Bernoulli’s principle

How it works

Water is almost incompressible, so the same volume must pass through every cross-section each second: the flow rate Q = A · v is the same everywhere, and the water speeds up in a constriction. Bernoulli’s equation expresses conservation of energy in steady flow: the sum of the pressure and the kinetic energy per unit volume ½ρv² stays constant, so where the speed is higher the pressure is lower. In the default Venturi tube (8 L/s, 50 mm ends, 22 mm throat) the water moves at 1.02 m/s at the ends and 5.26 m/s in the throat, where the gauge pressure falls from 100 to 86.7 kPa.

Q = A · vp + ½ρv² = const.A = πr²

Try it yourself

1. Choose “Venturi tube” and keep the measurement probe in the middle (x = 1.0 m). The speed is 5.26 m/s and the gauge pressure 86.7 kPa; at the ends it is 1.02 m/s and 100 kPa.
2. Click “Half the radius” (50 → 25 mm). Predict first: the area is a quarter, so the speed is four times higher – 4.07 m/s, not twice – and the gauge pressure falls to 92.2 kPa.
3. Click “Double the flow rate” and switch between 4 and 8 L/s. The speeds double, but the pressure drop in the throat grows four times because it depends on v².
4. Choose “Expansion”. At the widest point (70 mm) the water slows to 0.52 m/s and the gauge pressure rises slightly, to about 100.4 kPa.

Model limitations

The model is quasi-one-dimensional: an ideal incompressible liquid (ρ = 1000 kg/m³) in a horizontal pipe without viscosity, friction or turbulence, with the same speed across each cross-section. Real pipes lose energy, especially after an expansion, so the pressure does not fully recover. Cross-section sizes are enlarged in the drawing.

Related experiments

• Levers and torque
• Ideal gas
• Projectile motion