Flow resistance over fixed roughness elements
The underlying mechanism of flow resistance in open channels and pipelines over rough boundary is investigated. Different from Einstein's method, this work extends the principle of boundary shear stress summation in a mobile bed to the rigid boundary. It is found that the principle is valid to express the friction factor in all pipe flow regimes, mainly concerning the transition from laminar to turbulent flows, and between fully smooth and fully rough turbulent flows. This research also evaluates the concept developed by Einstein regarding the relationship between skin friction and form drag. Experimental data of Nikuradse are used to test the obtained results, indicating that the above-mentioned method yields the best agreement with experimental data, relative to the other friction factor formulas available in the literature.