Air 20°C: ν ≈ 1.5×10⁻⁵ m²/s, ρ ≈ 1.2 kg/m³. Water 20°C: ν ≈ 1.0×10⁻⁶ m²/s, ρ ≈ 998 kg/m³. Move the sliders to update the particle flow and the δ(x) envelope in real time.
Particles enter from the left at U and slow near the wall (no-slip u=0) / blue envelope = δ_99(x) growing as √x / white vertical line = evaluation position x / orange dashed = δ*, purple dashed = θ / profiles at stations = Blasius u(y)/U
For a zero-pressure-gradient laminar boundary layer on a flat plate, the Blasius similarity solution gives the following representative values.
Local Reynolds number. U is the freestream velocity, x is the distance from the leading edge, ν is the kinematic viscosity:
$$\mathrm{Re}_x = \frac{U\,x}{\nu}$$99% thickness, displacement thickness, momentum thickness:
$$\delta_{99} \approx \frac{5.0\,x}{\sqrt{\mathrm{Re}_x}},\quad \delta^{*} \approx \frac{1.721\,x}{\sqrt{\mathrm{Re}_x}},\quad \theta \approx \frac{0.664\,x}{\sqrt{\mathrm{Re}_x}}$$Local skin friction and wall shear stress. ρ is the fluid density:
$$C_f = \frac{0.664}{\sqrt{\mathrm{Re}_x}},\qquad \tau_w = \tfrac{1}{2}\,C_f\,\rho\,U^2$$Shape factor H = δ*/θ ≈ 2.59. For Re_x ≳ 5×10⁵ the layer transitions to turbulence and the Blasius formulas no longer apply.