Study On Mechanical Energy Equation And Mechanical Energy Loss For Total Flow In Open Channels

Open channel flow is a kind of flow which is widespread in nature and engineering and attracts much attention. Predecessors have done a lot of meticulous work on open channel flow. Although the energy equation(the mechanical energy equation) of steady flow has been built in hydraulics, it lacks rigorous theoretical derivation in hydrodynamics. At the same time, the influence of turbulence has not been considered (if the flow is turbulent), and there is no specific expression for the energy loss (the mechanical energy loss). So, the mechanical energy loss is often obtained by experimental results and prototype observation. Thus it can be seen that deducing a energy equation and studying the mechanical energy loss systematically are of great scientific importance and own a broad application prospect in flow calculation in practical engineering. Based on the systematic review of predecessors' research results, this paper investigates on the energy equation of total flow and the mechanical energy loss through theoretical analysis, numerical calculation and the analysis of measured data. The followings are obtained:(1) Based on the viscous fluid flow model, a energy equation for incompressible steady total flow of homogeneous fluid in open channel has been built. The explicit expression of mechanical energy transformation and loss is also given.(2) For the laminar steady uniform open channel flow, the non-homogeneous linear equation in the linear boundary conditions has been changed to homogeneous linear equations in the nonlinear boundary conditions. And the theoretical solution of the velocity distribution for the laminar uniform flow in open channel is obtained by the method of variable separation. The velocity and the shear stress of the laminar uniform flow in open channel has been analysed and the expression of mechanical energy loss coefficient for the laminar uniform open channel flow has been obtained based on the the explicit expression of mechanical energy loss and the theoretical solution of the velocity distribution. Further investigations have shown that the mechanical energy loss coefficient is concerned with the width-depth ratio and the Reynolds number and only when the width-depth ratio is larger than 6.5 can the mechanical energy loss coefficient of common open channel flow be replaced by that of the wide-shallow open channel flow.(3) The three-dimensional mathematical model closed by the Reynolds stress model is adopted to study the turbulent steady uniform flow(the ensemble average) in rectangular open channel. On the basis of mechanical energy loss explicit expression and the results of numerical simulation, the mechanical energy loss of the turbulent steady open channel total flow is calculated. The results show that the mechanical energy loss coefficient of the turbulent steady open channel total flow varies with the width-depth ratio when the Reynolds number is samll; however, the coefficient only varies with the Reynolds number when the Reynolds number is high and the results agrees well with the experimental results of 3erk?a.(4) The mechanical energy loss coefficient is calculated by using the measured hydrological data of natural river, and is compared with the coefficient of the mechanical energy loss of the turbulent steady total flow in open channels.(5) The hydraulic optimum section of uniform open channel flow in the existing hydraulics is the section of the maximum flow quantity with certain shape of the section, the fixed section area, the fixed roughness and the fixed slope of the channel slope. The roughness is calculated by applying the results of the mechanical energy loss of the turbulent steady total flow in open channels. The hydraulic optimum section is described as the section of the maximum flow quantity with certain shape of the section, the fixed section area and the fixed channel slope. The hydraulic optimum section of rectangle sections is investigated. It agrees well with that of the existing hydraulics when the Reynolds number is high but varied when the Reynolds number is small.