OPOpenPithMake curiosity visiblePhysics lab / Pressure and buoyancy

About this lab

Six experiments, one thread: a liquid pushes on everything inside it.

The first two look at liquid pressure itself: the gauge shows that pressure depends only on the liquid’s density and the depth, and the lock shows that connected liquids at rest stand at the same level. The other four go from pressure to buoyancy: the difference between the push on the bottom and on the top is the buoyant force, it equals the weight of the liquid pushed aside, and comparing it with the weight decides whether an object rises, hovers or sinks.

Every reading, curve and table row comes from the same physical model, not a pre-drawn animation. Change one parameter and all the data is recalculated together.

What the six experiments show

Six common ideas, overturned by data

01 Pressure gauge: “a wider container with more water presses harder at the bottom”

At 10 cm under water the pressure is 980 Pa whichever way the probe faces and whatever the container’s shape. The wide-topped container holds 48.27 N of water and the narrow-topped one only 17.06 N, yet both bases feel 26.60 N. Pressure depends only on density and depth: p = ρgh.

02 Ship lock: “a lock uses pumps to lift the boat”

Open the valve and the upper water flows into the chamber by itself, slower as the difference shrinks: with the default settings the levels meet after 4.2 s and 15.0 L has flowed in. Until the levels match the gate cannot open: connected vessels plus an interlock.

03 Weighing method: “the deeper an object goes, the more buoyancy it gets”

The iron block weighs 6.19 N in air and reads 5.41 N submerged, so the buoyant force is 0.78 N. Lower it further and the pushes on both faces grow, but their difference and the reading stay the same. An aluminium block of the same volume weighs 2.12 N and gets the same 0.78 N.

04 Overflow can: “buoyancy depends on how heavy the object is”

A 160 cm³ aluminium block under water makes the meter drop by 1.57 N, and the water in the bucket weighs exactly 1.57 N. The buoyant force equals the weight of the liquid pushed aside: F_b = ρ g V.

05 Submarine: “a submarine dives because its buoyancy gets smaller”

While the hull is under water the buoyant force stays at 9.80 N; it is the weight that changes. Flood the ballast tank and the average density passes that of water, so it sinks; empty it and the hull rises and floats with 80.0 % of its volume under water.

06 Ship: “steel is denser than water, so a steel ship must sink”

The same 0.6 kg of steel as a solid lump pushes aside only 76 cm³ of water, giving 0.74 N, less than its weight of 5.88 N, so it sinks. As an empty hollow hull it pushes aside 7.9 times as much. With 1.5 kg of cargo it sits 5.83 cm deep in fresh water and 5.66 cm in sea water: buoyancy equals the total weight in both, so it sits deeper in a river.

Model and sources

Model and sources

  • Liquid pressure: p = ρgh; U-tube difference Δh = p / (ρ_water g); absolute pressure = atmospheric pressure + p.
  • Ship lock: flow through the valve Q = Cd·a·√(2gΔ); chamber area × rate of level change = Q.
  • Buoyancy: F_b = F_up − F_down = G − F_reading = ρ g V_displaced.
  • Sinking and floating: when submerged compare F_b with G, that is, the average density with the liquid’s density; when floating F_b = G.
  • Ship: floating means ρ g S d = G, so the draft is d = m / (ρ S).

g is the textbook 9.8 N/kg and atmospheric pressure 1.013×10⁵ Pa. The densities of water, alcohol, sea water, aluminium and iron are the textbook’s rounded values (within 2 % of OpenStax’s 0.79, 1.025 and 7.8). Brine at 1.2×10³ kg/m³, the valve coefficient 0.6, the damping on the submarine and the lump, and the 7 cm load line are teaching assumptions for comparison only. Liquid colours are only for visibility.

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