Turbulent velocity profile
 

Hello, i'm trying to reconstract in matlab a turbulent velocity profile with the law of the wall, log law and power law.

first of all i calculate Reynolds number, then i use darcy weissbach law for calculate friction factor (f) and so wall shear stress (t_wall).
Now i calculated friction velocity, u+ and y+.

u+=y+ for 0<y+<5

u+ = 1/k *ln(y+) + 1.33 for 30<y+<500

u/V_max = (y/R)^(1/5) for outer region.

am i doing something wrong?

How can i attach those curves?

thanks