The turbulent boundary layer equation describes the behavior of a turbulent boundary layer, which forms when a fluid flows over a solid surface. In this region, the fluid velocity changes rapidly in the direction perpendicular to the surface due to the interaction between the fluid and the solid boundary. The equation for the turbulent boundary layer thickness ($\delta$) using the Prandtl mixing length model is given by:

Where:

• $\delta$ is the thickness of the turbulent boundary layer (m),
• uτ​ is the friction velocity, which characterizes the shear stress at the wall (m/s),
• $\kappa$ is the von Kármán constant, typically around 0.41.