Discussion of “Jacobian Matrix for Solving Water Distribution System Equations with the Darcy-Weisbach Head-Loss Model” by Angus Simpson and Sylvan Elhay

Brkić, Dejan

doi:10.1061/(asce)hy.1943-7900.0000529

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…Mathematical interpretation of the problem from both papers stands, but at the same time, everybody has to be aware that the Hazen-Williams equation used in both papers is obsolete and hence should not be used (Liou 1998;Brkić 2012c;Simpson and Elhay 2012). Zero flow can occur when the Hazen-Williams formula is used because the coefficient is always independent of flow.…”

Section: Zero Flow In the Hazen-williams Modelmentioning

confidence: 99%

“…In contrast, the zero-flow problem can occur when the DarcyWeisbach formula is used only if laminar flow takes place Simpson and Elhay 2011;Brkić 2012c). This is because the resistance is independent of flow when the DarcyWeisbach formula is in use only in the case of a laminar flow regime.…”

Section: Zero Flow In the Darcy-weisbach Modelmentioning

confidence: 99%

“…It is true that laminar flow resistance in the Darcy-Weisbach interpretation is a constant for a single pipe Simpson 2011, 2012;Brkić 2012c). This means that flow resistance, r ≠ rðλÞ, in the laminar regime does not depend on the value of the Darcy friction factor, λ (for the laminar regime, the Darcy friction factor can be calculated as λ ¼ 64=R, where R is the dimensionless Reynolds number).…”

Section: Analogy With Electrical Networkmentioning

confidence: 99%

“…The argument that the Hazen-Williams model can be used because it has been in common use for a very long time (Simpson and Elhay 2012) simply does not stand. The fact that the Hazen-Williams model is used for calculation in EPANET is also avoidable because this software equally allows the use of the Darcy-Weisbach model Brkić 2012c). Because the Darcy-Weisbach model with the Colebrook formula for the friction factor is theoretically more sound (Brkić 2011c(Brkić , 2012b, the use of the Hazen-Williams equation is strongly discouraged.…”

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Discussion of “Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems” by Nikolai B. Gorev, Inna F. Kodzhespirov, Yuriy Kovalenko, Eugenio Prokhorov, and Gerardo Trapaga

Brkić¹

2017

Preprint

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The authors of the discussed paper show a possible strategy for dealing with zero flows in solving the nonlinear equations for water distribution systems when the Hazen-Williams equation is used. Recently, Elhay and Simpson (2011) presented a similar method for solution of the zero-flow problem when the Hazen-Williams model is used, but they also explain and give a solution for the possible problem with zero flow when the Darcy-Weisbach model is used. In this discussion, a few simple remarks on how to avoid the zero-flow problem in a network of pipes will be highlighted. Also, possible physical interpretation related to the problem will be explained. Zero Flow in the Hazen-Williams ModelBoth contributions, by the authors of the original paper and by Elhay and Simpson (2011), to the solution of the zero-flow problem when the Hazen-Williams model is used cannot be disputed. Mathematical interpretation of the problem from both papers stands, but at the same time, everybody has to be aware that the Hazen-Williams equation used in both papers is obsolete and hence should not be used (Liou 1998;Brkić 2012c;Simpson and Elhay 2012). Zero flow can occur when the Hazen-Williams formula is used because the coefficient is always independent of flow. The argument that the Hazen-Williams model can be used because it has been in common use for a very long time (Simpson and Elhay 2012) simply does not stand. The fact that the Hazen-Williams model is used for calculation in EPANET is also avoidable because this software equally allows the use of the Darcy-Weisbach model Brkić 2012c). Because the Darcy-Weisbach model with the Colebrook formula for the friction factor is theoretically more sound (Brkić 2011c(Brkić , 2012b, the use of the Hazen-Williams equation is strongly discouraged. Finally, the Darcy-Weisbach model can also be used for calculation of gas distribution networks, whereas the Hazen-Williams model cannot be used in any circumstances (Brkić 2009(Brkić , 2011a. Zero Flow in the Darcy-Weisbach ModelIn contrast, the zero-flow problem can occur when the DarcyWeisbach formula is used only if laminar flow takes place Simpson and Elhay 2011;Brkić 2012c). This is because the resistance is independent of flow when the DarcyWeisbach formula is in use only in the case of a laminar flow regime. So, knowing that laminar flow can occur only rarely and only in a few pipes of a water distribution network, calculation for these pipes should be performed in the same way as for the other pipes in which turbulent flow takes place. Further calculation with this assumption will not introduce significant error in the final result. Existence of pipes with laminar flow only means that the model of the network is not rationally planned. This subsequently means that diameters of these pipes have to be changed. The network should be calculated for maximum possible nodal demands, which means that the network is rationally planned only if turbulent flow takes place in all pipes. Analogy with Electrical NetworksIt is true that laminar flow resist...

