Kinetic energy correction coefficient for rectangular drainage channels

Abstract

In urban water supply and drainage systems, rainwater channels or pipes are rectangular in design to help control the flow rate and adapt well to limited space. When the Bernoulli equation in fluid mechanics is used to solve the head loss of rectangular pipelines, the velocity parameter used in the kinetic energy term is usually the instantaneous or average velocity of the section at a certain point. Given that this velocity parameter is in exponential form, the smaller the error is, the greater the impact on the result will be. Thus, the kinetic energy term must be corrected. This study focuses on establishing a cross section velocity distribution model in a rectangular pipe and deriving the kinetic energy correction coefficient through the velocity distribution. Based on the Navier–Stokes equation, the partial differential equation describing the velocity distribution is further refined and simplified. Combined with the boundary conditions of the pipeline, the method of separating variables and Fourier transform are used to solve the equation. An example shows how to establish the velocity distribution model and find the analytical solution. Finally, the analytical formula of the kinetic energy correction factor of different cross section parameters and fluid properties is derived. To verify the accuracy of the analytical formula, the Fluent numerical simulation software is used for empirical verification, and then the Deming regression method is used to analyze the error between the theoretical and experimental values. The regression results of the kinetic energy correction coefficient prediction model established in this study are consistent with the actual values, and the confidence interval reaches 95%. This work provides strong guidance for the prediction of the kinetic energy correction coefficient in fluid mechanics and has an important theoretical and practical value.