Local theory of parallel approach of plates in an incompressible liquid
A flow of an incompressible liquid in a thin layer between two approaching disks or plates located in parallel, at the final stage of their symmetrical approach, is considered. It is assumed that the velocity of the body is assigned as a function of time. An inspection analysis of the problem has been made: the types of flows depending on the law of approaching plates and the conditions under which the pressure in the layer and, consequently, the acting forces increase infinitely have been determined. Approximate solutions in the plane and axisymmetric cases are suggested. Exact solutions have been obtained for infinitely small and infinitely high Reynolds numbers.
Keywordsincompressible liquid law of approaching plates viscous flow regime highly viscous flow regime inviscid flow regime
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- 1.M. G. Kotik, Dynamics of the Take-Off and Landing of Aeroplanes [in Russian], Mashinostroenie, Moscow (1981).Google Scholar
- 2.G. Yu. Stepanov, Hydrodynamic Theory of Air-Cushion Vehicles [in Russian], Mashgiz, Moscow (1963).Google Scholar
- 3.L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 6, Hydrodynamics [in Russian], Nauka, Moscow (1986).Google Scholar
- 4.G. K. Batchelor, An Introduction to Fluid Dynamics, Univ. Press, Cambridge (1970).Google Scholar
- 5.A. M. Vinogradov and I. S. Krasil’shchik, Symmetries and Conservation Laws of the Equations of Mathematical Physics [in Russian], Faktorial, Moscow (2005).Google Scholar
- 6.L. I. Sedov, Similarity and Dimensionality Methods in Mechanics [in Russian], Nauka, Moscow (1977).Google Scholar
- 7.A. F. Sidorov, Mathematics, Mechanics, Selected Works [in Russian], Fizmatlit, Moscow (2001).Google Scholar
- 8.H. Lugt, Vortex Flow in Nature and Technology, J. Wiley, New York (1983).Google Scholar
- 9.R. Berker, Integration des equations du movement d‘un fluide visqueux incompressible. Handbuch der Physik, Springer, Berlin (1963), Vol. VIII/2.Google Scholar
- 10.A. G. Terent’ev, Nonstationary motion of bodies in a fluid, in: A. A. Barmin (Ed.), Contemporary Mathematical Problems of Mechanics and Their Application [in Russian], Tr. Mat. Inst. im. V. A. Steklova, Nauka, Moscow (1989), pp. 182–191.Google Scholar