Blasius Boundary Layer Calculator

📏 Flat Plate Boundary Layer

📝 Configuration

Key Equations:

$\delta = \dfrac{5x}{\sqrt{\text{Re}_x}}\;\;\text{(Blasius)}$

$C_f = \dfrac{0.664}{\sqrt{\text{Re}_x}}\;\;\text{(laminar)}$

$\delta = \dfrac{0.37x}{\text{Re}_x^{1/5}}\;\;\text{(turbulent)}$

📊 Results

Configure inputs and click Calculate BL.

ℹ️ About Blasius

The Blasius solution (1908) gives the exact laminar boundary layer on a flat plate. The velocity profile is self-similar with η = y√(U/νx). Transition to turbulence occurs at Re_x ≈ 5×10⁵.

📘 Calculation Methodology

Theory

$$\delta_{\text{lam}}=\frac{5x}{\sqrt{\text{Re}_x}},\;\delta^*=\frac{1.72x}{\sqrt{\text{Re}_x}},\;\theta=\frac{0.664x}{\sqrt{\text{Re}_x}}$$ $$C_{f,\text{lam}}=\frac{0.664}{\sqrt{\text{Re}_x}},\;\;C_{f,\text{turb}}=\frac{0.0592}{\text{Re}_x^{1/5}}$$ $$\text{Nu}_{\text{lam}}=0.332\,\text{Re}_x^{1/2}\text{Pr}^{1/3}$$ $$\text{Nu}_{\text{turb}}=0.0296\,\text{Re}_x^{4/5}\text{Pr}^{1/3}$$

Worked Example

Problem: Air, U=30 m/s, x=0.5 m
ρ=1.225, μ=1.789e-5

1. ν = 1.46×10⁻⁵, Re_x = 30×0.5/1.46e-5 = 1.03×10⁶
2. x_trans = 5e5×1.46e-5/30 = 0.243 m
3. δ_lam = 5×0.5/√1.03e6 = 2.46 mm
4. δ_turb = 0.37×0.5/(1.03e6)¹/⁵ = 11.6 mm
5. C_f,lam = 6.54×10⁻⁴, C_f,turb = 3.72×10⁻³

References

Blasius, H. Z. Math. Phys., 56:1, 1908.
Schlichting, H. Boundary-Layer Theory, Springer.
Incropera & DeWitt Fundamentals of Heat and Mass Transfer.
Gupta, S. C. Applied CFD — §7.4.

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📏 Blasius Boundary Layer Calculator — δ, δ*, θ