# Law of the wall

## Description

In fluid dynamics, the law of the wall states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the “wall”, or the boundary of the fluid region. It is only technically applicable to parts of the flow that are close to the wall (<20% of the height of the flow), though it is a good approximation for the entire velocity profile of natural streams. Number 0.41 at the formula is the dimensionless von Kármán constant.

Related formulas## Variables

u | Mean flow velocity at height y above the boundary. (dimensionless) |

u_τ | Friction velocity (depends on the shear stress at the boundary of the flow) (dimensionless) |

y | The distance to the wall (dimensionless) |

y_{0} | Roughness length w(here u appears to go to zero) (dimensionless) |