handout01_09 - MECH 314 Introduction to Fluid Mechanics...

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MECH 314 Introduction to Fluid Mechanics February 16, 2009 American University of Beirut, Spring 2009 Handout # 1 Continuum Viewpoint and the Defining Aspect of a Fluid, and other stuff 1. The concept of a fluid: matter that undergoes continuous deformation under the action of tangential stress. 2. The continuum hypothesis and the underlying assumptions: check the handout on the continuum hypothesis. 3. Flow description: Lagrangian vs. Eulerian. Streamlines, streaklines, and pathlines. Lagrangian description of a fluid flow involves determination or measurement of properties of fluid particles as they move in time. Since fluid particles in general move relative to each other, Lagrangian flow description involves dividing the body of fluid into a large number of particles. Each particles i is then characterized by x i ( t ) , u i ( t ) i ( t ) ,T i ( t ), etc. For most applications, Lagrangian description imposes great difficulties on mathematical analysis. It is however very useful to employ the Lagrangian description in the physical understanding of fluid mechanics by asking questions such as: what are the forces acting on a small fluid particles as it moves? For certain flow conditions, what are the properties that are conserved as the parti- cle moves?. Lagrangian description is also employed in various computational fluid dynamics methods such as vortex methods. The trajectory traversed by a fluid element is a pathline . Alternatively one could describe fluid flow by monitoring the properties at fixed locations. In Eulerian description , all properties such as velocity, temperature, pressure etc. are function of time and space, Π = Π( x ,t ), where x is the position
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handout01_09 - MECH 314 Introduction to Fluid Mechanics...

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