Fluid flow – continuity, Bernoulli's principle and Torricelli's law
PhysicsForces & DynamicsAges 15–16
Loading…
Sign in to playA pipe with three sections whose cross-sections and height you can change: tracer particles show that the flow rate Q = Av stays constant, while three pressure gauges and a bar chart show that p + ½ρv² + ρgh is the same in every section (a Venturi meter). The second screen is a practical: a water tank with a small hole in its side; change the water depth H and the hole height, measure the range of the jet and test v = √(2gH) with a results table and a graph of v² against H.
Lesson: Fluid dynamics: the continuity equation, Bernoulli's equation, the Venturi meter and Torricelli's law
What it shows
In an ideal fluid that is incompressible and has no viscosity, the volume flow rate Q = Av is the same through every cross-section, so the fluid speeds up where the pipe narrows. Bernoulli's equation, p + ½ρv² + ρgh = constant, is conservation of energy per unit volume: where the speed or the height increases, the pressure falls. A Venturi meter uses that pressure drop to measure Q. Torricelli's law follows from the same equation: water leaves a small hole a depth H below the surface at v = √(2gH), like a body that has fallen through H.
How to use
On the Pipe flow (Venturi) screen, change Flow rate Q, the areas A₁, A₂ and A₃, Height h₃, Gauge pressure p₁ and Density ρ, and watch the gauges, the bars and the table. On the Draining tank (Torricelli) screen, set Water depth above hole H and Hole height y, press Record result for several depths, and read g from the graph of v² against H. Untick Keep water level constant to let the tank drain.
Parameters you can change
- Screen Pipe flow (Venturi), Draining tank (Torricelli)
- Flow rate Q 1–20 L/s
- Area of section 1 A₁ 10–100 cm²
- Area of the throat A₂ 5–100 cm²
- Area of section 3 A₃ 10–100 cm²
- Height of section 3 above section 1 h₃ 0–3 m
- Gauge pressure in section 1 p₁ 0–200 kPa
- Density of the liquid ρ 700–1300 kg/m³
- Water depth above the hole H 0.05–1 m
- Height of the hole above the floor y 0.1–1 m
- Hole diameter d 2–10 mm
- Keep the water level constant (topped up)
Questions to explore
- Why does the water move faster where the pipe narrows, and what happens to the pressure there?
- If the last section is raised but keeps the same area, how does the pressure in it change?
- Why does the jet speed not depend on the hole size, while the time to empty the tank does?
