Skin friction coefficient
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 ):
Schlichting (equation 21.16 footnote in )
Schultz-Grunov (equation 21.19a in ):
(equation 38 in ):
The following skin friction formulas are extracted from ,p.19. Proper reference needed:
Date Turnock (1999):
- 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.
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 
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) There should be a separation between local and total skin friction on the plate.grizos