01 / READ THE CHANGE
No slip at the wall
The computed velocity rises from zero at the surface to the local external-flow velocity. Layer thickness is greatly exaggerated in the scene for readability.
ZOOM INTO THE FLOW AT THE WALL.
Boundary Layer & Flow Separation
Explore a laminar boundary layer under a favourable or adverse pressure gradient. Move the probe and inspect the calculated velocity profile.
INTERACTIVE CALCULATED DIAGRAMB · LIVE
Diagram · drag background to pan
Drag the turquoise handles, or focus a handle and use arrow keys. The sliders provide the same controls.
Preparing the calculation…
A · no saved reference
02 / READ THE CHANGE
Pressure gradient changes the profile
A decelerating external flow has an adverse pressure gradient. The attached laminar similarity family approaches zero wall shear near its separation limit.
03 / READ THE CHANGE
Stop where the model stops
Below m ≈ −0.0904, this attached solution is unavailable. The page marks separation without fabricating a separated wake or a stall curve.
THE SAME MODEL, CONNECTED VIEWS
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B · solid turquoise A · dashed amber
Compare A and B
| Quantity | A · saved | B · live | B − A | Unit |
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A remains fixed until saved again. Export includes the model version, settings and plotted data.
Equations, assumptions & sources
Read the balance, then connect each symbol to the model. Open a symbol key for definitions and units. Long equations can be scrolled sideways.
01 · The Falkner–Skan similarity equation
Primes denote derivatives with respect to the similarity coordinate η.
Symbols & units
- Dimensionless stream-function similarity function.
- External-velocity power-law exponent and pressure-gradient parameter; m is not mass in this equation.
02 · No slip at the wall; match the outer flow
The first condition represents the wall; the second matches the undisturbed outer velocity.
Symbols & units
- Analytical far-field boundary condition. The numerical integration uses a finite similarity domain.
03 · Reconstruct the velocity profile
The same similarity solution produces the local velocity profile shown above.
Symbols & units
- Local streamwise velocity and outer-flow velocity, m/s.
- Along-wall and normal coordinates, m; kinematic viscosity, m²/s. η is dimensionless.
Steady two-dimensional incompressible laminar Falkner–Skan similarity flow with power-law external speed. Numerical shooting to η = 8, step 0.02. Surface display starts at x/L = 0.05 to avoid the leading-edge singularity. No turbulent closure, transition prediction, reattachment or post-stall flow. Reynolds numbers above 500000 are flagged as requiring transition consideration, not asserted to be turbulent.
NASA · boundary layer ↗Physical relations and teaching sources support the stated concepts. Generic coefficients are explicitly illustrative; they are not measured manufacturer data. Numerical verification is separate from experimental validation. Model version: applied-labs-v1.1.