If the aim is to determine the skin friction from available data, there are a number of methods besides the Clauser chart method that could be used. Few are referenced here:

Örlü, R., Fransson, J.H.M. & Alfredsson, P.H., 2010. On near wall measurements of wall bounded flows--The necessity of an accurate determination of the wall position. Progress in Aerospace Sciences, 46, pp.353–387.

You might check out the use of Irwin sensors for a direct measurement.  I am not sure it will meet your needs but it may give you some ideas. See the citation below.

Best wishes,

Ted 

Walker, I. J., and Nickling, W. G., 2003, Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel: Earth Surf. Process. Landf., v. 28, no. 10, p. 1111-1124.

Thanks for the answer. I will add some explanation regarding of this. I want to use skin-friction for log law analysis inside wind tunnel. The data that I have is a serial of lateral velocity fields side by side from the floor to the center to investigate a thorough boundary layer profile. For now, I used an estimation of wall skin-friction for smooth pipe in my analysis but the results seems not too good. When I calculated the result, the graph that I got not exactly followed log of the law rule for inner and outer law. I'm still wondering what exactly is the problem. What can I predict right now is, maybe my assumption to use wall skin friction for smooth pipe was not good enough for this experimental result. That's why I tried to have a question in this group to open a discussion regarding of this.

You can use Spalding's law-of-the-wall. I found this on the web that you could easily download.

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990081113.pdf

An alternative to the methods mentionned above, easy to implement an accurate as long as you have a precise measurment of the oil viscosity:

Best wishes,

Laurent

Experiments in Fluids 2009 Vol: 47(2):195-207. DOI: 10.1007/s00348-009-0650-5

Friction measurement in zero and adverse pressure gradient boundary layer using oil droplet interferometric method

Guy Pailhas; P. Barricau; Y. Touvet; L. Perret

Dear Annuar,

I understand that you have mean velocity data, from the wind tunnel center to the wind tunnel wall, in your hands and you are going to determine the skin friction now. Before you go for the skin friction, you need to check reliability of your mean velocity data and stability of the wind tunnel. Streamwise pressure gradient also be checked. Near-wall velocity measurement is very delicate: if you are using a hot-wire anemometer, you should consider thermal conduction effect to the wall; and. if your are using a pitot tube, you should correct the mean velocity data with the turbulent kinetic energy and with the velocity gradient effect. It is a difficult task.  Good luck to you!      -Ji-

Dear Annuar,

Let me add one thing. Assuming that your mean velocity data are reliable enough, calculate the momentum thickness based Re number in order to check if the turbulence field is fully-developed enough. Direct simulation result and discussion of Spalart at NASA Ames will also guide you in interpreting your marginal skin friction error.

 http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19870008597.pdf

This report was published in J. Fluid Mech.   -Ji-

Indeed, as Laurent pointed out, OFI, is the technique of choice when it comes to skin friction measurements. However, as I understood it, the experiments are already performed and he is looking for a way to estimate the friction velocity from available mean velocity profile measurements. As mentioned before here, it is important to ensure that one utilizes techniques that are meant for the flow case under investigation, i.e. if certain law of the wall descriptions are thought to be used, than one needs to ensure that the flow under consideration is in deed a fully developed turbulent boundary layer free of pressure gradient effects or upstream reminiscence. An extension to Spalart's seminal work can be found in:

https://www.researchgate.net/publication/231762015_Assessment_of_direct_numerical_simulation_data_of_turbulent_boundary_layers

and

https://www.researchgate.net/publication/261218845_Simulation_and_validation_of_a_spatially_evolving_turbulent_boundary_layer_up_to_Re8300

where some other indications are given that are worth of being compared.

Article Assessment of direct numerical simulation data of turbulent ...

Article Simulation and validation of a spatially evolving turbulent ...

I have the same concern How can I estimated wall shear stress using Clauser chart method as friction velocity is not constant and varies with y. I have experimental field velocity measurements.