# Skin friction coefficient

(Difference between revisions)
 Revision as of 17:46, 7 April 2008 (view source)← Older edit Revision as of 14:45, 25 February 2011 (view source)Peter (Talk | contribs) Newer edit → Line 5: Line 5: Where $\tau_w$ is the local [[wall shear stress]], $\rho$ is the fluid density and $U_\infty$ is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet). Where $\tau_w$ is the local [[wall shear stress]], $\rho$ is the fluid density and $U_\infty$ is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet). + For a turbulent boundary layer several approximation formulas for the local skin friction can be used: - It is related to the momentum thickness as follows: C_f = 2(d theta)/ (d x) + 1/7 power law: - An empirical relation you may use for comparison is: C_f = 0.0583/(Re )^0.2 + $C_f = 0.0576 Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7$ + 1/7 power law with experimental calibration (equation 21.12 in [1]): - ''Someone should add some correlations and references for them here'' + $C_f = 0.0592 \, Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7$ (equation 21.12 in [1]) + + Schlichting (equation 21.16 footnote in [1]) + + $C_f = [ 2 \, log(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad 5 \cdot Re_x < 10^9$ + + Schultz-Grunov (equation 21.19a in [1]): + + $C_f = 0.370 \, [ log(Re_x) ]^{-2.584}$ + + == References == + + # {{reference-book|author=Schlichting, Hermann |year=1979|title=Boundary Layer Theory|rest=ISBN 0-07-055334-3, 7th Edition}} + + == To do == + + ''Someone should add more data about total skin friction approximations, Prandtl-Schlichting skin-friction formula, and the Karman-Schoenherr equation.'' {{stub}} {{stub}}

## Revision as of 14:45, 25 February 2011

The skin friction coefficient, $C_f$, is defined by:

$C_f \equiv \frac{\tau_w}{\frac{1}{2} \, \rho \, U_\infty^2}$

Where $\tau_w$ is the local wall shear stress, $\rho$ is the fluid density and $U_\infty$ is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet).

For a turbulent boundary layer several approximation formulas for the local skin friction can be used:

1/7 power law:

$C_f = 0.0576 Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7$

1/7 power law with experimental calibration (equation 21.12 in [1]):

$C_f = 0.0592 \, Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7$ (equation 21.12 in [1])

Schlichting (equation 21.16 footnote in [1])

$C_f = [ 2 \, log(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad 5 \cdot Re_x < 10^9$

Schultz-Grunov (equation 21.19a in [1]):

$C_f = 0.370 \, [ log(Re_x) ]^{-2.584}$

## References

1. Schlichting, Hermann (1979), Boundary Layer Theory, ISBN 0-07-055334-3, 7th Edition.

## To do

Someone should add more data about total skin friction approximations, Prandtl-Schlichting skin-friction formula, and the Karman-Schoenherr equation.