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Application of the duality theory in modeling hydraulic systems with flow regulators

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Abstract

We consider mathematical models of the operation of pipelines with automatic flow regulators installed on several sections. We present a system of equations and inequalities that describes the flow distribution in such pipelines. We prove that the stated system gives optimality conditions for two mutually dual convex programming problems. This enables us to obtain conditions for the unique existence of a solution to this system.

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Authors and Affiliations

  1. Institute of Energy Systems, Siberian Branch of Russian Academy of Sciences, ul. Lermontova 130, P. O. Box 309, Irkutsk, 664033, Russia

    S. P. Epifanov

  2. Irkutsk State University, bul’v. Gagarina 20, Irkutsk, 664003, Russia

    V. I. Zorkal’tsev

Authors
  1. S. P. Epifanov
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  2. V. I. Zorkal’tsev
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Corresponding author

Correspondence to S. P. Epifanov.

Additional information

Original Russian Text © S.P. Epifanov and V.I. Zorkal’tsev, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 9, pp. 76–81.

Submitted by Ya.I. Zabotin

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Epifanov, S.P., Zorkal’tsev, V.I. Application of the duality theory in modeling hydraulic systems with flow regulators. Russ Math. 54, 67–70 (2010). https://doi.org/10.3103/S1066369X10090070

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  • DOI: https://doi.org/10.3103/S1066369X10090070

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