### Abstract

Original language | English |
---|---|

Article number | 77 |

Pages (from-to) | 478 |

Number of pages | 490 |

Journal | Applied Mathematical Modelling |

Publication status | Published - Jan 2020 |

### Fingerprint

### Keywords

- transitional flow regime
- critical flow regime
- pipe roughness
- Colebrook-White
- Darcy-Weisbach
- laminar-turbulent boundary

### Cite this

**Transitional Water Flow in Steady-State.** / Kaltenbacher, Stefan; Steinberger, Martin; Horn, Martin.

Research output: Contribution to journal › Article › Research › peer-review

}

TY - JOUR

T1 - Transitional Water Flow in Steady-State

AU - Kaltenbacher, Stefan

AU - Steinberger, Martin

AU - Horn, Martin

PY - 2020/1

Y1 - 2020/1

N2 - 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.

AB - 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.

KW - transitional flow regime

KW - critical flow regime

KW - pipe roughness

KW - Colebrook-White

KW - Darcy-Weisbach

KW - laminar-turbulent boundary

M3 - Article

SP - 478

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

M1 - 77

ER -