The problems of different sections of physics and mechanics share a mathematical model that is based on the Poisson equation with a constant right-hand side and a zero (constant) value of the sought function on the contour of a two-dimensional region. A set of exact solutions to the formulated problem is presented in the "plane" region of certain form to describe the following problems: flow of a liquid in the channel at small Reynolds numbers; motion of an ideal liquid during the rotation of the contour bounding the region; torsion of a rod; deflection of the membrane at the zero displacement on the boundary of the region; heating of the rod. The possibility to construct approximate solutions for certain cross sections of the channel, etc. by using these exact solutions is noted. Examples are given.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 96, No. 1, pp. 225–235, January–February, 2023.
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Moshinskii, A.I. Certain Exact Solutions to the Problem of Liquid Flow in Prismatic Tubes. J Eng Phys Thermophy 96, 224–235 (2023). https://doi.org/10.1007/s10891-023-02679-z
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DOI: https://doi.org/10.1007/s10891-023-02679-z