A Modified Chezy Formula for One-Dimensional Unsteady Frictional Resistance in Open Channel Flow

Abstract

It has been observed in literature that for unsteady flow conditions the one-to-one relationships between flow depth, cross-sectional averaged velocity, and frictional resistance as determined from steady uniform flow cases may not be appropriate for these more complex flow systems. Thus, a general friction resistance formula needs to be modified through the addition of new descriptive terms to account for flow unsteadiness, in order to eliminate errors due to uniform and steady-flow assumptions. An extended Chezy formula incorporating both time and space partial derivatives of hydraulic parameters was developed using dimensional analysis to investigate the relationship between flow unsteadiness and friction resistance. Results show that the proposed formula performs better than the traditional Chezy formula for simulating real hydrograph cases whereby both formula coefficients are individually identified for each flood event and coefficients are pre-determined using other flood events as calibration cases. Although the extended Chezy formula as well as original Chezy formula perform worse with the increasing degree of flow unsteadiness, its results are less dramatically affected by unsteadiness intensity thereby improving estimations of flood routing. As a result, it tends to perform much better than traditional Chezy formula for severe flood events. Under more complex conditions whereby peak flooding events may occur predominantly under unsteady flow, the extended Chezy model may provide as a valuable tool for researchers, practitioners, and water managers for assessing and predicting impacts for flooding and for the development of more appropriate mitigation strategies and more accurate risk assessments.

MATLAB‐based program for computation of open‐channel flow profiles

“…The basic formula for calculating the water depth for steady flow in an open channel is the energy equation. When the flow state is uniform, the hydraulic gradient J is equal to the bottom slope i , which is computed by the Chézy formula [34]: $$$v=C\sqrt{RJ},$$$where C and R represent the Chézy coefficient and hydraulic radius. However, when the flow state is not uniform and the hydraulic gradient is not equal to the bottom slope, the energy equation is simplified as [32]: $$$\frac{dh}{ds}=\frac{i-J}{1-F{r}^{2}},$$$where Fr represents the Froude number.…”

“…The use of CFD as a Teaching tool to enhance engineering education [7,14,15,22,34] is a solution to improve software visualization. It should be remarked that rather than focusing on mathematical processes, the aim of engineering training should be focused on the stimulation of modeling and designing creativity.…”

“…When the flow state is uniform, the hydraulic gradient J is equal to the bottom slope i, which is computed by the Chézy formula [34]:…”