Methodology:
R_e =\frac{\rho U L_c}{\mu}
C_f = f(R_e)
\tau_w = \frac{C_f\rho U^2 }{2}
u_{\tau} =\sqrt{\frac{\tau_w}{\rho}}
\Delta y =\frac{y^+ \mu}{u_{\tau} \rho}
Correlations of wall friction coefficients C_f = f(R_e) :
Schlichting:
C_f = \frac{1}{(2log(R_e)-0.65)^{-2.3}}
ITTC 1957:
C_f = \frac{0.075}{(log(R_e)-2)^{-2}}
Prandtl’s one-seventh-power law:
C_f = \frac{0.027}{(R_e)^{-1/7}}
Blasius solution:
C_f = \frac{0.664}{(R_e)^{-1/2}}