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Abstract

This article considers the oscillatory laminar flow of an incompressible fluid in a rectangular duct and expresses the flow rate due to an oscillatory pressure gradient using a frequency transfer function. For the description of the frequency characteristics, selection of a reference length suitable to the duct cross section is important. The selected reference length in this article is the radius of a circular tube whose flow rate is equal to that of the rectangular duct when the fluids are the same, and applied steady pressure gradients are the same. This reference length makes it easier to distinguish changes in the dynamic characteristics due to magnitude variation of duct cross sections from those due to shape variation of the duct cross sections. Numerical investigation of the exact transfer function reveals that a first-order system accurately approximates the transfer function. The aspect ratio of the rectangle determines the cut-off frequency of the first-order system.

Keywords

Rectangular duct oscillating flow frequency transfer function equal flow radius fluid impedance dimensionless frequency first-order system approximation

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The frequency response of rectangular ducts

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