One dimensional modeling of branched free surface flow – A research report by National Institute of Hydrology

In this report, a mathematical model capable of computing the flow depth and discharge in each of the branched flows is developed using gradually varied flow equations. This model can handle three flow situations viz. temporary flow diversion, a cut-off channel and a single river island. Computational capability of the model is increased to handle irregular cross sections of a river.

Occurrence of branched flow situation is quite common and flow diversion is one of the techniques used to reduce flooding of a downstream city. The flow may rejoin the stream taking a circuitry route. Sometime, river length is reduced by means of cut-off channel as a channel improvement scheme. The diverted flow may take lower velocity than the main. On the other hand the flow takes a cut-off diversion and rejoins at a downstream point.

Flow computations in such situations need special attention as the computed flow depths need to satisfy certain conditions at the junction. Parametric studies have been carried out using this in order to find out the effect of the diversion channel width on the discharge it can carry for different values of bed roughness and bed slope.

A relationship is established between the divided flow, width, slope and roughness coefficient in a dimensionless form for each of the flow situations using the least square method. These equations are derived for rectangular channels. However, it is found that approximation to irregular geometry can be applied and the derived equations can be employed with confidence.    `

The model development and the results discussed in the report are for relatively simpler cases compared to the flow situations normally encountered. Suggestions are also given to improve this model further. To make the model a potent tool for analyses of branched flows the following are recommended –

• The model should be extended to two-dimensional cases.
• Time variation of different flow parameters should be computed by unsteady flow modeling.
• Modeling of bank erosion, channel bed aggradation and degradation should be performed.
• Depth averaged turbulence modeling (K-ε) should be included to account for the flow patterns near the junction.