Pressure and Velocity Profiles over a Weir Using Potential Flow Model

Abstract

A potential flow model of the semi-inverse type is proposed to simulate flow over round crested weirs. This technique involves the construction of only streamlines over the weir instead of constructing the entire flow net. A Serre–Green–Naghdi (SGN) equation is employed to determine the initial free-surface profile, which is solved using a combined finite volume-finite difference scheme. The potential flow equations were numerically solved using a five-point central finite difference scheme. The model was applied to define the pressure and velocity fields in channel controls involving transcritical flow, such as the Gaussian weir, parabolic weir, and semicircular weir. The impact of streamline curvature on pressure and velocity distributions was investigated in the study. The curvature of the streamline strongly influenced the rise and drop of the bed pressures along the test section. A semicircular weir experiment was also conducted to validate the pressure and velocity profiles obtained using the proposed 2-D fluid flow model. The computed pressure and flow profiles from the solution of the potential flow equation agree perfectly with the present experiment and similar experiments available in the literature. In conclusion, the SGN equation provides an excellent initial profile to solve a 2-D ideal fluid flow numerically.

Keywords

• semi-inverse mapping
• transcritical flow
• potential flow
• Laplace equation
• round crested weir