# Is the viscous sublayer size universal?

We know the non-dimensionalized distance of the viscous sub-layer is 5 wall units for a turbulent boundary layer. It is common to see this in Fluid Mechanics books but seems somewhat arbitrary.

I want to know if this true for all conditions or does it depend on the Reynolds number (high viscosity, high speed, etc).

I am not sure if you can derive the value $y^+=5$ without experimental evidence. However, it is common to, in plus units, write the expression for the viscous sublayer as
$$u^+=y^+$$
$$u=\frac{du}{dy}y,$$ which, close enough to the boundary, is always true as a linearization. Of course this close enough highly depends on the viscosity and velocity, but that is exactly the reason to write it in non-dimensional for. The definition of this close enough is actually the thickness of the viscous sublayer (and called viscous because that is the dominant force, leaving it linear).