Mathematical Modeling for Fluid Flow In Open Rectangular Channel

Abstract

The discharge-depth relationships in regular channels have been rarely investigated to make it more useful flow measuring devices. The authors, for the first time, have proposed a theoretical investigation on the flow in open rectangular channel and it is found that even in rectangular channel, it is possible to get a near linear depth-discharge relationship. In this paper, the flow parameters are determined through a new general optimization procedure presented. It is found that the near linear depth-discharge relationship is valid from Y_A(b) to Y_B(b), within a deviation of ±2 percent error, where b is the half base width of the channel. The proposed linear equation is given by is the discharge in the channel, y is the flow depth, C is Chezzy’s Constant and S is the channel bed slope. Chezzy’s C can also be substituted by Manning’s n by the simple equation, where R the Hydraulic mean radius could be computed as a being the cross-sectional area of flow and P the wetted perimeter.

The significance of proposed research is that, the shift is from measurement of discharge through computations to direct reading of the discharge with a piezometer.