Mathematical modelling of open-channel dividing flow in various channel forms for estimating discharge and flow depth ratio

Dividing flow in open-channel is a great contributor to river and drainage management suggested by the authority to reduce overflow during heavy rainfall. Our systematic literature review have identified the general equations of dividing flow in trapezoidal and rectangular cross-sectional channels. Therefore, the objectives of this study is to develop a mathematical model of open-channel dividing flow in V-shaped crosssectional channel. To enhance the model’s accuracy and applicability, new dividing flow equations for trapezoidal, rectangular and V-shaped cross-sectional channels are derived which takes into account the Reynold’s number. In addition, a new non-linear polynomial equation is formulated for predicting flow characteristics and evaluate the effect of division angles on flow depth using the Newton-Raphson method for trapezoidal, rectangular and V-shaped channels. Furthermore, dimensionless expressions for the width and length of the separation zone in the V-shaped channel are introduced to improve prediction of the discharge distribution. Maple software is used to implement the proposed equations produce the discharge and flow depth ratio. The results indicate that the discharge ratios in all channels remain below the critical discharge ratio at certain dividing angles, preventing the channel from overflow. Incorporating the Reynold’s number as an alternative parameter in the proposed model demonstrates good agreement with FLOW-3D simulation data. The non-linear polynomial equations accurately predict flow depth while the separation zone expressions further improve prediction of discharge ratio. Additional analysis shows that Froude number and discharge ratio influence the behavior of flow depth in both channels. Lastly, the results indicate that the proposed models are capable of accurately estimating the discharge ratio and flow depth, with strong agreement observed when compared to experimental data from previous studies. These findings validate the capability of the mathematical models proposed in the study and demonstrate its potential for practical applications in open-channel hydraulic design.