Skin-friction coefficient#

$$C_f \stackrel{\text{def}}{=} \frac{\tau}{\rho U^{2}} \sim \frac{\text{wall shear stress}}{\text{dynamic pressure}}$$

Measures wall shear stress normalized by dynamic pressure. It indicates the frictional part of momentum loss along a surface.

Name	Symbol	SI units	Dimension
shear stress	$\tau$	$\mathrm{Pa}$	$\text L^{-1}\,\text M\,\text T^{-2}$
mass density	$\rho$	$\mathrm{kg}\,\mathrm{m}^{-3}$	$\text L^{-3}\,\text M$
velocity	$U$	$\mathrm{m}\,\mathrm{s}^{-1}$	$\text L\,\text T^{-1}$

Wall bounded flow

Range	Regime	Description
0 – 0.001	low friction	Wall shear is small compared with the dynamic pressure scale, as in high Reynolds number streamlined flows.
0.001 – 0.01	moderate friction	Wall shear is a measurable part of the momentum balance.
0.01 – ∞	high friction	Wall shear is large relative to dynamic pressure, often indicating strong viscous effects or roughness.

Name	Symbol	SI units	Dimension
shear stress	\(\tau\)	\(\mathrm{Pa}\)	\(\text L^{-1}\,\text M\,\text T^{-2}\)
mass density	\(\rho\)	\(\mathrm{kg}\,\mathrm{m}^{-3}\)	\(\text L^{-3}\,\text M\)
velocity	\(U\)	\(\mathrm{m}\,\mathrm{s}^{-1}\)	\(\text L\,\text T^{-1}\)