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Skin Friction and Stanton Number

Laminar and turbulent skin friction coefficient (\(c_f\)) and Stanton number (\(C_h\)) estimates for compressible boundary layers.

The skin-friction coefficient is defined as:

\[ c_f \equiv \frac{\tau_w}{\tfrac{1}{2}\rho_e U_e^2}, \]

with \(\tau_w\) being the wall shear stress,

\[ \tau_w = \mu_w\left.\frac{\partial u}{\partial y}\right|_w \]

The Stanton number is defined as:

\[ C_h \equiv \frac{q_w}{\rho_e U_e c_p\,(T_r - T_w)}, \]

with \(q_w\) being the wall heat flux, commonly written as

\[ q_w = -k\left.\frac{\partial T}{\partial y}\right|_w. \]

Mode and Method Theory Map

Laminar Estimates

Method Theory page
blasius Blasius Laminar Method
eckert_reference Eckert Reference-Temperature Method
similarity Similarity Method

Turbulent Estimates

Method Theory page
van_driest_ii van Driest II Method
spalding_chi Spalding-Chi (1964) Method
sommer_short Sommer-Short Method
white_christoph White-Christoph Method