Computational fluid dynamics for sub-atmospheric pressure analysis in pipe drainage By Mohsen Besharat, Oscar Enrique Coronado-Hernández, Vicente Samuel Fuertes-Miquel, Maria Teresa Viseu and Helena Margarida Ramos, J. Hydraulic Res. 58(4), 2020, 553–565, 10.1080/00221686.2019.1625819

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Closure to “Computational fluid dynamics for sub-atmospheric pressure analysis in pipe drainage” by Mohsen Besharat, Óscar E. Coronado-Hernández, Vicente S. Fuertes-Miquel, Maria Teresa Viseu and Helena Margarida Ramos, J. Hydraulic Res. 58(4), 2020, 553–565, https://doi.org/10.1080/00221686.2019.1625819

Acknowledgements

The Discussers would like to express their gratitude to the Natural Sciences and Engineering Research Council of Canada (NSERC) for the financial support.

Notation

L	=	pipe length (m)
D	=	pipe diameter (m)
$x_{\text{0}}$	=	initial air length (m)
S	=	pipe slope (–)
$t_{\text{0}}$	=	time of valve operation (s)
$\tau$	=	valve-opening ratio
V	=	velocity (m s−1)
t	=	time variable (s)
g	=	gravitational constant (m s−2)
x	=	distance variable (m)
$S_f$	=	friction loss (–)
a	=	acoustic wave speed (m s−1)
f	=	friction factor (–)
$h_a$	=	absolute air pressure head (m)
h	=	absolute water pressure head (m)
${\mathrm{\forall }}_a$	=	air volume (m3)
$C_D$	=	discharge coefficient (–)
$h_{atm}$	=	atmospheric pressure head (m)

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada: [Grant Number RGPIN-2020-06979].