Quick answer: Fluids obey a few linked rules: density is mass per volume, pressure rises with depth as P = P₀ + ρgh, buoyant force equals the weight of fluid displaced, continuity says Av is constant in a pipe, and Bernoulli shows that faster flow means lower pressure. This AP Physics 1 worksheet on fluid mechanics gives 20 problems from easy to hard: density of a metal block, drawing pin pressure and tyre pressure. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These problems train the five ideas of AP Physics 1 unit 8: density, pressure and depth, buoyancy, continuity and Bernoulli’s equation. They begin with one-step calculations and finish with multi-part reasoning in the style of free-response questions. Use g = 9.81 m/s², ρwater = 1000 kg/m³ and P₀ = 1.01 × 10⁵ Pa unless told otherwise. Show every formula and write units with each final answer.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 8
Problem 1 Density of a metal block ★★★
Mei in Singapore measures an aluminium block with a mass of 0.54 kg and a volume of 2.0 × 10⁻⁴ m³.1. State the SI unit of density.
2. Then calculate the density of the block.
3. Finally, convert your answer to g/cm³.
Problem 2 Drawing pin pressure ★★★
Wanjiru presses a drawing pin into a noticeboard with a force of 20 N. The tip has an area of 5.0 × 10⁻⁷ m² and the head has an area of 1.0 × 10⁻⁴ m².1. Calculate the pressure under the tip.
2. Then calculate the pressure on her thumb at the head.
3. Finally, explain why the tip enters the board.
Problem 3 Tyre pressure ★★★
A tyre gauge in Lahore reads 2.20 × 10⁵ Pa. Take P₀ = 1.01 × 10⁵ Pa.1. Convert 250 kPa to pascals.
2. Then calculate the absolute pressure inside the tyre.
3. Finally, state what the gauge actually measures.
Problem 4 Pressure in a water tank ★★★
A farm tank in Kenya holds fresh water 5.0 m deep and is open to the air.1. Calculate the gauge pressure at the bottom.
2. Then calculate the absolute pressure at the bottom.
Problem 5 Aquarium base ★★★
Emma’s aquarium has a rectangular base of 0.60 m by 0.30 m and holds water 0.40 m deep.1. Calculate the gauge pressure on the base.
2. Then calculate the force of the water on the base.
3. Finally, calculate the weight of the water and compare.
Problem 6 Fully submerged stone ★★★
Diego lowers a stone of volume 3.0 × 10⁻⁴ m³ fully into a bucket of fresh water.1. Calculate the volume of water displaced.
2. Then calculate the buoyant force on the stone.
Problem 7 Flow rate in a pipe ★★★
A pipe has a cross-sectional area of 4.0 × 10⁻⁴ m². Water flows through it at 1.5 m/s.1. Calculate the volume flow rate in m³/s.
2. Then calculate the volume that passes in one minute, in litres.
Problem 8 Pressure against depth graph ★★★
Kofi records the absolute pressure at different depths in a water tank (graph shown).2. Then use it to estimate the fluid density.
3. Finally, predict the pressure at 8 m.
Problem 9 Float or sink ★★★
Three solid blocks of the same size are released in fresh water. Their densities are 500, 1000 and 1200 kg/m³.1. Predict what each block does.
2. Then calculate the fraction of the 500 kg/m³ block that is under water.
3. Finally, explain why the 1000 kg/m³ block can stay at any depth.
Problem 10 Iceberg ★★★
An iceberg of density 917 kg/m³ floats in seawater of density 1025 kg/m³ off Greenland.1. Calculate the fraction of the iceberg that is below the surface.
2. Then state the fraction above the surface.
Problem 11 Weight in air and in water ★★★
A metal sample hangs from a scale (shown). It reads 4.90 N in air and 4.20 N fully submerged in water.2. Then calculate the volume of the sample.
3. Finally, calculate its density.
Problem 12 Garden hose nozzle ★★★
Bilal’s garden hose has a diameter of 1.8 cm. Water travels at 1.2 m/s inside it and leaves through a nozzle of diameter 0.60 cm.1. Calculate the exit speed.
2. Then calculate the flow rate in litres per minute.
Problem 13 Hydraulic car lift ★★★
A garage lift (shown) has a small piston of area 4.0 × 10⁻³ m² and a large piston of area 0.16 m². A force of 150 N pushes on the small piston.2. Then calculate the force on the large piston.
3. The small piston moves 0.80 m. Calculate how far the large piston rises.
Problem 14 Pressure drop in a fast section ★★★
Water at 1.0 m/s and pressure 2.40 × 10⁵ Pa flows along a horizontal pipe that narrows so that the speed becomes 5.0 m/s.1. Calculate the new pressure.
2. Then state by how many pascals the pressure drops.
Problem 15 Roof in a strong wind ★★★
Wind of 20 m/s blows over a flat tin roof of area 8.0 m² and mass 150 kg in Nairobi. The air under the roof is still. Use ρair = 1.2 kg/m³.1. Calculate the pressure difference across the roof.
2. Then calculate the net upward force from the air.
3. Finally, decide whether the roof lifts if it is not fixed.
Problem 16 Jet from a tank ★★★
A wide open tank of fresh water has a small hole 3.2 m below the surface and 1.0 m above the ground.1. Use Bernoulli’s equation to find the exit speed of the jet.
2. Then calculate the time for water to fall to the ground.
3. Finally, calculate the horizontal distance reached.
Problem 17 Venturi flow meter ★★★
A horizontal pipe has a wide section of area 2.0 × 10⁻³ m² and a narrow section of area 5.0 × 10⁻⁴ m². The pressure difference between the sections is 1.5 × 10⁴ Pa for water.1. Write v₂ in terms of v₁.
2. Then use Bernoulli’s equation to find v₁.
3. Finally, calculate the volume flow rate.
Problem 18 Ball held under water ★★★
A ball of mass 0.50 kg and volume 2.0 × 10⁻³ m³ is held fully under water by a string tied to the bottom of a pool.1. Calculate the buoyant force.
2. Then draw a free-body diagram in words and calculate the tension.
3. The string is cut. Calculate the initial acceleration, ignoring drag.
Problem 19 Oil in a U-tube ★★★
Water fills a U-tube (shown). Oil of density 800 kg/m³ is poured into the right arm until it is 12.0 cm deep.2. Then calculate the height of the water in the left arm above the interface.
3. Finally, calculate how far the oil surface is above the left water surface.
Problem 20 Loaded barge ★★★
A flat-bottomed barge is 6.0 m long and 2.0 m wide, has a mass of 3000 kg and sides 0.80 m high. It floats in river water.1. Calculate how deep the empty barge sits.
2. Then calculate the depth after loading 2400 kg of sand.
3. Next, calculate the largest load it can carry before water reaches the top of the sides.
4. Finally, calculate the depth of the loaded barge (5400 kg in total) if it moves into seawater of density 1025 kg/m³.
