Using the pressure probes
Drag the coloured tip of A above the airfoil and B below it. Compare pressure and speed. Turn the wing with the round handle, or change the wind speed. Capture a reading, change one variable, then capture again.
Smoke and dye tests
Turn on Smoke test, choose a colour and jet width, then press and hold anywhere in the fluid. Drag to move the source. Release to follow the detached packet, or pause to inspect it. The pipe bench uses passive dye in water. Handles still move the apparatus.
The Hold to release button uses the last nozzle position. On the stage, arrows position the nozzle and holding S releases colour. Escape stops injection. Clear smoke removes only the colour. Smoke mode solves time-dependent viscous flow. Separate tracers follow its local velocity; the Particle trails button reveals their recent paths. Vorticity develops at solid boundaries and can roll into a shedding wake. Choose “Airfoil wakes and vortex shedding” for a ready example. Colour and flow history are transient; saved readings retain the model used. Leaving smoke mode clears its flow and returns to the ideal investigation.
Viscous wake model
The wind tunnel solves a two-dimensional viscous flow; the water view solves a planar channel using the circular pipe’s equivalent inlet speed. Both probes sample the same evolving velocity and pressure as the tracers. Bernoulli’s steady ideal-flow relation does not apply across these viscous wakes. The Reynolds number shown on the bench describes this resolved model. Effective viscosity is scaled with inlet speed and narrow gaps to keep the flow numerically resolved; it is not the molecular viscosity of air or water. These are laminar wake investigations, not predictions of full-scale turbulent stall or three-dimensional wingtip vortices.
No-slip walls create shear and vorticity. Pressure comes from the numerical flow field, not from the smoke colour. The airfoil plot samples just outside the discretised surface; the pipe plot averages across the planar gap. The grid approximates solid boundaries to about one cell. Tracer trails are recent position histories, not extra material left behind; opacity and soft edges are illustrative. Adaptive slow motion preserves the physical clock and the fixed fluid timestep.
Ideal-flow views
Streamlines show the local flow direction. Tracers move through that field at a slowed pace. Faster flow has lower static pressure in the ideal wind tunnel. The pressure forces over the entire surface produce lift. Fluid parcels above and below the wing do not need to meet at the trailing edge.
p + ½ρv² = constant · Q = Au
What the probes measure
The coloured ring is the sampling point. Gauge pressure is relative to 101,325 Pa; absolute pressure includes this reference. Air probes sample the local field. In ideal mode, pipe probes show section-average pressure and axial speed. In smoke/dye mode, both benches sample local time-dependent flow. A tip in a solid or outside the pipe has no reading. Resolution: 0.1 Pa and 0.01 m/s.
Ideal airfoil model and full rotation
Steady, two-dimensional, incompressible, inviscid Joukowski flow with Kutta circulation. Lift is per metre of span. Shape changes alter the same flow solution used by the probes and pressure plot. The plotted surface coefficient is Cₚ = (p − p∞)/(½ρU²).
The wing rotates freely through 360°. Beyond ±15° the display is an ideal mathematical continuation; real separation, stall, wakes and drag are not predicted. ±15° is a teaching warning, not a computed stall angle. This model cannot establish performance at reversed or broadside incidence. The wind tunnel is an unbounded flow view, not a confining duct.
Ideal pipe model and its limits
A horizontal circular pipe with imposed volume flow, smooth diameter changes and on-axis spheroidal inserts. The open area is π(R² − r²). Tracer paths depict annular streamtubes; their axial motion follows section-average speed. This is a quasi-one-dimensional teaching model, not a resolved boundary layer or turbulent wake.
Ideal flow recovers its pressure after a constriction. With losses enabled, Darcy wall friction reduces total pressure; each insert adds Kρu²/2 using its throat speed. K is an illustrative adjustable coefficient. Water density is 1,000 kg/m³. A computed absolute pressure below 2,300 Pa is outside the single-phase model and produces no probe reading. Large gradients are only qualitative.
Saving and playback
Setup and notebook recover locally when storage is available. Switching benches retains their setups. Reset restores the active prepared investigation and tracer clock; the notebook stays. Save experiment creates a reopenable JSON. CSV keeps each sample's settings. Tracer time is physical model time with explicit display slowdown. Pausing stops tracers; editing a steady-flow apparatus updates its readings immediately. Ideal mode has no settling transient. Smoke mode retains its evolving wake through live shape edits; affected fluid adjusts over time.
Physics references
NASA Glenn: conformal mapping
NASA Glenn: Bernoulli and Newton
NASA Glenn: boundary layers and separation
Latt & Chopard: regularised lattice Boltzmann flow
A-level enrichment; qualitative exploration is also suitable for GCSE. For hydrostatic pressure and buoyancy, visit the Pressure, Density & Upthrust Lab.
