 8: Fluids

Why this unit

A 100 000 tonne steel ship floats, but a steel bolt sinks. Your ears hurt at the bottom of a pool. Water squirts faster when you put your thumb over a hose. Unit 8 explains all three with ideas you already know: Newton's laws (Unit 2) and conservation of energy and mass (Units 3 and 4), now applied to liquids and gases.

The College Board's big questions for this unit: Why do some objects float while others sink? Why don't we feel the miles of air above us?

On the exam

Exam weight10–15% of the multiple-choice section: about 4 to 6 of the 42 questions. Fluids can also appear in any of the 4 free-response questions.
Class timeAbout 12–17 class periods in a typical course.
Equations on the sheetρ = m/V · P = F⊥/A · P = P0 + ρgh · Pgauge = ρgh · Fb = ρVg · A1v1 = A2v2 · P1 + ρgy1 + ½ρv1² = P2 + ρgy2 + ½ρv2² (see the equation sheet explained)
Not on the sheet, but neededWater's density 1000 kg/m³ · volume flow rate V/t = Av · Torricelli v = √(2gh) · floating means Fb = mg
Exam rule"Fluids are assumed to be ideal, and pipes are assumed to be completely filled by fluid, unless otherwise stated." Ideal = incompressible, no viscosity.

Source: AP Physics 1 Course and Exam Description (College Board, effective fall 2024).

Topics (do them in order)

  1. 8.1 Internal Structure and Density: what a fluid is, ρ = m/V, ideal fluids. Story: is this "gold" bar real?
  2. 8.2 Pressure: force per area, pressure grows with depth, gauge vs absolute pressure. Story: a diver's ears.
  3. 8.3 Fluids and Newton's Laws: the buoyant force, floating and sinking, apparent weight. Story: a steel ship and a steel bolt.
  4. 8.4 Fluids and Conservation Laws: continuity, Bernoulli, Torricelli. Story: a garden hose and a leaking barrel.
  5. Games: sink or float, cargo loader, pipe flow, pressure at depth. Levels and a score.
  6. Practice set: a full Unit 8 set in AP style, multiple choice and free response, with worked answers.

The whole unit on one screen

  1. Density ρ = m/V belongs to the material. Compare densities to predict floating. 8.1
  2. Pressure P = F⊥/A is a scalar. In a still fluid it grows straight-line with depth: P = P0 + ρgh. Same depth, same pressure, whatever the container's shape. 8.2
  3. Buoyant force: deeper water pushes up harder on the bottom of an object than on its top. The net upward push equals the weight of the displaced fluid: Fb = ρfluidVsubg. Then use Newton's second law as usual. 8.3
  4. Moving fluids: mass is conserved (A1v1 = A2v2, narrow = fast) and energy is conserved (Bernoulli: fast = low pressure at the same height). A pressure difference is what pushes a fluid to speed up. 8.4

Stuck? The free resources page lists videos and notes matched to each topic.