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Skin friction coefficient

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Where <math>\tau_w</math> is the local [[wall shear stress]], <math>\rho</math> is the fluid density and <math>U_\infty</math> is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet).
Where <math>\tau_w</math> is the local [[wall shear stress]], <math>\rho</math> is the fluid density and <math>U_\infty</math> is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet).
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For a turbulent boundary layer several approximation formulas for the local skin friction can be used:
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For a turbulent boundary layer several approximation formulas for the local skin friction for a flat plate can be used:
1/7 power law:  
1/7 power law:  
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Schlichting (equation 21.16 footnote in [1])
Schlichting (equation 21.16 footnote in [1])
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<math>C_f = [ 2 \, log(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad Re_x < 10^9 </math>
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<math>C_f = [ 2 \, log_{10}(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad Re_x < 10^9 </math>
Schultz-Grunov (equation 21.19a in [1]):
Schultz-Grunov (equation 21.19a in [1]):
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<math>C_f = 0.370 \, [ log(Re_x) ]^{-2.584} </math>
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<math>C_f = 0.370 \, [ log_{10}(Re_x) ]^{-2.584} </math>
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 +
(equation 38 in [2]):
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<math>1.0/C_f^{1/2} = 1.7 + 4.15 \, log_{10} (Re_x \, C_f) </math>
== References ==
== References ==
# {{reference-book|author=Schlichting, Hermann |year=1979|title=Boundary Layer Theory|rest=ISBN 0-07-055334-3, 7th Edition}}
# {{reference-book|author=Schlichting, Hermann |year=1979|title=Boundary Layer Theory|rest=ISBN 0-07-055334-3, 7th Edition}}
 +
# {{reference-book|author=von Karman, Theodore |year=1934|title=Turbulence and Skin Friction|rest=J. of the Aeronautical Sciences, Vol. 1, No 1, 1934, pp. 1-20}}
== To do ==
== To do ==

Revision as of 17:12, 28 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 for a flat plate 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

Schlichting (equation 21.16 footnote in [1])

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

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

C_f = 0.370 \, [ log_{10}(Re_x) ]^{-2.584}

(equation 38 in [2]):

1.0/C_f^{1/2} = 1.7 + 4.15 \, log_{10} (Re_x \, C_f)

References

  1. Schlichting, Hermann (1979), Boundary Layer Theory, ISBN 0-07-055334-3, 7th Edition.
  2. von Karman, Theodore (1934), Turbulence and Skin Friction, J. of the Aeronautical Sciences, Vol. 1, No 1, 1934, pp. 1-20.

To do

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


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