Rough pipe flow is modelled by smooth pipe flow with an artificially large near-wall viscosity chosen to simulate the effect of roughness elements on near-wall velocity profile. Traditional explanations for behaviour differences for different roughness types are shown to be incorrect. The Colebrook-White friction equation for naturally rough pipes, and the friction equation for hydraulically smooth conditions, are derived. Predicted velocity profiles for these conditions, including those for the near-wall region, agree with published experimental data.
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