AP Physics 1 fluids explained
Fluids is the final unit of AP Physics 1. It applies forces and energy to liquids and gases.
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Density and pressure
- Density ρ = m/V.
- Pressure P = F/A, measured in pascals.
- Pressure in a fluid increases with depth: P = P0 + ρgh.
Buoyancy
A fluid pushes up on a submerged object because the pressure below it is greater than the pressure above it. Archimedes' principle says the buoyant force equals the weight of the fluid displaced: Fb = ρfluidVg. An object floats when the buoyant force can balance its weight.
Fluid flow
- Continuity: A1v1 = A2v2. Fluid speeds up where a pipe narrows.
- Bernoulli's equation applies conservation of energy to flowing fluids: where the speed is higher, the pressure is lower, for the same height.
Common mistakes
- Using the density of the object instead of the fluid in the buoyancy equation.
- Forgetting atmospheric pressure when asked for absolute pressure.
- Thinking the buoyant force depends on depth for a fully submerged object. It does not, for a fluid of constant density.
How to study fluids
Because fluids comes last, it is easy to leave it short of time. Treat it like forces and energy with new variables, and practise free-body diagrams for floating and submerged objects.
Worked examples
Example 1: pressure at depth
Find the absolute pressure 10 m below the surface of a lake. Use ρ = 1000 kg/m³ and P0 = 1.01 × 105 Pa.
- P = P0 + ρgh = 1.01 × 105 + 98,000 ≈ 1.99 × 105 Pa, almost double atmospheric pressure.
Example 2: does it float?
A 600 kg/m³ wooden block floats in water. What fraction is submerged?
- Floating: weight = buoyant force, so ρwoodV = ρwaterVsub.
- Vsub/V = 600/1000 = 0.6: 60% of the block is under water.
Example 3: apparent weight
A 2 kg metal block of volume 2.5 × 10−4 m³ hangs from a spring scale, fully under water. What does the scale read?
- Weight = 19.6 N. Buoyant force = 1000 × 2.5 × 10−4 × 9.8 = 2.45 N.
- Scale reading = 19.6 − 2.45 ≈ 17.2 N.
Example 4: continuity
Water flows at 2 m/s through a pipe of area 0.01 m² into a section of area 0.004 m². Find the new speed.
- A1v1 = A2v2: 0.01 × 2 = 0.004v, so v = 5 m/s.
Practice questions
Try each one before opening the answer.
Q1. A cube of side 0.1 m is fully submerged in water. Find the buoyant force.
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Q2. Why does the pressure at the bottom of a swimming pool not depend on the pool's width?
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Q3. In a horizontal pipe, water speeds up through a narrow section. What happens to the pressure there?
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Frequently asked questions
Why does a steel ship float?
Its hollow shape displaces a large volume of water. The ship floats when the weight of that water equals the ship's total weight.
Is fluids a big part of the exam?
It is one of eight units. Check the current unit weightings on AP Central, and do not skip it just because it comes last.
The key ideas in more depth
Pressure is not a force
Pressure is force per unit area. A sharp knife works because a small area gives a large pressure. In a fluid at rest, pressure acts in all directions and depends only on depth, the fluid's density and the pressure at the surface.
Buoyancy from pressure
The buoyant force is not a separate force that appears from nowhere. It comes from the pressure difference between the bottom and top of an object. Because pressure grows with depth, the upward push on the bottom is larger than the downward push on the top. Archimedes' principle is a short way to calculate that difference.
Flowing fluids
For an incompressible fluid, the volume flowing past any point each second is the same, which gives the continuity equation. Bernoulli's equation then applies conservation of energy per unit volume: pressure energy, kinetic energy and gravitational energy add to a constant along a streamline.
Exam tips
- Draw free-body diagrams for floating and submerged objects: weight, buoyant force and any tension.
- Use the fluid's density in the buoyant force, not the object's.
- Check whether a question wants absolute pressure or gauge pressure.
More practice
Try each one before opening the answer.
Q1. An ice cube floats in water. Ice has density 920 kg/m³. What fraction is above the water?
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Q2. Water leaves a hose of area 2 cm² at 3 m/s. A nozzle reduces the area to 0.5 cm². Find the new speed.
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One more worked example
Example 5: a hydraulic lift
A hydraulic lift has a small piston of area 0.01 m² and a large piston of area 0.5 m². What force on the small piston lifts a 1000 kg car?
- Pressure is transmitted equally (Pascal's principle): F1/A1 = F2/A2.
- F2 = 1000 × 9.8 = 9800 N, so F1 = 9800 × 0.01/0.5 = 196 N.
- The small force moves much further: energy is still conserved.
Extra practice
Try each one before opening the answer.
Q1. A diver goes from 5 m to 15 m deep in sea water (ρ ≈ 1025 kg/m³). By how much does the pressure increase?
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Q2. A block floats with half its volume submerged in water. What is its density?
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More questions students ask
Why do my ears hurt at the bottom of a pool?
Pressure increases with depth, so the pressure outside your eardrum becomes larger than inside until your ears equalise.
Does a heavier object feel a bigger buoyant force?
Not necessarily. The buoyant force depends on the volume of fluid displaced, not on the object's weight.
Key takeaways
- Pressure in a fluid increases with depth: P = P0 + ρgh.
- The buoyant force equals the weight of the fluid displaced.
- Floating objects displace their own weight of fluid.
- Fluid speeds up where a pipe narrows: A1v1 = A2v2.
- Faster flow means lower pressure, by Bernoulli's equation.