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Turbulent flows over rough surfaces can be encountered in a wide range of engineering applications. Despite the progress made after several decades of studies, the prediction of drag and roughness function from the surface geometrical parameters remains an open question. Several methods have shown encouraging results. However, they lack generality and present some scatter in the data. In this paper we propose a new parameter, the effective distribution ($$ED$$), which lays foundation on the effective slope with some changes to take into account the sheltering effect of large roughness elements and the drag induced by pinnacles higher than the average roughness elements. To develop this new correlation between geometrical features of the wall and the drag, we performed a set of simulations of the turbulent flow over a rough surface made of triangular elements varying their height and spatial distribution. The$$ED$$correlates quite well both with the drag and the roughness function for a wide range of cases having different mean roughness height, skewness and kurtosis. To further validate the$$ED$$, and assessing how it can be generalized to real rough wall, an irregular wall made from the superposition of random sinusoidal function was considered. Results were consistent with the correlation here presented. 

With the development of advanced micro/nanoscale technologies, two-dimensional materials have emerged from laboratories and have been applied in practice. To investigate the mechanisms of solid– liquid interactions in potential applications, molecular dynamics simulations are employed to study the flow behavior of n-dodecane (C12) molecules confined in black phosphorus (BP) nanochannels. Under the same external conditions, a significant difference in the velocity profiles of fluid molecules is observed when flowing along the armchair and zigzag directions of the BP walls. The average velocity of C12 molecules flowing along the zigzag direction is 9-fold higher than that along the armchair direction. The friction factor at the interface between C12 molecules and BP nanochannels and the orientations of C12 molecules near the BP walls are analyzed to explain the differences in velocity profiles under various flow directions, external driving forces, and nanochannel widths. The result shows that most C12 molecules are oriented parallel to the flow direction along the zigzag direction, leading to a relatively smaller friction factor hence a higher average velocity. In contrast, along the armchair direction, most C12 molecules are oriented perpendicular to the flow direction, leading to a relatively larger friction factor and thus a lower average velocity. This work provides important insights into understanding the anisotropic liquid flows in nanochannels.