It is demonstrated that for kinematically similar potential flows of an ideal liquid, the ratio of the velocities is inversely proportional to the ratio of the areas of the corresponding equipotential surfaces S 1/S 2 = K v , and directly proportional to the ratio of the flows. In that case when the flow rates of two flows are equal, the function of the velocity potential and the velocity of one flow can be expressed in terms of these characteristics multiplied by the dimensionless coefficient K v — the velocity correction of the other flow. Using the velocity correction K v , the flow caused by a cylinder flow of finite length, which is placed on an impervious cylinder in an infinite space filled with an ideal liquid is investigated in a cylindrical coordinate system. Analytical relationships are derived for the equipotential surfaces, and the flow and velocity surfaces; examples of the analysis are cited.
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L. G. Loitsyanskii, Fluid and Gas Mechanics [in Russian], Nauka, Moscow (1970).
I. E. Mikhailov, “A three-dimensional linear flow of finite length with uniform intensity distribution over he length,” Gidrotekh. Stroit., No. 4, 20 – 26 (1014).
I. E. Mikhailov, “Spatial linear flows of finite length with nonuniform intensity distribution,” Vestn. MGSU, No. 2, 164 – 170 (2014).
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Translated from Gidrotekhnicheskoe Stroitel’stvo, No. 2, February 2015, pp. 32 – 44.
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Mikhailov, I.E. New Approach to Investigation of Potential Flows with No Analytical Expression of the Velocity-Potential Function. Power Technol Eng 49, 110–118 (2015). https://doi.org/10.1007/s10749-015-0583-5
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DOI: https://doi.org/10.1007/s10749-015-0583-5