Formula & Calculator
Blasius Laminar Boundary Layer Thickness
Thickness of a laminar boundary layer growing over a flat plate at distance x from the leading edge.
Interpretation
Blasius laminar boundary layer thickness: δ = 5.0·x / √(Re_x), where Re_x is local Reynolds number. It gives the thickness of the laminar boundary layer. Example: x=1 m, Re_x=1e6 → δ = 5×1/1000 = 0.005 m = 5 mm.
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
Frequently Asked Questions
It estimates the thickness of a laminar boundary layer growing over a flat plate at a distance x from the leading edge, using the Blasius solution.
δ = boundary layer thickness (m) – defined as the height where velocity reaches 99% of freestream
x = distance from leading edge (m)
Rex = Reynolds number based on x
It determines the region of viscous effects, influences heat transfer, and affects the effective body shape for aerodynamics.
- Confusing the 99% velocity thickness δ with displacement thickness δ* or momentum thickness θ, which use different coefficients.
- Applying the laminar formula after transition.
- Using the wrong reference length.
At x = 1 m, Rex = 6.67×10⁵ (from previous example). δ = 5.0 × 1 / √(6.67×10⁵) = 5.0 / 816.5 ≈ 0.00612 m = 6.12 mm.
δ ∝ √x, so the boundary layer grows parabolically with distance from the leading edge.
δ* = ∫(1 − u/U)dy, and for the Blasius solution, δ* ≈ 1.72·x/√Rex. It represents the outward displacement of streamlines.
θ = ∫(u/U)(1 − u/U)dy, and for Blasius, θ ≈ 0.664·x/√Rex. It is used to compute momentum deficit.
A favourable pressure gradient (accelerating flow) reduces δ, while an adverse pressure gradient increases δ and may cause separation.
It determines the shear stress distribution and hence the skin friction drag. A thicker boundary layer often means higher drag.