# Skin friction coefficient

(Difference between revisions)
 Revision as of 17:42, 7 April 2008 (view source)← Older edit Revision as of 06:52, 23 September 2011 (view source)Bluebase (Talk | contribs) mNewer edit → (10 intermediate revisions not shown) 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 for a flat plate can be used: - It is related to the momentum thickness as follows: $C_f \equiv 2\frac{\diff{theta}}{\diff{x}} + 1/7 power law: + :[itex]C_f = 0.0576 Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7$ + 1/7 power law with experimental calibration (equation 21.12 in [[#References|[3]]]): - ''Someone should add some correlations and references for them here'' + :$C_f = 0.0592 \, Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7$ + + Schlichting (equation 21.16 footnote in [[#References|[3]]]) + + :$C_f = [ 2 \, log_{10}(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad Re_x < 10^9$ + + Schultz-Grunov (equation 21.19a in [[#References|[3]]]): + + :$C_f = 0.370 \, [ log_{10}(Re_x) ]^{-2.584}$ + + (equation 38 in [[#References|[1]]]): + + :$1.0/C_f^{1/2} = 1.7 + 4.15 \, log_{10} (Re_x \, C_f)$ + + The following skin friction formulas are extracted from [[#References|[2]]],p.19. Proper reference needed: + + Prandtl (1927): + :$C_f = 0.074 \, Re_x^{-1/5}$ + + Telfer (1927): + :$C_f = 0.34 \, Re_x^{-1/3} + 0.0012$ + + Prandtl-Schlichting (1932): + :$C_f = 0.455 \, [ log_{10}(Re_x)]^{-2.58}$ + + Schoenherr (1932): + :$C_f = 0.0586 \, [ log_{10}(Re_x \, C_f )]^{-2}$ + + Schultz-Grunov (1940): + :$C_f = 0.427 \, [ log_{10}(Re_x) - 0.407]^{-2.64}$ + + Kempf-Karman (1951): + :$C_f = 0.055 \, Re_x^{-0.182}$ + + Lap-Troost (1952): + :$C_f = 0.0648 \, [log_{10}(Re_x \, C_f^{0.5})-0.9526]^{-2}$ + + Landweber (1953): + :$C_f = 0.0816 \, [log_{10}(Re_x) - 1.703]^{-2}$ + + Hughes (1954): + :$C_f = 0.067 \, [log_{10}(Re_x) - 2 ] ^{-2}$ + + Wieghard (1955): + :$C_f = 0.52 \, [log_{10}(Re_x)] ^{-2.685}$ + + ITTC (1957): + :$C_f = 0.075 \, [log_{10}(Re_x) - 2 ] ^{-2}$ + + Gadd (1967): + :$C_f = 0.0113 \, [log_{10}(Re_x) - 3.7 ] ^{-1.15}$ + + Granville (1977): + :$C_f = 0.0776 \, [log_{10}(Re_x) - 1.88 ] ^{-2} + 60 \, Re_x^{-1}$ + + Date Turnock (1999): + :$C_f = [4.06 \, log_{10}(Re_x \, C_f) - 0.729]^{-2}$ + + + == References == + # {{reference-paper|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}} + # {{reference-paper|author=Lazauskas, Leo Victor |year=2005|title=Hydrodynamics of Advanced High-Speed Sealift Vessels|rest=Master Thesis, University of Adelaide, Australia ([http://digital.library.adelaide.edu.au/dspace/bitstream/2440/37729/1/02whole.pdf download])}} + # {{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.'' + ''Add proper reference for equations in [2]'' {{stub}} {{stub}}

## Revision as of 06:52, 23 September 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 [3]):

$C_f = 0.0592 \, Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7$

Schlichting (equation 21.16 footnote in [3])

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

Schultz-Grunov (equation 21.19a in [3]):

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

(equation 38 in [1]):

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

The following skin friction formulas are extracted from [2],p.19. Proper reference needed:

Prandtl (1927):

$C_f = 0.074 \, Re_x^{-1/5}$

Telfer (1927):

$C_f = 0.34 \, Re_x^{-1/3} + 0.0012$

Prandtl-Schlichting (1932):

$C_f = 0.455 \, [ log_{10}(Re_x)]^{-2.58}$

Schoenherr (1932):

$C_f = 0.0586 \, [ log_{10}(Re_x \, C_f )]^{-2}$

Schultz-Grunov (1940):

$C_f = 0.427 \, [ log_{10}(Re_x) - 0.407]^{-2.64}$

Kempf-Karman (1951):

$C_f = 0.055 \, Re_x^{-0.182}$

Lap-Troost (1952):

$C_f = 0.0648 \, [log_{10}(Re_x \, C_f^{0.5})-0.9526]^{-2}$

Landweber (1953):

$C_f = 0.0816 \, [log_{10}(Re_x) - 1.703]^{-2}$

Hughes (1954):

$C_f = 0.067 \, [log_{10}(Re_x) - 2 ] ^{-2}$

Wieghard (1955):

$C_f = 0.52 \, [log_{10}(Re_x)] ^{-2.685}$

ITTC (1957):

$C_f = 0.075 \, [log_{10}(Re_x) - 2 ] ^{-2}$

$C_f = 0.0113 \, [log_{10}(Re_x) - 3.7 ] ^{-1.15}$

Granville (1977):

$C_f = 0.0776 \, [log_{10}(Re_x) - 1.88 ] ^{-2} + 60 \, Re_x^{-1}$

Date Turnock (1999):

$C_f = [4.06 \, log_{10}(Re_x \, C_f) - 0.729]^{-2}$

## References

1. von Karman, Theodore (1934), "Turbulence and Skin Friction", J. of the Aeronautical Sciences, Vol. 1, No 1, 1934, pp. 1-20.