Dear colleagues,
Anyone knows how to correlate the frictional coefficient (Cf) measurement in a turbulence flow channel with a flat plate meansurement in a towing tank? We can get Cf from the pressure drop measurement in turbulence flow channel and Cf from resistance measurement but they are based on different Reynolds number definitions. Can we correlate these two types of measurements and how? Many thanks for your answers.
Weichao
It's not clear what you exactly mean by correlating the Cf measurements in a channel and over a flat plate. However, the following may help you get started:
1. Assuming that you are making pressure loss measurements in the fully developed portion of the channel and you have adequate characterization of the hydraulic diameter of the channel cross-section and the surface roughness (in terms of effective sand-grain roughness), you may compare the measured friction coefficient for the channel with the value obtained via an iterative solution to the empirical Colebrook–White equation (see, for instance, https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae)
2. Since you are measuring the total drag over the flat plate, the average skin friction coefficient will be influenced by the relative extent of the laminar+transitional regions over the plate (which will depend on whether or not you are tripping the flat plate boundary layer). However, if the flow over most of the plate length were to be turbulent, then there are other empirical correlations for turbulent skin friction over a smooth flat plate, as well as for different equivalent roughness heights, analogous to the channel flow. Schlichting's classic text on boundary layers may have some information on this, but I am not sure about it.
However, effectively, you would simply be validating the accuracy of your measurements against the established correlations and, if you already believe those correlations, then you can use those to correlate the friction coefficients for the channel and the flat plate, and you don't need the measurements!
Meelan Choudhari ,
Thanks very much for your kind reply and pointing out these documents. Let me clarify my question a bit further.
1. The channel flow measurement can give us the results, like you mentioned, Cf and Re (based on mean bulk velocity, or shear velocity etc.)
2. The flat plate test give us also a Cf and Re, but this is for open flow and the Re is based on the length and freestream velocity.
But for the same surface, how I can understand these two Cf and Re results so that to find the links between. I am assuming they should have some links because the surface is the same and they have the same U+ and Y+ distribution. Any function can link these two results.
Hope I have clarified my question. Many thanks.
Note that the U+ and Y+ computations require the friction velocity, i.e., (local) Cf, which is related to the bulk parameters in the empirical expressions. Thus, the point was that, if you take those empirical laws to be correct, then you should be able to back out the equivalence relations from those, without requiring any measurements. The measurements will simply provide additional information to confirm consistency with the empirical expressions (an additional check, if you will, and provided that the measurements cover all of the required input parameters and are sufficiently accurate). Hope this helps.
These two types of flows are of different natures. That's why though there were available empirical charts for pipe flows, naval architects still had to work out something similar for the flat plates.
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