text: For Reynolds number greater than 4000, the flow is turbulent; the resistance to flow follows the Darcy–Weisbach equation: it is proportional to the square of the mean flow velocity. Over a domain of many orders of magnitude of  (), the friction factor varies less than one order of magnitude (). Within the turbulent flow regime, the nature of the flow can be further divided into a regime where the pipe wall is effectively smooth, and one where its roughness height is salient.