Physic Labs

Fluid mechanics

The Venturi tube and airflow past an obstacle

Visually verify the inverse relationship between velocity and pressure (Bernoulli), and find the Reynolds number threshold at which airflow starts shedding alternating vortices (the Kármán vortex street). Measure flow speed and cross-sectional area in the tube, then check Q=AvQ = Av and the Bernoulli relation where losses are small.

Undergraduate

Equipment

  • Virtual Venturi tube with adjustable area ratio
  • Virtual wind tunnel (Lattice Boltzmann D2Q9 simulation)
  • Three obstacle shapes: cylinder, flat plate, tilted airfoil

Procedure

  1. Measure pressure along the Venturi tube

    Gradually narrow the d₂/d₁ ratio and watch the fluid level in the throat's pressure gauge drop. If narrowed too much, pressure reaches zero and a cavitation warning appears. Compare the observed quantities with p+ρv2/2+ρgh=constantp + ρv²/2 + ρgh = constant.

  2. Find the threshold for the Kármán vortex street

    With the cylinder obstacle, gradually increase the Reynolds number Re from low values. Watch the flow transition from smooth to alternating vortex shedding around Re ≈ 47. Switch to the tilted airfoil and notice the flow deflecting downward behind it. Compare the observed quantities with Re=ρvD/μRe = ρvD/μ.

  3. Compare Bernoulli and continuity

    In the Venturi tube, vary the area ratio and read pressure at the wide section and throat; observe speed rise as area falls. Check Q = Av and p + ρv²/2 + ρgh ≈ constant, noting model deviations and losses. Compare the displayed values with p+ρv2/2+ρgh=constantp + ρv²/2 + ρgh = constant.

Simulation

Experiment history

Fluid mechanics studies how liquids and gases move, from pipe flow to vortices behind an obstacle. Daniel Bernoulli related pressure, speed, and elevation through an energy balance for ideal flow, while continuity adds the condition that volume flow is conserved. When a viscous fluid passes an obstacle, inertia and friction can cause separation, recurring vortices, and a Kármán vortex street downstream. The Reynolds number Re = ρvD/μ compares the relative influence of inertia and viscosity, but transition thresholds depend on geometry and flow conditions rather than being universal constants. The Lattice Boltzmann method models flow by updating particle-like distributions on a grid, approximating the resulting fluid structures. The two simulations serve distinct purposes: the Venturi tube demonstrates pressure difference and speed, while the obstacle highlights separation, vortices, and limits of an ideal-flow account.

Related physicists

Daniel Bernoulli

Related library topics

The Bernoulli equationThe continuity equationTurbulent flow and the Kármán vortex street