Boundary Layer Thickness Calculator (Blasius)

Boundary layer thickness (delta) is the distance from a solid surface, measured perpendicular to the flow, at which the fluid velocity reaches 99% of the free-stream velocity U. Inside this thin layer, viscous effects slow the fluid down from U at the edge to zero at the wall (the no-slip condition).

The Blasius solution is an exact solution to the laminar boundary layer equations for steady, incompressible flow over a flat plate with zero pressure gradient, found by Paul Richard Heinrich Blasius in 1908. It gives the 99% boundary layer thickness as delta = 5.0x / sqrt(Re_x), where x is distance from the leading edge and Re_x is the local Reynolds number.

The value 5.0 comes from numerically solving the Blasius similarity equation and finding where the velocity profile reaches 99% of the free-stream value. Some references use 4.91 or 5.2 depending on the exact percentage chosen (99% versus 99.9%) or rounding convention, but 5.0 is the standard textbook value for the 99% thickness.

The Blasius solution assumes laminar flow, which holds until the local Reynolds number Re_x reaches roughly 5x10^5 (the classic transition value for a flat plate). Beyond that point the boundary layer becomes turbulent, and a turbulent correlation such as delta = 0.37x / Re_x^0.2 should be used instead.

Re_x = rho U x / mu, where rho is fluid density, U is free-stream velocity, x is distance from the leading edge, and mu is dynamic viscosity. It is called 'local' because it changes with position x along the plate, unlike a single characteristic-length Reynolds number for an entire object.

C_f,x = 0.664 / sqrt(Re_x) is the local skin friction coefficient from the Blasius solution, a dimensionless measure of the wall shear stress relative to the flow's dynamic pressure at that point on the plate. It decreases with distance x because the boundary layer thickens and the velocity gradient at the wall becomes gentler.

Wall shear stress tau_w = C_f,x times 0.5 rho U squared, combining the local skin friction coefficient with the fluid's dynamic pressure. It has units of pascals (Pa) and represents the drag force per unit area the fluid exerts on the plate surface at that location.

This calculator takes fluid density (rho) and dynamic viscosity (mu) as separate inputs and computes everything from those, matching how most textbooks and material property tables present the data. Kinematic viscosity, if you have it instead, is nu = mu / rho, so multiply nu by rho to recover mu before entering it.

The Blasius similarity solution shows that viscous diffusion spreads perpendicular to the wall proportional to sqrt(x/U), while the fluid has only had time x/U to diffuse outward from the leading edge. This square-root dependence means the boundary layer thickens quickly near the leading edge and then more slowly further downstream.

For air at 10 m/s flowing 0.3 m from the leading edge of a flat plate, the Blasius boundary layer thickness is only about 3.3 mm, illustrating how thin laminar boundary layers typically are at everyday lab-scale speeds and distances, even though they have an outsized effect on drag and heat transfer.

No, the Blasius solution is specifically derived for a flat plate with zero pressure gradient. Curved surfaces introduce a pressure gradient that changes the boundary layer growth rate, and internal pipe flow has a different geometry entirely (the boundary layers from opposite walls eventually merge), so neither case can use this formula directly.