What is law of wall?

The law of wall, also known as the law of the wall, is a fundamental concept in fluid dynamics that describes how the velocity of fluid near a surface changes as the distance from the surface increases. It is essential for predicting and interpreting the behavior of fluids in a wide range of settings, including aerodynamics, oceanography, and meteorology.

The law of wall states that the velocity of fluid near a surface is proportional to the logarithm of the distance from the surface, and this relationship is valid in the viscous sublayer of fluid near the surface. The viscous sublayer is a thin layer of fluid where the shear stresses that arise due to the viscosity of the fluid are significant enough to affect the velocity profile.

The law of wall is based on the assumption of a fully developed turbulent flow, where there are no changes in velocity over the direction of flow and it is independent of the inlet conditions. It is derived based on the balance between the viscous and inertial forces in the fluid, and it provides a useful relationship for estimating the drag force on objects moving through fluids.

The law of wall has important practical applications in engineering and science, as it is used to model fluid flow in various contexts, including the design of ships and aircraft, the distribution of pollutants in the atmosphere, and the prediction of thermal mixing in industrial processes.