Transitional Water Flow in Steady-State

Stefan Kaltenbacher*, Martin Steinberger, Martin Horn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we derive a mathematical description of the steady-state water flow in the transitional Reynolds area, i.e. between Reynolds numbers 2000 and 4000. Specifying the flow as two dimensional function of the pressure drop and the roughness of a conduit pipe, a description is obtained which not only satisfies the boundary conditions, but also the gradient on the laminar-transitional as well as the transitional-turbulent boundary to a sufficient degree of accuracy. This is motivated by the need to identify individual friction parameters per pipe in a water supply network, a necessity for being able to detect and localise faults reliably. It occurs that although some flows have never been in the turbulent regime, one often yet mistakenly tries to find roughness values for corresponding pipes during the network's calibration. In order to let the calibration algorithm itself decide if an appropriate pipe flow has been laminar or turbulent, a continuous and smooth description in between is needed. Effectively, this work lays part of the foundation for water network calibration algorithms, which fully account for the different flow regimes using pressure sensors primarily.
Original languageEnglish
Pages (from-to)478-490
Number of pages13
JournalApplied Mathematical Modelling
Publication statusPublished - Jan 2020


  • transitional flow regime
  • critical flow regime
  • pipe roughness
  • Colebrook-White
  • Darcy-Weisbach
  • laminar-turbulent boundary
  • Critical Reynolds regime
  • Laminar-turbulent boundary
  • Colebrook–White
  • Darcy–Weisbach
  • Transitional flow regime
  • Pipe roughness

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation


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