Mechanical & Aerospace
Bernoulli / Venturi Lab
Two conservation laws explain the venturi. CONTINUITY (A₁v₁ = A₂v₂) says that when the tube narrows the fluid must accelerate — you can watch the particles bunch up and race through the throat. BERNOULLI (p + ½ρv² = const along a streamline) then says that faster fluid is at LOWER pressure, so the pressure trace dips exactly where the flow is quickest, by Δp = ½ρ(v₂² − v₁²). Drag the inlet velocity, the throat-to-inlet area ratio and the fluid density to see how hard the throat sucks. Run it backwards and a measured pressure drop gives the flow rate — Q = A₂·√(2Δp / (ρ(1 − (A₂/A₁)²))) — which is exactly how a venturi flow meter works, and the same low-pressure-where-it's-fast principle that generates lift over a wing.
2.00 m/s
Inlet v₁
5.00 m/s
Throat v₂
10.50 kPa
Pressure drop Δp
20.00 L/s
Flow rate Q
The method, with your numbers
Continuity + Bernoulli
- 1
Volumetric flow rate
Q = A₁·v₁
Q = 0.01·2 = 0.02 m³/s (20 L/s)
Incompressible flow: the volume passing any cross-section per second is the same everywhere in the tube.
- 2
Continuity — speed through the throat
A₁·v₁ = A₂·v₂ → v₂ = v₁·(A₁/A₂)
v₂ = 2·(0.01/0.004) = 5 m/s
The same Q must squeeze through a smaller area, so the fluid speeds up — watch the particles bunch and accelerate at the throat.
- 3
Bernoulli — pressure drop at the throat
p₁ + ½ρv₁² = p₂ + ½ρv₂² → Δp = ½ρ(v₂² − v₁²)
Δp = ½·1000·(5² − 2²) = 10500 Pa = 10.5 kPa
Faster fluid sits at LOWER pressure — the trace above dips exactly where the particles speed up. Same effect that lifts a wing.
- 4
Invert it — the venturi meter
Q = A₂·√( 2Δp / (ρ·(1 − (A₂/A₁)²)) )
Q = 0.004·√(2·10500 / (1000·(1 − 0.16))) = 0.02 m³/s
Same Q as step 1 — a real venturi meter runs this backwards: measure Δp with two pressure taps and read off the flow.
Drag any control above — every number here recalculates. Want this method for any problem? Step Sheets →
Continuity (A₁v₁ = A₂v₂) forces the fluid to speed up through the narrow throat — watch the particles bunch and accelerate. Bernoulli then says the faster fluid is at LOWER pressure (the trace dips), so Δp = ½ρ(v₂² − v₁²). It's why a venturi meter reads flow from a pressure difference, and the same effect that lifts a wing.
How to use this simulation
Two conservation laws explain the venturi. CONTINUITY (A₁v₁ = A₂v₂) says that when the tube narrows the fluid must accelerate — you can watch the particles bunch up and race through the throat. BERNOULLI (p + ½ρv² = const along a streamline) then says that faster fluid is at LOWER pressure, so the pressure trace dips exactly where the flow is quickest, by Δp = ½ρ(v₂² − v₁²). Drag the inlet velocity, the throat-to-inlet area ratio and the fluid density to see how hard the throat sucks. Run it backwards and a measured pressure drop gives the flow rate — Q = A₂·√(2Δp / (ρ(1 − (A₂/A₁)²))) — which is exactly how a venturi flow meter works, and the same low-pressure-where-it's-fast principle that generates lift over a wing.
Everything runs in your browser — no sign-up, no download. Change a value and the result updates instantly, so you can build a feel for how each input shapes the outcome. It pairs with Crameleon's practice exams and step sheets when you want to go from intuition to working the problems.