Development of Inverse Mathematical Model of Rouse Formula to Estimate Suspended Sediment Concentration Along Width of Channel

Abstract
Background/objective: The sedimentation is a burning issue all around the world; hence this research will help the irrigation engineers to solve the sedimentation problems related to irrigation channels, hydraulic structures as well as in the field of agriculture. In this present research study, the inverse mathematical model of Rouse formula is developed to calculate the suspended sediment concentration along the width of an open channel.

Methodology/analysis: For derivation of the model, a well-known differential advection–diffusion equation is solved analytically with respect to x-axis along the width of channel. The model is also validated and checked with experimental results and calculated results by the newly developed model.

Findings: A mathematical model has been developed for suspended sediment concentration along the width of channel. Furthermore, this model applied and compared with experimental results and observations which were conducted in open channel. Finally, for more validation and reliability of a newly developed model, the average maximum and minimum percentage errors are computed. These errors indicate that the proposed model has the best accuracy and resemblance when percentage errors of the newly developed model are computed.

Application: A newly developed model can be applied to estimate suspended sediments concentration from open channels. This model is also useful for irrigation engineers to find out suspended sediments concentration profiles along the horizontal direction from the centre to channel banks at the mid-depth of water.

Keywords: Advection–Diffusion Equation, Rouse Number, Mass Diffusivity, Suspended Sediment Concentration, Irrigation Channels.