Please see the book "Boundary Layer Theory" by Schlichting.

This is a classical problem of wall-bounded parallel flow. Let D be the pipe diameter, Re the Reynolds Number, nu the kinematic viscosity, Ro the fluid density and y is the distance to the wall. In the logarithmic zone, the turbulent shear stress Ro*u*2 is constant where u* is the friction velocity. We should have:

Ro*u*2*Pi*D*dx=dp*pi*D2/4 so that we have:

(dp/dx)=4*Ro*u*2/D

So if we may calculate the pressure loss (dp/dx) using for example Blasius Formula for smooth pipe : (dp/dx)=Lamda*Ro*V2/2D with Lamda=0.316/Re0.25 (or any other head loss formula for rough pipes) we will thus be in a position to calculate the friction velocity u*. Let's define the Reynolds number y+(adimensional distance to the wall) y+=u*y/nu The thickness for internal viscous sublayer (y) is so that y+=11