Mathematical modeling and simulation of flow velocity profile for rectangular open channels

Abstract

The accuracy of discharge measurement in open channels using propeller current meters can be improved considerably by optimizing the number and locations of the current meters to be deployed for this purpose. The optimization is possible if the nature of the flow profile in the channel can be assessed. This paper reports development of a mathematical model of the flow velocity profile of rectangular open channels. One-dimensional velocity profile equation is taken as a sum of logarithmic and parabolic terms and used to determine the unit-width discharge profile across the width of the channel. The unit-width discharge equation comprises two logarithmic terms along with a beta function. The two equations together involve 10 mathematical parameters, which are linked to the physical conditions, geometry, and configuration of the channel. MATLAB code has been developed to account for these parameters and obtain the velocity profile of flow in any rectangular open channel. Flow under similar conditions is simulated using computational fluid dynamics (CFD) and the results for six different cases are used for validating the mathematical model. The CFD based simulation, in turn, is validated by carrying out actual measurements in a rectangular open channel using an acoustic Doppler current profiler.

Keywords:

• One-dimensional velocity profile
• open channel
• mathematical model
• acoustic Doppler current profiler
• computational fluid dynamics