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I'm trying to figure out what is the drag force per unit of length on the circular string loop rotating in air around its symmetry axis. In particular I'm interested how this force depends on the strings speed. The string has length of approximately one meter, circular crossesction with the radius of $2.5\;[mm]$ and it is spinning with $v=10\;[\frac{m}{s}]$.

I have done research about the skin friction of long cylinder air flow parallel to its axis of revolution. I have found some empirical data, according to which for $10^5<Re<10^{7}$ skin friction coefficient decreases linearly with Reynolds number. However I'm not sure that thin cylinder in parallel flow is fully equivalent to the loop about which I'm asking. I would be very grateful also for any source were I could find an answer.

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