Abstract

Comparison between hydraulic and hydrologic computational methods is conducted in this study, regarding prismatic open channels under unsteady subcritical flow conditions. One-dimensional unsteady flow continuity and momentum equations are solved using explicit and implicit finite difference schemes for a symmetrical trapezoidal cross section, where the flow discharge and depth are the dependent variables. The results have been compared to those derived from Muskingum-Cunge hydraulic/hydrologic method as well as the commercial software HEC-RAS. The results from explicit and implicit code compare well to those from commercial software and hydraulic/hydrologic methods for long prismatic channels, thus directing the hydraulic engineer to quick preliminary design of prismatic open channels for unsteady flow with satisfactory accuracy.

Highlights

  • Different types of open channels such as prismatic canals or natural streams usually operate under unsteady flow conditions

  • The unsteady, subcritical flow in prismatic open channels of trapezoidal, symmetrical cross section is studied, and the results of four different implementation methods are compared in this manuscript

  • Two finite difference numerical schemes have been implemented in Matlab®

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Summary

Introduction

Different types of open channels such as prismatic canals or natural streams usually operate under unsteady flow conditions. The assumptions used to derive the equations of motion above include (1) the hydrostatic pressure distribution, (2) the uniform velocity over the channel section, (3) the small average channel bed slope, and (4) the homogeneous and incompressible flow. From these assumptions β = 1, and substitution of V = Q/A in Equation (2) yields:. The Muskingum-Cunge method dated back in 1969 can be used for flood routing calculation It is based on the storage equation (continuity equation) and considering the momentum equation it relates the storage S, the input and output flow rates I and Q respectively, with a linear relationship in a specific channel reach. The computational results will be compared to those derived from the application of unsteady one dimensional HEC-RAS v. 4.1 software [16] and from the Muskingum-Cunge method

Numerical Solution Methods—Explicit and Implicit Scheme
Explicit Algorithm
Implicit Algorithm
Conclusions

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