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:
\(C_f = \frac{0.664}{(R_e)^{-1/2}}\)