Journal of Hydraulics

Journal of Hydraulics

Lateral velocity distribution for circular open channels

Document Type : Research Article

Authors
Abdolreza Zahiri 1
Soroosh Sharifi 2
1 Water Engineering Department, Gorgan University of agricu
2 Dept. of Civil and environment Engineering, Birmingham University, UK.
10.30482/jhyd.2024.480078.1721
Abstract
Introduction
Pipes that are only partially filled with water exhibit similarities to canals and rivers but are more complex due to the specific geometries of their beds and walls. These structures are prevalent in sewers and under road culverts. Managing sedimentation is crucial for maintaining the optimal operation of sewer systems. Accordingly, it is essential to define specific flow patterns and minimum velocity thresholds to prevent sedimentation. Additionally, these pipes are instrumental in road culverts that facilitate fish passage, requiring that flow velocities be maintained within certain limits to ensure safe passage. Previous studies have focused primarily on utilizing the Manning equation or developing empirical equations to compute average cross-sectional velocity. More sophisticated methods, such as computational fluid dynamics, have been employed to map out detailed flow patterns and identify critical velocity points. However, these methods are often limited by their complexity and the extensive time required to run the models. This research introduces a novel application of quasi-two-dimensional mathematical models to address the flow in partially-filled pipes.

Methodology
The methodology of this study involves applying the Shiono and Knight quasi-two-dimensional model (SKM) to predict flow velocities within partially-filled pipes. This model calculates the lateral distribution of depth-averaged velocities and boundary shear stresses. It incorporates three key coefficients: the Darcy-Weisbach friction factor, turbulent eddy viscosity, and secondary flow coefficient (denoted as f, λ, and β) which are calibrated using data from controlled laboratory experiments. The flow within the pipe is segmented into multiple panels or slices, which serve as computational nodes. Known parameters such as flow depth, lateral slope, and longitudinal slope, along with the three calibrated coefficients, are inputted for each node to compute the velocity. The finite difference method is employed to discretize the governing differential equation, with the resulting matrix solved analytically to obtain the velocity distribution.

Results and Discussion
Application of the SKM to a laboratory-scale partially-filled pipe (Knight and Sterling, 2000) demonstrated that the model accurately predicts lateral velocity profiles at various flow depths, closely aligning with empirical data. This model effectively estimated the minimum, maximum, and average velocities, with calibration constants of 0.07 for eddy viscosity and -0.2 for secondary flow coefficients proving effective. Comparisons of the model's flow discharge predictions with actual measurements showed a maximum error of 5.7% at the lowest flow depth, with an overall average error of 3.6%. These findings underscore the model's robustness and accuracy in simulating real-world conditions.

Conclusion
This research has developed a novel analytical approach based on the Shiono and Knight model to perform hydraulic analyses of circular sections with a free surface flow. The results confirm the model's capacity to replicate measured data on velocity distributions and flow discharges accurately. Moreover, this approach enables the calculation of shear stress distribution based on velocity profiles, suggesting its potential for broader applications, including the analysis of specialized sewer pipe sections like egg-shaped pipes.
Keywords
Partially-filled pipes
Quasi-two-dimensional mathematical model
Finite difference method
Sewer pipes
Stage-discharge curve

Subjects

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  • Receive Date 26 September 2024
  • Revise Date 18 November 2024
  • Accept Date 21 December 2024