Streamlines and Bernoulli simulation

Streamlines show the path fluid takes. Around an obstacle they squeeze together where the flow speeds up, and Bernoulli’s principle says that is also where the pressure drops.

Interactive, free and runs in your browser. Part of the Fluid Dynamics simulations.

What you will see

Ideal (inviscid, incompressible) flow passes a cylinder. Streamlines bend symmetrically round it, coloured by speed: slow at the stagnation points front and back, fastest over the shoulders. The background shows the pressure coefficient, lowest where the flow is fastest.

Try this

  1. Find the two stagnation points where the flow stops.
  2. Compare the spacing of streamlines at the shoulders with far upstream.
  3. Notice the pattern is the same front and back: in ideal flow there is no drag.

Common misconception

Ideal flow predicts zero drag on the cylinder (d’Alembert’s paradox). Real fluids have viscosity, which creates a wake and drag; that is what the vortex shedding view shows.

Exam-style question

Water (ρ = 1000 kg/m³) speeds up from 2 m/s to 4 m/s along a streamline. What is the pressure drop?

Bernoulli: Δp = ½ρ(v₂² − v₁²) = ½ × 1000 × (16 − 4) = 6000 Pa.

Key equations

  • p + ½ρv² = constant
  • C_p = 1 − (v / U)²

Curriculum

Enrichment: fluid mechanics.

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