Erratum for “Local Sensitivity of Pressure-Driven Modeling and Demand-Driven Modeling Steady-State Solutions to Variations in Parameters”

Piller, Olivier; Elhay, Sylvan; Deuerlein, Jochen; Simpson, Angus R.

doi:10.1061/(ASCE)WR.1943-5452.0000813

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May 27, 2017

Erratum for “Local Sensitivity of Pressure-Driven Modeling and Demand-Driven Modeling Steady-State Solutions to Variations in Parameters”

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Authors: Olivier Piller, Sylvan Elhay [email protected], Jochen Deuerlein, and Angus R. SimpsonAuthor Affiliations

Publication: Journal of Water Resources Planning and Management

Volume 143, Issue 8

https://doi.org/10.1061/(ASCE)WR.1943-5452.0000813

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The following corrections should be made to Tables 2 and 3 on page 04016074-3 of the original paper:

1.

In each row, in the denominators of the formulas for the

β_{k}

terms in Table 2, the symbol

\ln^{3} \hat{ζ}

should be replaced with

\ln^{3} \hat{τ}

.

2.

The footnote to Table 2 should have the following definition added to it:

\hat{τ} = b ϵ / D + 5.74 / {4,000}^{9 / 10}

.

3.

In Table 3, the column headed “Diagonal terms in

F

” should have the following corrections made:

a.

In the second row (transitional flow), the term

\frac{9 c}{10} \frac{β_{k}}{D^{2}}

should be replaced with

\frac{9 c}{10} \frac{β_{k}}{θ^{2}}

, and the term

(α_{k} + β_{k} / D)

should be replaced with

(α_{k} + β_{k} / θ)

.

b.

In the third row (turbulent flow), the term

\frac{a_{3} L}{D^{5}} \frac{| q |}{\ln {}^{2}D} (1 + \frac{9 c ρ}{5 D \ln D})

should be replaced with

\frac{a_{3} L}{D^{5}} \frac{| q |}{\ln {}^{2}θ} (2 + \frac{9 c ρ}{5 θ \ln θ})

.

The final tables are as shown.

Table 2. Coefficients of the Cubic Interpolating Spline Defining the Friction Factor for

2,000 < R < 4,000

$k$	$α_{k}$	$β_{k}$
0	$5 / (ξ^{2} \ln^{2} \hat{τ})$	$ζ / (ξ^{3} \ln^{3} \hat{τ})$
1	$0.128 - 12 / (ξ^{2} \ln^{2} \hat{τ})$	$- 5 ζ / (2 ξ^{3} \ln^{3} \hat{τ})$
2	$- 0.128 + 9 / (ξ^{2} \ln^{2} \hat{τ})$	$2 ζ / (ξ^{3} \ln^{3} \hat{τ})$
3	$0.032 - 2 / (ξ^{2} \ln^{2} \hat{τ})$	$- ζ / (2 ξ^{3} \ln^{3} \hat{τ})$

Note: The constants are $ζ = 0.00514215$ , $ξ = - 0.86859$ , and $\hat{τ} = b ε / D + 5.74 / {4,000}^{9 / 10}$ .

Table 3. Diagonal Terms of the Matrix

F

for the Darcy-Weisbach Head-Loss Model

Range of $R$	Diagonal terms in $F$
$R \leq 2,000$ laminar flow	$\frac{a_{1} L}{D^{4}}$
$2,000 < R < 4,000$ transitional flow	$\frac{a_{2} L}{D^{5}} \| q \| \sum_{k = 0}^{3} {\frac{9 c}{10} \frac{β_{k}}{θ^{2}} {\| \frac{D}{Q} \|}^{9 / 10} + (2 + k) (α_{k} + β_{k} / θ)} η^{k}$
$R \geq 4,000$ turbulent flow	$\frac{a_{3} L}{D^{5}} \frac{\| q \|}{\ln {}^{2}θ} (2 + \frac{9 c ρ}{5 θ \ln θ})$

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Journal of Water Resources Planning and Management

Volume 143 • Issue 8 • August 2017

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Received: Mar 21, 2017

Accepted: Mar 29, 2017

Published online: May 27, 2017

Published in print: Aug 1, 2017

Discussion open until: Oct 27, 2017

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Authors

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Olivier Piller

Senior Research Scientist, Irstea, Water Dept., Bordeaux Regional Centre, Cestas F-33612, France.

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Sylvan Elhay [email protected]

Visiting Research Fellow, School of Computer Science, Univ. of Adelaide, SA 5005, Australia (corresponding author). E-mail: [email protected]

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Jochen Deuerlein

Senior Researcher, 3S Consult GmbH, Karlsruhe, Germany; Adjunct Senior Lecturer, School of Civil, Environmental and Mining Engineering, Univ. of Adelaide, SA 5005, Australia.

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Angus R. Simpson

Professor, School of Civil, Environmental and Mining Engineering, Univ. of Adelaide, SA 5005, Australia.

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