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
KW - Critical Reynolds regime
KW - Laminar-turbulent boundary
KW - Colebrook–White
KW - Darcy–Weisbach
KW - Transitional flow regime
KW - Pipe roughness
UR - http://www.scopus.com/inward/record.url?scp=85073704688&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2019.07.041
DO - 10.1016/j.apm.2019.07.041
M3 - Article
SN - 0307-904X
VL - 77
SP - 478
EP - 490
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
ER -