A Single Equation for Calculating Z0N for Hydraulically Smooth, Transitionally Rough, and Fully Rough Turbulent Flows

Stephen C. Ertman


The velocity-profile data from NIKURADSE'S (1950) seminal study was reexamined with modern curve-fitting software. A single equation was derived that describes the influence of bottom roughness on the velocity profile over a wide range of flow conditions, including hydraulically smooth, transitionally rough, and fully rough turbulent flows.


Nikuradse's roughness parameter; sand-grain roughness; shear velocity; shear stress; roughness Reynolds number

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