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A model of liquid level measurements

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Abstract

A model of measuring the level of a viscous incompressible liquid in a tank as based on the liquid level in a measuring tube is investigated. The tank is in the field of gravity, and the tank liquid level varies according to some law. As a result, a Dirichlet boundary value problem for a nonlinear integrodifferential equation of parabolic type is obtained. A global existence and uniqueness theorem is proved for a weak solution of the problem. In the case of a tank level decreasing linearly with time, it is shown numerically that the liquid level in the measuring tube oscillates with a decaying amplitude with respect to the tank level.

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Authors and Affiliations

  1. Samara State University, Samara, 443090, Russia

    O. P. Filatov

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  1. O. P. Filatov
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Correspondence to O. P. Filatov.

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Original Russian Text © O.P. Filatov, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 12, pp. 2115–2124.

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Filatov, O.P. A model of liquid level measurements. Comput. Math. and Math. Phys. 56, 2084–2093 (2016). https://doi.org/10.1134/S0965542516120095

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  • DOI: https://doi.org/10.1134/S0965542516120095

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