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.
Determination of local boundary shear stress is an important topic in hydraulic engineering. When attempting to determine this from a very thin boundary region, it is a difficult one because it requires special skills and instruments to treat the measured data. With the advent of new equipment, like the acoustic Doppler velocity profilers (ADVP), all the velocity profiles in the primary flow region can be simultaneously measured, and it is necessary to develop a new method to estimate the boundary shear stress using the primary flow data. This paper presents such a method called the momentum balance method (MBM). A theoretical relationship between the boundary shear stress and parameters of the primary flow region has been established. The results obtained from MBM agree reasonably well with other methods, indicating that the new method is workable in closed duct flows, and possibly its applicability can be extended to a wide range of boundary conditions.
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