The effects of obstacles on surface levels and boundary resistance in open channels

Abstract

Simple momentum considerations are used to show how the increase in water levels due to obstacles in a natural channel can be calculated. This requires use of a numerical method for solving nonlinear equations, which is not difficult. However it is more insightful to consider an approximate explicit theory, which shows the important quantities governing the problem, and which is accurate enough for practical purposes. It is applicable to obstacles of arbitrary extent and location, in both subcritical and supercritical flow in channels of arbitrary section. A method for the numerical refinement of this is presented, but it will usually not be necessary. The methods are compared with a theory and experimental results for a rectangular channel with vertical cylinders extending the whole depth. Then momentum-loss considerations are applied to explaining the nature of friction laws in open channels. Instead of boundary shear, momentum loss from discrete elements is used as the means of modelling resistance. It is found that the behaviour of Gauckler-Manning's law for wide channels in successfully mimicking the frictional behaviour over a range of depths can be explained, but it does not yet provide a comprehensive theory for general cross-sections.