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Unsteady draining flows from a rectangular tank

journal contribution
posted on 2023-05-16, 19:40 authored by Lawrence ForbesLawrence Forbes, Hocking, GC
Two-dimensional, unsteady flow of a two-layer fluid in a tank is considered. Each fluid is inviscid and flows irrotationally. The lower, denser fluid flows with constant speed out through a drain hole of finite width in the bottom of the tank. The upper, lighter fluid is recharged at the top of the tank, with an input volume flux that matches the outward flux through the drain. As a result, the interface between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain hole. However, waves are present at the interface, and they have a strong effect on the time at which the interface is first drawn into the drain. A linearized theory valid for small extraction rates is presented. Fully nonlinear, unsteady solutions are computed by means of a novel numerical technique based on Fourier series. For impulsive start of the drain, the nonlinear results are found to agree with the linearized theory initially, but the two theories differ markedly as the interface approaches the drain and nonlinear effects dominate. For wide drains, curvature singularities appear to form at the interface within finite time. © 2007 American Institute of Physics.

Funding

Australian Research Council

History

Publication title

Physics of Fluids

Volume

19

Issue

8

Pagination

082104

ISSN

1070-6631

Department/School

School of Natural Sciences

Publisher

American Institute of Physics, Circulation and Fulfillment Division

Place of publication

Melville, USA, NY

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the physical sciences

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