Distribution of flows in a channel network under steady flow conditions

Abstract

Aim of the study The article presents an algorithm for calculating the distribution of flow in a junction of open channel network under steady flow conditions. Material and methods The presented algorithm is based on the continuity equation and a simplified energy equation. To describe the relationship between the depth of water and the flow rate, the Manning’s equation was used to express discharge in the main channel, whereas in case of other channels, with hydraulic structures, appropriate equations describing the flow over a weir and through the culverts were used. Substitution of the abovementioned relationships into the continuity equation leads to a non-linear algebraic equation with respect to the water level. The resulting equation can be solved with iterative numerical methods. Calculation example using the proposed algorithm was carried out for the hydraulic system located on the Strzyża stream in Gdańsk. Results and conclusions The presented approach can be an alternative to analytical-graphic method and it does not require formulation of the boundary problem for the system of ordinary differential equations describing the gradually varied flow in the open channel network.

Keywords

• division of flows
• open channel network
• steady gradually varied flow
• nonlinear equation
• flow through weir and culvert