Theoretical solution for laminar flow in partially-filled pipes

Junke Guo, Robert N. Meroney

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)408-416
Number of pages9
JournalJournal of Hydraulic Research
Issue number4
StatePublished - Aug 1 2013


  • Laminar flow
  • open channel
  • partially-filled pipe
  • shear stress
  • velocity distribution

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology


Dive into the research topics of 'Theoretical solution for laminar flow in partially-filled pipes'. Together they form a unique fingerprint.

Cite this