Generalized Inner Region Velocity Distribution Equation

Abstract

The inner layer of a turbulent boundary layer consists of a linear layer in which the velocity distribution is linear, the log-law region having a logarithmic velocity distribution and a buffer layer lying in between them. Separate equations are available for the linear layer and the log-law region. The available inner region equations pertain to flow over smooth boundary and they are explicit (containing involved expressions) or implicit. No equation is available that includes the effect of roughness. Presented herein is a generalized equation for velocity distribution in the inner law region of a turbulent boundary layer. The equation includes linear and logarithmic velocity distributions and it is valid for hydraulically smooth and rough boundaries and the transition range in between.