Fluid Statics & Bernoulli's Principle

What is Fluid Statics & Bernoulli's Principle?

A 250,000-ton oil tanker rides high in the harbor. A scuba diver feels different pressure at every depth. A hydraulic lift turns a foot tap into a multi-ton hoist. All three rely on a tiny set of rules for fluids at rest. Archimedes figured out the first in a bathtub: any immersed object feels a buoyant force equal to the weight of fluid it displaces. Less-dense objects float; denser ones sink while still feeling that upward push. Pascal added: pressure applied to an enclosed fluid transmits equally in all directions, so a small piston can lift a car balanced on a large one. The third rule is hydrostatic pressure: every meter of depth adds ρgh, which is why ears pop in the deep end. This lab lets you drop objects of different densities into different fluids and watch them float, sink, or settle.

Parameters explained

Fluid Density (ρ)(kg/m³)

Fluid Density sets ρ in both P = P₀ + ρgh and F_b = ρgV. Fresh water is about 1000 kg/m³, sea water is a little denser, and heavy lab fluids can be denser still. Raising this slider makes each meter of depth add more pressure, so the color gradient darkens more strongly toward the bottom. It also increases the buoyant force on the orange sphere because the same displaced volume weighs more. Use Fresh Water as the baseline, Sea Water to test a small density change, and Dense Fluid to see the largest combined pressure and buoyancy effect.

Total Depth (h)(m)

Total Depth sets the h value used for the pressure-at-depth readout. In an incompressible static fluid, gauge pressure grows linearly with depth: doubling h doubles the ρgh term when fluid density and surface pressure stay fixed. The tank also redraws taller or shorter, so students can connect the geometric depth they see with the numerical pressure value. Keep Fluid Density at 1000 kg/m³ and Surface Pressure at 101 kPa, then move only this slider to isolate the depth relationship. The Sea Water and Dense Fluid presets give quick deeper comparison cases.

Surface Pressure (P₀)(kPa)

Surface Pressure sets P₀, the pressure already acting on the top of the fluid before the weight of the fluid column is added. Normal atmospheric pressure is about 101 kPa, so the Fresh Water and Sea Water presets begin there. Increasing this slider adds the same extra pressure everywhere in the tank, which illustrates Pascal's principle: an applied pressure is transmitted through the fluid. It does not change the ρgh slope created by depth and density, but it raises the absolute pressure readout at every selected depth. Compare 101 kPa and 150 kPa while holding the other sliders steady.

Common misconceptions

• MisconceptionHeavy things sink, light things float.

  CorrectDensity wins, not weight. A 250,000-ton ship floats; a 50-gram steel marble sinks. What matters is the average density of the object compared to the fluid's density. Hollow objects effectively lower their average density by enclosing air, which is the trick steel ships use.

• MisconceptionA fully submerged object feels more buoyant force the deeper it goes.

  CorrectBuoyant force depends only on the volume of fluid displaced, not on depth. Once the object is fully submerged, F_b = ρ_fluid · g · V is the same at 1 m or 100 m down. What does change with depth is the surrounding pressure (P = P₀ + ρgh) — but that pressure squeezes the object equally from all sides and the net upward push (buoyancy) stays the same.

• MisconceptionIncreasing surface pressure only affects the top layer of the fluid.

  CorrectIn a static enclosed fluid, an added surface pressure is transmitted throughout the fluid. The pressure at depth is P = P₀ + ρgh, so raising P₀ by 20 kPa raises the pressure readout at every depth by 20 kPa. The depth term still depends on ρ and h, but the whole pressure profile shifts upward together.

• MisconceptionHeat and temperature mean the same thing in fluids.

  CorrectTemperature is the average kinetic energy per molecule (intensive); heat is energy transferred between systems (extensive). Two pools of water at the same temperature can hold very different total thermal energy depending on their volume. In the basic fluid statics here we treat density and pressure at fixed temperature, but if you heat a fluid, ρ drops and buoyancy changes — that's why hot air rises.

• MisconceptionPressure inside a hydraulic press is the same as the input force, just transmitted.

  CorrectPressure is force per area. Pascal's law says the pressure transmits through the fluid uniformly — but the force on a piston equals pressure times that piston's area. Push 1 N on a 1 cm² piston (P = 10,000 Pa) and the fluid pushes 100 N on a 100 cm² piston. You traded distance for force, not magic — the small piston has to move 100 times farther.

How teachers use this lab

1. Depth-linearity lab: keep Fluid Density at 1000 kg/m³ and Surface Pressure at 101 kPa, then have students record pressure at several Total Depth values. They should graph pressure vs. depth and identify the constant ρg slope.
2. Fresh vs. sea comparison: run Fresh Water and Sea Water back to back, then ask students to explain why the sea-water case gives slightly higher pressure and buoyant-force readings at similar depths.
3. Pascal's principle check: hold Fluid Density and Total Depth constant while raising Surface Pressure from 101 kPa to 150 kPa. Students should predict and verify that the pressure-at-depth readout increases by the same 49 kPa.
4. Dense-fluid case study: use the Dense Fluid preset, then have students separate which part of the larger pressure reading comes from density, which part comes from depth, and which part comes from surface pressure.
5. AP free-response warmup: ask students to write P = P₀ + ρgh and F_b = ρgV before touching the controls, then use the sliders as evidence for how each variable changes pressure or buoyant force.