[enr_venkat]

Hello,

I'm trying to calculate Y+ analytically based on the following procedure:

1. Calculate Reynolds number [velocity refers to free stream velocity]
2. Need to calculate friction velocity based on wall shear stress
3. But wall shear stress needs to be calculated based on skin friction coefficient, density and velocity of the fluid [What velocity does it refer to ?]
4. Skin friction coefficient could be calculated based on certain empirical relations that are dependent on Reynolds number [preferably schlichting relation]
5. Based on skin friction coefficient and the wall shear stress,friction velocity is calculated
6. Based on friction velocity, first nodal distance from the wall is calculated.

The question is that how do I calculate wall shear stress if I don't know what velocity does it refer to. [ideally wall shear depends on friction velocity. So in order to know the friction velocity, we need to know the wall shear stress]. If the flow is turbulent, does this relation hold good,
Tau = Mu * du/dy. Again should I consider free stream velocity in place of du/dy ? Free stream velocity is the only value that is known prior calculating Y+. How can we consider free stream velocity if we think of near wall bounded flow ? Sounds contradictory to me. Please correct me if i'm wrong. Appreciate every expert's suggestion on this discussion