Blasius Laminar Boundary Layer Thickness Calculator
Estimate the laminar boundary layer thickness on a flat plate: δ = 5.0 · x / √Rex.
Inputs
Drag the handle (or focus it and press ↑/↓) to reorder. Scientific notation such as 1.2e3 is accepted. Pick any unit; conversion is automatic.
Results
Enter values and press Calculate. Your answer will appear here.
Boundary layer growth along the plate
Thickness grows with the square root of distance. The dot is your input. If the dashed amber line appears, the plate reaches Re = 5×10⁵ there, beyond which the layer normally becomes turbulent.
What is being calculated
Common examples
| Case | Rex | δ |
|---|
Illustrative inputs, not manufacturer data.
Typical fluid properties (approximate)
| Fluid | ν (m²/s) | μ (Pa·s) |
|---|---|---|
| Air, 15 °C | 1.46×10⁻⁵ | 1.81×10⁻⁵ |
| Air, 20 °C | 1.51×10⁻⁵ | 1.82×10⁻⁵ |
| Water, 10 °C | 1.31×10⁻⁶ | 1.31×10⁻³ |
| Water, 20 °C | 1.00×10⁻⁶ | 1.00×10⁻³ |
Viscosity varies with temperature; use values for your actual conditions.
Unit conversions
| Quantity | Conversion |
|---|---|
| Kinematic viscosity | 1 cSt = 1 mm²/s = 10⁻⁶ m²/s · 1 St = 10⁻⁴ m²/s · 1 ft²/s = 0.092903 m²/s |
| Dynamic viscosity | 1 cP = 1 mPa·s = 10⁻³ Pa·s · 1 P = 0.1 Pa·s · 1 lb/(ft·s) = 1.48816 Pa·s |
| Speed | 1 m/s = 3.6 km/h = 2.23694 mph = 3.28084 ft/s |
| Length | 1 in = 0.0254 m · 1 ft = 0.3048 m · 1 mm = 1000 µm |
Formula
- δ: boundary layer thickness, where the velocity reaches 99 % of U (m)
- x: distance from the leading edge (m)
- Rex: local Reynolds number (dimensionless)
- U: free-stream velocity (m/s)
- ν = μ / ρ: kinematic viscosity (m²/s)
Example: air, U = 10 m/s, x = 0.5 m, ν = 1.5×10⁻⁵ m²/s. Rex = 10 × 0.5 ÷ 1.5×10⁻⁵ = 333,333, √Rex = 577.35, so δ = 5 × 0.5 ÷ 577.35 ≈ 4.33 mm.
The constant 5.0 is the usual rounded value; the exact Blasius solution gives about 4.91 for the 99 % thickness, which you can select in Advanced. Advanced mode also reports δ* = 1.7208·x/√Rex, θ = 0.664·x/√Rex, Cf = 0.664/√Rex and the average drag coefficient 1.328/√Rex. The result applies to a smooth flat plate with zero pressure gradient and laminar flow, normally for Rex below about 5×10⁵.
References
- Wikipedia, Blasius boundary layer: the solution and its constants
- NASA Glenn, Boundary Layer: overview of boundary layers
- Engineering ToolBox, Air viscosity: fluid property values
How to Use This Tool
- Pick a preset, or enter the distance x from the leading edge.
- Enter the free-stream velocity U and the kinematic viscosity ν with their units.
- In Advanced, use μ and ρ instead of ν, choose 4.91 or 5.0, or pick the thickness unit.
- Click Calculate.
- Read δ in the highlighted result, check the Reynolds number warning and the growth chart.
What This Tool Offers
- Basic and Advanced modes on one calculation engine
- Length, speed and viscosity unit conversion
- Reynolds number with a laminar-validity check
- Displacement and momentum thickness, skin friction and wall shear (Advanced)
- Growth chart and labelled flat-plate diagram
- Ready-made presets and a mobile-friendly layout
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| δ | Boundary layer thickness | m |
| x | Distance from leading edge | m |
| Re_x | Local Reynolds number |
What it means
The Blasius solution provides the laminar boundary layer thickness for a flat plate. The boundary layer thickness is defined as the distance from the wall where the velocity reaches 99% of the freestream. It grows as √x. This thickness is important for calculating displacement thickness and momentum thickness, which affect aerodynamic drag and pressure distribution. It is also used in heat transfer analysis. Understanding this relation is essential for boundary layer theory and for evaluating the effects of surface roughness and transition.
Worked example
Boundary Layer Thickness – Two Examples
Real‑World| Parameter | Value |
|---|---|
| x | 0.5 m |
| Re_x | 1×10⁵ |
| Parameter | Value |
|---|---|
| x | 1.0 m |
| Re_x | 3×10⁵ |
Common mistakes
- Blasius laminar boundary layer thickness: δ = 5.0 · x / √Re_x.
- δ: Boundary layer thickness (where u = 0.99 U∞).
- x: Distance from leading edge.
- Re_x: Local Reynolds number.
- Valid for laminar flat plate flow.
Applications
Blasius laminar boundary layer thickness, δ = 5.0·x/√(Re_x), gives the thickness of the laminar boundary layer on a flat plate. It is used to assess the region of the flow influenced by viscosity and to design laminar flow control systems. Engineers use it to position transition trips, to design suction slots, and to evaluate the potential for laminar flow. The thickness grows with the square root of distance, so laminar flow is more likely near the leading edge. By understanding boundary layer thickness, aerospace engineers can design surfaces to delay transition and reduce drag.
- Laminar flow control system design (suction, shaping)
- Transition prediction and surface roughness tolerance
- Boundary layer instrumentation placement
- Drag reduction studies for low‑drag configurations
- Educational application of boundary layer theory
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