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In this work, the effective average height of the roughness elements, the relative increase of the pressure gradients, the relative decrease of the permeability are derived based on the fractal geometry theory and technique for laminar flow through tree-like branching networks with roughened channels. The relationships among the effective average height, the structural parameters and pressure drops as well as permeability are studied. It is found that the total pressure drop across a tree-like branching network with roughened channels is increased by a factor of $1/{(1-\epsilon )}^4$, and the permeability for the network with roughened channels is decreased by a factor of ${(1-\epsilon )}^2$, where $\epsilon$ is the relative roughness of surfaces of channels, compared to those with smooth channels.

In this work, a novel fractal model for the laminar flow in roughened cylindrical microchannels is proposed. The average height of rough elements is derived using the fractal theory. The effects of relative roughness on the friction factor and the Poiseuille number are discussed. It is found that the Darcy friction factor and the Poiseuille number increase with the increase in the relative roughness in the cylindrical microchannel. Besides, it is observed that the Darcy friction factor decreases with the increase in the Reynolds number. Each parameter of the proposed model has a clear physical meaning. The present model can properly reveal some mechanisms that affect the laminar flow in roughened cylindrical microchannels. The present model improves the understanding of the physical mechanisms of fluid flows through roughened cylindrical microchannels. Our model predictions are compared with the existing experimental data, and good agreement can be found.

Based on the statistical geometry theory and the fractal theory, a theoretical model to predict the pressure drop of fluid flowing through porous media has been derived in this work. This model is expressed as a function of specific surface, porosity, tortuosity, the pore fractal dimension, maximum pore size, which have clear physical meaning. To verify this model, experiments have been carried out with air using glass beads of three samples. For each sample, the present model fits the experimental data well. Besides, a comparison between the Ergun equation and present model has been made, the result shows that the present model fits the experimental data much better than the Ergun equation and has good accuracy in the range of $200<\mathrm{\text{Re}}<1000$.

Surge waves resulting from dam breaks have been responsible for numerous losses of life. A related situation is the tsunami surges advancing on dry coastal plains. Herein a simple dam break wave solution is presented. The results yield some simple expressions of the instantaneous free-surface profile and flow depths that compare well with well-known dam break wave data. The results are applied to tsunami surges on dry coastal plains and compared with some data set. The present development offers simple analytical expressions that compare well with both experimental data and more advanced theoretical solutions, and that are further well-suited for pedagogical purposes, computational model validation, and accurate real-time predictions of tsunami surges.

In this paper, steady incompressible micropolar fluid flow through a non-uniform channel with multiple stenoses is considered. Assuming the stenoses to be mild and using the slip boundary condition, the equations governing the flow of the proposed model are solved, and closed-form expressions for the flow characteristics (resistance to flow and wall shear stress) are derived. The effects of different parameters on these flow characteristics are analyzed. It is observed that both the resistance to the flow and the wall shear stress increase with the heights of the stenoses and the slip parameter; but decrease with the Darcy number. Furthermore, the effects of the wall exponent parameter, the cross-viscosity coefficient and the micropolar parameter on the flow characteristics are discussed.

This chapter deals with the calibration of a new simplified experimental method to evaluate absolute roughness of vegetated channels. The method is based on boundary layer measurements in a short channel rather than on uniform flow measurements, as usual. The proposed method can be applied to any kind of rough bed, but it is particularly useful in vegetated beds where long channels are difficult to prepare. In this paper a calibration coefficient is experimentally obtained. In order to perform suitable comparisons with literature data relationships between ε absolute roughness and Manning's n coefficient are deepened. The results are successfully compared with literature experimental data with a very good fit. Finally, a particular dependence of ε values on the vegetation density are explained through further experiences. In conclusion it is possible to state that the proposed method, once calibrated, can provide reliable prediction of absolute roughness in vegetated channels.

The seabuckthorn flexible dam is a kind of new biological measure which can effectively confine soil erosion and trap sediment in gully channel in the Pisha Sandstone area. A filed experiment on the hydraulic features of steady flow through the seabuckthorn flexible dam was conducted in Mei country of Shaanxi Province. Based on the experimental data, the resistance effect of the seabuckthorn flexible dam on water flow in the trapezoidal test bed was analyzed to investigate the impact of the seabuckthorn flexible dam on water flow features under the different planting parameters, indicated from the lengthwise and transverse variation of water depth and velocity. The results showed that the seabuckthorn flexible dam can increase the resistance of water flow and reduce flow velocity and shear stress, which is beneficial to longitudinal sediment siltation. It is found that the resistance effect of the seaubkchtorn flexible dam on flow is striking under various planting parameters. This study can lay the foundation for further studying the sediment retention mechanism of the seabuckthorn flexible dam, and then provide a theoretical basis for the spreadwide planting of the seabuckthorn flexible dam within the Pisha Sandstone area of Loess Plateau of China.