Definition The skin friction coefficient is defined as: c_{f} = \frac{\tau_w}{\frac{1}{2}\rho_\infty v_\infty^2} where: • c_{f} is the skin friction coefficient. • {\rho_\infty} is the density of the free stream (far from the body's surface). • {v_\infty} is the free stream speed, which is the velocity magnitude of the fluid in the free stream. • {\tau_w} is the skin shear stress on the surface. • {\frac{1}{2}\rho_\infty v_\infty^2\equiv q_\infty} is the
dynamic pressure of the free stream. The skin friction coefficient is a dimensionless skin shear stress which is nondimensionalized by the dynamic pressure of the free stream. The skin friction coefficient is defined at any point of a surface that is subjected to the free stream. It will vary at different positions. A fundamental fact in aerodynamics states that ({\tau_w})_{laminar} . This immediately implies that laminar skin friction drag is smaller than turbulent skin friction drag, for the same inflow. The skin friction coefficient is a strong function of the Reynolds number ; as increases, decreases. ===
Laminar flow===
Blasius solution c_{f} = \frac{0.664}{\sqrt{\mathrm{Re}_x}} \ where: • Re_x = \frac{\rho vx}{\mu}, which is the
Reynolds number. • is the
density of the fluid (
SI units: kg/m3) • is the
flow speed (m/s) • is the
dynamic viscosity of the
fluid (Pa·s or N·s/m2 or kg/(m·s)) • is a
characteristic length (m), in this case the distance from the reference point at which a
boundary layer starts to form. The above relation is derived from the
Blasius boundary layer, which assumes constant pressure throughout the boundary layer and a thin boundary layer. The above relation shows that the skin friction coefficient decreases as the
Reynolds number (Re_x ) increases.
Transitional flow The Computational Preston Tube Method (CPM) CPM, suggested by Nitsche, estimates the skin shear stress of transitional boundary layers by fitting the equation below to a velocity profile of a transitional boundary layer. K_1(Karman constant), and {\tau}_w(skin shear stress) are determined numerically during the fitting process. :u^{+} = \int_0^{Y^+}\frac{2(1+K_3y^+)}{1+[1+4(K_1 y^+)^2(1+K_3y^+)(1-exp(-y^+\sqrt{1+K_3y^+}/K_2))^2]^{0.5}}\,dy^+ where: • u^{+} = \frac{u}{u_{\tau}},~u_{\tau}=\sqrt{\frac{{\tau}_w}{\rho}},~y^+=\frac{u_{\tau}y}{\nu} • y is a distance from the wall. • u is a speed of a flow at a given y. • K_1 is the Karman constant, which is lower than 0.41, the value for turbulent boundary layers, in transitional boundary layers. • K_2 is the Van Driest constant, which is set to 26 in both transitional and turbulent boundary layers. • K_3 is a pressure parameter, which is equal to \frac{\nu}{\rho}{u_{\tau}}^3\frac{dp}{dx} when p is a pressure and x is the coordinate along a surface where a boundary layer forms. ===
Turbulent flow===
Prandtl's one-seventh-power law c_{f} = \frac{0.0576}{Re_x^{1/5}}\ The above equation, which is derived from Prandtl's one-seventh-power law, provides a reasonable approximation of the
drag coefficient of low-Reynolds-number turbulent boundary layers. Compared to laminar flows, the skin friction coefficient of turbulent flows lowers more slowly as the Reynolds number increases.
Skin friction drag A total skin friction drag force can be calculated by integrating skin shear stress on the surface of a body. F = \int\limits_{\text{surface}}c_f \frac{\rho v^{2}}{2}dA == Relationship between skin friction and heat transfer ==