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Nobody can yet compute that number from a measured map of a surface without testing the surface in a flow.","posed_since":"","precise":"In fully rough wall turbulence the mean-velocity shift is $\\Delta U+ = (1/\\kappa)\\ln k_s+ + \\mathrm{const}$, which defines the equivalent sand-grain height $k_s$. Determine whether $k_s/k$ ($k$ a roughness height) is a function of a finite set of topographic statistics (rms height, effective slope, skewness, correlation lengths) for generic random surfaces, give that function, and predict the transitionally rough curve $\\Delta U+(k_s+)$. Answer: a relation with error well below 10 percent on surfaces not used for calibration.","problem_ref":null,"references":"","settled_by":"Blind predictions of $k_s$ for new random surfaces confirmed by roughness-resolved DNS or experiments in the fully rough regime.","status_note":"Prediction uncertainty for full-scale drag is at least 10 percent (Chung, Hutchins, Schultz, Flack, Annual Review of Fluid Mechanics 2021).","title":"Predicting rough-wall drag from surface topography 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