Skin friction coefficient
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+ | With regards to the 1/7th power law, in Schlichtings book (see references) the formula describing Cf over a flat plate , without pressure gradient, is Cf=0.0725*Re^(-1/5) and it is valid between 5x10^5<Re<10^7 with the assumption of the flow being turbulent from the leading edge (page 639) | ||
+ | This is found in page 638 , formula 21.11. | ||
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+ | Taking into account that the flow is laminar for the first part of the plate and using Blasius's equeation, after providing corrective some corrective factors , Schlichting in page 644 states: | ||
+ | Cf=0.02666*Rl^(-0.139) |
Revision as of 19:03, 13 January 2016
The skin friction coefficient, , is defined by:
Where is the local wall shear stress, is the fluid density and 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:
1/7 power law with experimental calibration (equation 21.12 in [3]):
Schlichting (equation 21.16 footnote in [3])
Schultz-Grunov (equation 21.19a in [3]):
(equation 38 in [1]):
The following skin friction formulas are extracted from [2],p.19. Proper reference needed:
Prandtl (1927):
Telfer (1927):
Prandtl-Schlichting (1932):
Schoenherr (1932):
Schultz-Grunov (1940):
Kempf-Karman (1951):
Lap-Troost (1952):
Landweber (1953):
Hughes (1954):
Wieghard (1955):
ITTC (1957):
Gadd (1967):
Granville (1977):
Date Turnock (1999):
References
- von Karman, Theodore (1934), "Turbulence and Skin Friction", J. of the Aeronautical Sciences, Vol. 1, No 1, 1934, pp. 1-20.
- Lazauskas, Leo Victor (2005), "Hydrodynamics of Advanced High-Speed Sealift Vessels", Master Thesis, University of Adelaide, Australia (download).
- 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. Add proper reference for equations in [2]
Edit:
With regards to the 1/7th power law, in Schlichtings book (see references) the formula describing Cf over a flat plate , without pressure gradient, is Cf=0.0725*Re^(-1/5) and it is valid between 5x10^5<Re<10^7 with the assumption of the flow being turbulent from the leading edge (page 639)
This is found in page 638 , formula 21.11.
Taking into account that the flow is laminar for the first part of the plate and using Blasius's equeation, after providing corrective some corrective factors , Schlichting in page 644 states: Cf=0.02666*Rl^(-0.139)