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Assessment of Boussinesq Approximation in a Fluid Mechanics Course

Abstract

There is an absolute need for an in-depth coverage of certain important topics in an undergraduate engineering curriculum especially in the area of Thermodynamics and Fluid Mechanics. This need arises basically from the feedback received from the alumni and also from some members of the Industrial Advisory Board. A small group of employers has also indicated that there is a need for increasing the academic rigor in certain courses. The author is of the opinion that all undergraduate engineering students must know, in addition to various other topics, the five theorems that are normally encountered while treating the subject matter of Thermodynamics and Fluid Mechanics. The five theorems are Green’s Theorem, Gauss’ Theorem, Stokes’ Theorem, Buckingham-Pi Theorem and Boussinesq approximation. The author considers this ‘set’ as a part of accommodating academic rigor. The author has tried to meet these needs while he was teaching courses in Thermodynamics and Fluid Mechanics. In this presentation, the author describes how he has tried to incorporate the principles of Boussinesq approximation in a junior level fluid mechanics course. He has also outlined methods to assess students’ knowledge in certain specific areas.

Introduction

Boussinesq approximation is named after the French physicist and mathematician Joseph Valentin Boussinesq for his invaluable contributions in the area of hydraulics and fluid mechanics. Boussinesq was the professor of mechanics at the Faculty of Sciences of Paris, before retiring in 1918.

There are several mathematical models to describe Boussinesq approximation and Boussinesq equations. Boussinesq approximation is normally encountered in three general areas.

1. Buoyancy: Assuming small differences in density of the fluid, one can utilize Boussinesq approximation for determining buoyancy-driven flow calculations.

2. Waves: Assuming gravitational actions, one can utilize Boussinesq approximation for analyzing the propagation of long water waves on the surface of fluid layer.

3. Viscosity: Eddy Viscosity to model Reynold’s Stresses is another area where Boussinesq approximation has helped in Turbulence modeling.

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Narayanan, M. (2010, June), Assessment Of Boussinesq Approximation In A Fluid Mechanics Course Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--17006