Universal velocity distribution for turbulent flow in a pipe

9 Universal velocity distribution for turbulent flow in a pipe 

Consider a fully developed turbulent flow through a pipe of circular cross section. A turbulent boundary layer will exist with a thin viscous sublayer immediately adjacent to the wall, beyond which is the buffer or generation layer and finally the fully turbulent outer part of the boundary layer. 

In the viscous sublayer, the magnitude of the time-averaged value of the shear stress f is given by Newton s law of viscosity which can be written in this case as 

The term rjp in equation 2.53 is a constant and has the dimensions of velocity squared. Thus a quantity can be defined by 

A dimensionless velocity and dimensionless distance y+ from the wall may be defined by 

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