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Journal of Engineering Research

Journal of Engineering Research

DOI

https://doi.org/10.70259/engJER.2025.921991

Abstract

In investigations of gradually varied flow, open channels are categorized according to bed slope as horizontal, mild, critical, steep, and adverse. A canal is referred to as horizontal if its bed slope is zero. In open-channel hydraulics, calculating the water surface profile in an open channel is regarded as a crucial part of channel design. The objective of this present study is to solve the gradually varied flow in open circular channel with horizontal slope by using two mathematical methods called; direct integration method and Runge-Kutta method. The presented study used the experimental works to offer an explicit closed-form semi-analytical solution for a circular channel based on Manning's equation with variable roughness. Laboratory experimental runs in circular flume for eleven different discharges were carried in circular cross-section flume with horizontal slope. The results obtained from the laboratory are compared with the results obtained from the two mathematical methods.

The direct integration method has a minimum percentage error of 1.5% and a maximum of 10.7% for the length of H3 curves. The direct integration method has a minimum percentage error of 1.57% and a maximum of 21.23% for the length of H2 curves. For the water depths of H3 curves, the Runge-Kutta method exhibits a minimum percentage error of 0.04% and a maximum of 5.11%.

The maximum error in water surface for all runs using the Runge-Kutta method is 2.99% for H2 curves given the same curve length and minimum 0.00%. The suggested techniques are suitable for the early design phase of circular channels with horizontal bed slope, with the aim of lowering the computational cost involved at this stage.

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