Irrotational flow (of a magnetic field or incompressible fluid) around a screen with a slot

S.F. Garanin^†, S.D. Kuznetsov
All-Russian Scientific Research Institute of Experimental Physics — Federal Nuclear Centre, prosp. Mira 37, Sarov, Nizhny Novgorod region, 607190, Russian Federation

Problems concerning irrotational flows past obstacles may have physical applications in magneto- and electrostatics, as well as in the description of hydrodynamical flows of incompressible fluids. It is shown that for a magnetic field flow (or a flow of incompressible fluid in the hydrodynamical case) around an ideally conducting (impermeable) screen of width D with a narrow slot of width Δ a substantial flux passes trough the slot, so that, for example, a magnetic field (the velocity in the hydrodynamical problem) averaged over a slot with the width Δ = 0.01 D will be 26 times greater than its far upstream value. The hydrodynamical problem is also formulated for an axisymmetric case for a circular screen and orifice. In this case, if the orifice is small enough, the flux of fluid proves to be proportional to the orifice diameter Δ, whereas fluid speed in the orifice increases as 1/Δ if Δ is decreased, i.e., even faster than in plane geometry.

Keywords: magnetic field, plane problem, axisymmetric problem, screen with a slot
PACS: 02.30.Em, 41.20.Cv, 41.20.Gz, 47.15.Hg, 47.15.km (all)
DOI: 10.3367/UFNe.2020.03.038733
URL: https://ufn.ru/en/articles/2020/10/e/
Web of Science

000604419100005
Scopus

2-s2.0-85099879150
ADS NASA

2020PhyU...63.1037G
Citation: Garanin S F, Kuznetsov S D "Irrotational flow (of a magnetic field or incompressible fluid) around a screen with a slot" Phys. Usp. 63 1037–1042 (2020)

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Received: 31st, January 2020, revised: 28th, February 2020, accepted: 12th, March 2020

Оригинал: Гаранин С Ф, Кузнецов С Д «Обтекание потенциальным течением (магнитным полем или несжимаемой жидкостью) экрана с отверстием» УФН 190 1109–1114 (2020); DOI: 10.3367/UFNr.2020.03.038733

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