handout01_09

# 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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