SHAP EEFFECTS ON RESISTANCE TO UNIFORM FLOW IN OPEN CHANNELS

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Abstract
The effects of the shape of the cross-section on flow resistance in open channels has received considerable attention from hydraulic engineers for many years. Many investigators have tried to introduce parameters to represent the cross-section shape effect but their results have been inconclusive. Some of the techniques previously used to deal with this problem are reviewed and their shortcomings are discussed. A new method for dealing with shape effect is developed in this paper from considerations of dimensional analysis and using the experimental data of TRACY and LESTER and of SHIH and GRIGG. This method, which is referred to as KAZEMIPOUR'S method, employs new parameters more representative of the effect of cross-sectional shape on flow resistance in open channels than those previously used and offers solutions more rational than those previously proposed. The shape factor developed is ϕ = ϕ 1/ϕ 2, where ϕ 1, equal to , reflects the effects of non-uniform distribution of shear stress on the boundary as the shape of cross-section departs from an infinitely wide rectangle and tp., is a function of the width/average depth, or aspect ratio of the cross-section. It is demonstrated that application of this shape factor shifts the experimental data for open channel resistance on to the universal diagrams for flow resistance in circular pipes for a variety of cases. The shape factor establishes a simple correlation between open channel and pipe flow and permits the universal resistance diagrams and formulae available for pipe flow to be used to calculate the friction factor and average velocity in open channel flow. The effectiveness of the method has been demonstrated for smooth turbulent flow in rectangular, triangular and trapezoidal cross-sections and for rough and transitional turbulent flow in rectangular cross-sections and this suggests that its applicability may be much wider.

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