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Stokes' and Lamb's viscous drag laws

Eames, I; Klettner, CA; (2017) Stokes' and Lamb's viscous drag laws. European Journal of Physics , 38 (2) , Article 025003. 10.1088/1361-6404/aa5444. Green open access

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Abstract

Since Galileo used his pulse to measure the time period of a swinging chandelier in the 17th century, pendulums have fascinated scientists. It was not until Stokes' (1851 Camb. Phil. Soc. 9 8–106) (whose interest was spurred by the pendulur time pieces of the mid 19th century) treatise on viscous flow that a theoretical framework for the drag on a sphere at low Reynolds number was laid down. Stokes' famous drag law has been used to determine two fundamental physical constants—the charge on an electron and Avogadro's constant—and has been used in theories which have won three Nobel prizes. Considering its illustrious history it is then not surprising that the flow past a sphere and its two-dimensional analog, the flow past a cylinder, form the starting point of teaching flow past a rigid body in undergraduate level fluid mechanics courses. Usually starting with the two-dimensional potential flow past a cylinder, students progress to the three-dimensional potential flow past a sphere. However, when the viscous flow past rigid bodies is taught, the three-dimensional example of a sphere is first introduced, and followed by (but not often), the two-dimensional viscous flow past a cylinder. The reason why viscous flow past a cylinder is generally not taught is because it is usually explained from an asymptotic analysis perspective. In fact, this added mathematical complexity is why the drag on a cylinder was only solved in 1911, 60 years after the drag on a sphere. In this note, we show that the viscous flow past a cylinder can be explained without the need to introduce any asymptotic analysis while still capturing all the physical insight of this classic fluid mechanics problem.

Type: Article
Title: Stokes' and Lamb's viscous drag laws
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6404/aa5444
Publisher version: https://doi.org/10.1088/1361-6404/aa5444
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Social Sciences, Science & Technology, Physical Sciences, Education, Scientific Disciplines, Physics, Multidisciplinary, Education & Educational Research, Physics, fluid mechanics, low Re flows, drag, CHARGE, SPHERE, MOTION, FLOW
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Mechanical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/10073838
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