Stokes equation in a toy CD hovercraft

• Published in: European journal of physics Vol. 32; no. 1; pp. 89 - 99
• Main Authors: de Izarra, Charles, de Izarra, Grégoire
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.01.2011; Institute of Physics Publishing; Institute of Physics
• Subjects: College Science; Communication, education, history, and philosophy; Equations (Mathematics); Exact sciences and technology; General physics; Mechanics (Physics); Physics; Physics literature and publications; Science Experiments; Science Instruction; Scientific Principles; Surveys and tutorial papers, resource letters; Toys; Undergraduate Students; Fluid mechanics; Higher education; Stokes equation; Reynolds number; Physics; Navier-Stokes equations; Pressure gradients
• ISSN: 0143-0807; 1361-6404
• DOI: 10.1088/0143-0807/32/1/008

This paper deals with the study of a toy CD hovercraft used in the fluid mechanics course for undergraduate students to illustrate the lubrication theory described by the Stokes equation. An experimental characterization of the toy hovercraft (measurements of the air flow value, of the pressure in the balloon and of the thickness of the air film under the hovercraft) allows us to evaluate a reduced Reynolds number R*. Since R* less than 1, it is possible to simplify the Navier-Stokes equation that is reduced to the Stokes equation, on the basis of the lubrication theory. The pressure gradient in the air flow is calculated, allowing us to establish the lifting force applied on the toy hovercraft. In addition, these results are applied to a larger scale hovercraft. (Contains 9 figures.)