Do logarithmic terms exist in the drag coefficient of a single sphere at high Reynolds numbers?

• Obtain predictive models for the drag coefficient of a sphere using symbolic regression. The depends on logarithmic terms Reynolds number. have higher extrapolation range than power-based models. can predict crisis at high numbers. proper behaviour low number regime. At beginning second half twentieth century, Proudman and Pearson (J. Fluid. Mech.,2(3), 1956, pp.237-262) suggested that functional form ( C D ) single subjected to uniform fluid flow consists series power Re ). In this paper, we will explore validity above statement numbers up 10 6 by regression machine learning method. algorithm is trained available experimental data from well-known correlations literature ranging 0.1 2 × 5 . Our results show contains powers log , plus Stokes term. expressions generalize (extrapolate) better beyond training pure are first in with acceptable accuracythe onset rapid decrease (drag crisis) but also follow right towards zero We find connection between root -dependent expression point laminar separation. generalization equations worse logarithmic-based ones, especially regime which they give non-physical results. based correctly describes physics crisis. Also, applying minor modification equations, an oblate spheroid