Theoretical solution for laminar flow in partially-filled pipes

Partially-filled pipe flow as occurs in subsurface drains and sewers is computed by Manning's resistance equation or using the cross-sectional velocity distribution. Yet, Manning's equation is valid only for turbulent flow and no theoretical solutions and experiments are available for lami...

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Bibliographic Details
Published in:Journal of hydraulic research 2013-08, Vol.51 (4), p.408-416
Main Authors: Guo, Junke, Meroney, Robert N.
Format: Article
Language:English
Subjects:
Boundary conditions
Computational fluid dynamics
Cross-sections
Discharge
Distribution
Drainage systems
Drains
Earth sciences
Earth, ocean, space
Empirical analysis
Engineering and environment geology. Geothermics
Exact sciences and technology
Fluid flow
Fourier transforms
Hydrology
Hydrology. Hydrogeology
Laminar flow
Mathematical analysis
Mathematical models
Mechanical stimuli
Navier-Stokes equations
open channel
partially-filled pipe
Pipe flow
Pipes
Pollution, environment geology
Sewer systems
Sewerage
Sewers
Shear stress
Solutions
Stress concentration
Subsurface drains
Turbulence
Turbulent flow
Velocity
Velocity distribution
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Summary:Partially-filled pipe flow as occurs in subsurface drains and sewers is computed by Manning's resistance equation or using the cross-sectional velocity distribution. Yet, Manning's equation is valid only for turbulent flow and no theoretical solutions and experiments are available for laminar, partially-filled pipe flow, although fully-filled pipe flow is well understood. This research solves the Navier-Stokes equations, using bipolar coordinates and the Fourier transform, for partially-filled pipe flow under steady uniform conditions, resulting in theoretical solutions for the cross-sectional velocity distribution, discharge, boundary shear stress and friction coefficient. Although the solutions are not tested with laminar flow data (a research need), they satisfy all boundary conditions and special cases. Particularly, their graphical interpretations agree qualitatively with related turbulent flow data, providing a benchmark for formulating analytical or empirical solutions for turbulent flow in the future. The proposed stage-discharge relationship is also useful for discharge measurements in drainage and sewerage systems.
ISSN:0022-1686
1814-2079
DOI:10.1080/00221686.2013.784881