Upthrust

Upthrust is the upward force a liquid or gas exerts on an object that is partly or fully submerged in it. It happens because the pressure in a fluid increases with depth, so the pressure on the bottom of the object is greater than the pressure on its top, giving a resultant force upwards. If the upthrust can balance the object's weight, the object floats.

What causes upthrust?

A fluid is a liquid or a gas. The pressure in a fluid pushes at right angles on every surface, and it gets bigger the deeper you go, because there is more fluid above pressing down. For a liquid:

Now think about a block held under water. Its bottom face is deeper than its top face, so the water pushes up on the bottom harder than it pushes down on the top. The forces on the sides are equal and cancel. The result is an overall upward force: the upthrust.

Upthrust doesn't depend on how deep the object is, once it is fully under: going deeper raises the pressure on both faces by the same amount, so the difference stays the same.

Calculating upthrust from pressure

Example 1: a block under water

A cube with sides of 0.20 m is held under water with its top face 0.30 m below the surface. Find the upthrust. Use a water density of 1000 kg/m³ and g = 9.8 N/kg.

1. Pressure on the top face (depth 0.30 m): p = 0.30 × 1000 × 9.8 = 2940 Pa.
2. Pressure on the bottom face (depth 0.50 m): p = 0.50 × 1000 × 9.8 = 4900 Pa.
3. Pressure difference: 4900 − 2940 = 1960 Pa.
4. Area of each face: 0.20 × 0.20 = 0.040 m².
5. Upthrust = pressure difference × area = 1960 × 0.040 = 78.4 N.

Compare this with the weight of the water the cube pushes aside: its volume is 0.20³ = 0.008 m³, its mass is 0.008 × 1000 = 8 kg, and its weight is 8 × 9.8 = 78.4 N. The same answer. That is Archimedes' principle: the upthrust equals the weight of fluid displaced.

The buoyancy calculator guide uses this principle to work out upthrust (called buoyant force in the US) for any volume and fluid.

Measuring upthrust with a newtonmeter

Hang an object from a newtonmeter and read its weight in air. Then lower it into water and read it again. The reading drops, because the upthrust is helping to hold the object up:

Example 2: a stone

A stone reads 6.0 N in air and 3.6 N when fully under water. The upthrust is 6.0 − 3.6 = 2.4 N. That is the weight of the water displaced, so the volume of the stone is 2.4 ÷ (1000 × 9.8) = 2.4 × 10⁻⁴ m³, or about 240 cm³.

Check your understanding.

Floating and sinking

Two forces act on an object in a fluid: its weight, downwards, and the upthrust, upwards.

• Upthrust less than weight: the resultant force is downwards, so the object sinks.
• Upthrust equal to weight: the forces are balanced, so the object floats (or stays still under water).
• Upthrust greater than weight when fully under: the object rises until enough of it is above the surface for the upthrust to equal its weight, then it floats.

Whether it floats comes down to density. An object less dense than the fluid can displace its own weight of fluid before it is fully submerged, so it floats. An object denser than the fluid can't, so it sinks.

Example 3: how much of a floating object is under water?

For an object that floats, the fraction under the surface equals its density divided by the fluid's density. A block of wood of density 600 kg/m³ floats in water with 600 ÷ 1000 = 60% of its volume under water. With typical values of 917 kg/m³ for ice and 1025 kg/m³ for seawater, about 917 ÷ 1025 ≈ 89% of an iceberg is below the surface.

Ships, submarines and balloons

• A steel ship floats because its hollow hull displaces a large volume of water, enough to weigh as much as the ship.
• A submarine dives by letting water into its ballast tanks, making it heavier than the upthrust, and rises by blowing the water out with compressed air.
• A hot air balloon rises because air is a fluid too: the balloon displaces cold air whose weight is greater than the weight of the balloon, its hot air and its load.

Common mistakes

• Saying objects weigh less in water. Their weight is the same; the upthrust partly balances it.
• Explaining upthrust with "water pushes up" only. Explain the pressure difference between the top and bottom surfaces.
• Thinking upthrust increases with depth. Once fully submerged, it stays the same.
• Saying heavy objects sink and light ones float. It depends on density, not weight: a huge ship floats.
• Forgetting gases. Air gives a small upthrust too.

Practice questions

1. What is upthrust?
2. A rock reads 15.0 N in air and 9.5 N in water. Calculate the upthrust.
3. The pressure on the top of a submerged block is 3000 Pa and on its bottom is 3500 Pa. Each face has an area of 0.050 m². Calculate the upthrust.
4. A plastic block of density 900 kg/m³ is put in water. Does it float? What fraction is under water?

Answers: 1) The upward force a fluid exerts on an object in it, caused by greater pressure on the bottom of the object than on the top. 2) 15.0 − 9.5 = 5.5 N. 3) (3500 − 3000) × 0.050 = 25 N. 4) Yes, because it is less dense than water; 900 ÷ 1000 = 90% is under water.

Practise with a short timed paper

Forces and pressure in fluids come up in GCSE Physics. The daily GCSE Physics Higher paper is a short timed paper of 8 questions, with a new one every day. Try your own values in the Pressure Calculator.

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