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Section: Zero Flow In the Hazen-williams Modelmentioning

confidence: 99%

Section: Zero Flow In the Darcy-weisbach Modelmentioning

confidence: 99%

Section: Analogy With Electrical Networkmentioning

confidence: 99%

mentioning

confidence: 99%

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Discussion of “Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems” by Nikolai B. Gorev, Inna F. Kodzhespirov, Yuriy Kovalenko, Eugenio Prokhorov, and Gerardo Trapaga

Brkić¹

2017

Preprint

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“…Similar principle applies as in the original Hardy Cross method, but only with opposite approach. Still, as an intermediate step, correction of pressure has to be calculated [12][13][14] (in the original method by Hardy Cross this is correction of flow [15][16][17]), and then after that, pressure as a final result of iteration has to be calculated using complex algebraic rules. Pressure can be expressed in different quantities, such lengths of water elevation or similar.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Iterative Method for Looped Pipe Network Hydraulics

Brkić¹,

Praks²

2019

Preprint

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Original and improved version of the Hardy Cross iterative method with related modifications are today widely used for calculation of fluid flow through conduits in loops-like distribution networks of pipes with known node fluid consumptions. Fluid in these networks is usually natural gas for distribution in the municipalities, water in waterworks or hot water in district heating system, air in the case of ventilation systems in buildings or mines, etc. Since, the resistances in these networks depend of flow, problem is not linear like in electrical circuits, and iterative procedure must be used. In both version of the Hardy Cross method, in original and in the improved one, initial results of calculation in iteration procedure is not flow, but rather the correction of flow. Unfortunately, these corrections should be added to or subtracted from a flow calculated in previous iteration according to complicate algebraic rules. After the here presented node-loop method, final results in each of the iterations is flow directly rather than flow correction. In that way complex algebraic scheme for sign of flow correction is avoided, while the final results still remain unchanged. Numbers of required iterations for the same results are comparable with the improved Hardy Cross method.All methods from this paper assume equilibrium between pressure and friction forces in steady and incompressible flow. As a result, they cannot be successfully used in unsteady and compressible flow calculations with large pressure drop where inertia force is important. Gas flow in a municipal distribution network [5], air flow in a ventilation system in buildings and mines [6], and of course water flow in waterworks [7] or district heating systems [8] and cooling systems [8] can be treated as incompressible flow since the pressure drop in these kinds of networks are minor even to compress significantly natural gas or air. The same applies to pipelines for distribution of mixed natural gas and hydrogen [9]. Overview of existing methods for calculation of flow distribution in a looped network of pipes Loop-oriented methods; Original and improved Hardy Cross methodThe Hardy Cross method [1] introduced in 1936 is the first useful procedure for the calculation of flow distribution in looped networks of pipes. Further step was made by introduction of the modification in the original Hardy Cross method in 1970 by Epp and Fowler [2]. The original Hardy Cross method [1] as a sort of single adjustment method, first of all, as an intermediate step in calculation, determines correction of flow for each loop independently and then applies this corrections to compute new flow in each conduit. It is not efficient as the improved Hardy Cross method [2,3] that considers entire system simultaneously. The improved Hardy Cross method [2], still firstly as an intermediate step, determines corrections for each loop but treated all network system simultaneously, and then applies this correction to compute new flow in each conduit such as in the original version [1...

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Planning the restoration of membranes in RO desalination using a digital twin

Rooij

Scarf

2021

Desalination

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Discussion of “Jacobian Matrix for Solving Water Distribution System Equations with the Darcy-Weisbach Head-Loss Model” by Angus Simpson and Sylvan Elhay

Cited by 9 publications

References 12 publications

Discussion of “Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems” by Nikolai B. Gorev, Inna F. Kodzhespirov, Yuriy Kovalenko, Eugenio Prokhorov, and Gerardo Trapaga

Discussion of “Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems” by Nikolai B. Gorev, Inna F. Kodzhespirov, Yuriy Kovalenko, Eugenio Prokhorov, and Gerardo Trapaga

An Efficient Iterative Method for Looped Pipe Network Hydraulics

Planning the restoration of membranes in RO desalination using a digital twin

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