Flow resistance in open channels with intermediate scale roughness

Abstract

Many environmental and engineering projects require prediction of the velocity of flow in river channels, in terms of those channel properties and flow characteristics which induce resisting forces or an energy loss to the flow. Relationships such as the Manning, Chézy and Darcy-Weisbach equations have been in use for a century or more. All of them account for resistance with a single coefficient of resistance, and the central problem is evaluation of this coefficient. Experimental results by different researchers have shown that Manning’s n varies strongly with the ratio of flow depth to roughness height. It is constant for values of this ratio above about 4, but increases significantly for lower values. This suggests that the equation is not suitable in its original form for the case of intermediate-scale roughness. The roughness is intermediate-scale if the relative submergence ratio of flow depth to roughness elements height lies between 1 and 4. The influence of the roughness elements on flow resistance in this regime is caused by a combination of both element drag and boundary shear, or friction. The results of an experimental study with hemispherical roughness elements are presented, showing how the roughness element size, spacing and pattern influence flow resistance. For the range of conditions tested, Manning’s n appears to depend on roughness element size, spacing and pattern.