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1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 4 FLUID IN MOTIONS

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2 Two Descriptions of Fluid Flow We are interested in the evolution of fluid particle in a space Lagrangian description is to observe the fluid properties at different location following the same particles at different time instant Eulerian description is to observe the fluid properties of different fluid particles passing through the fixed location at different time instant

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3 Lagrangian Description Example When we are driving a car on the road, we are interested in the our car velocity on only. We are not interested in the car velocity distribution on the road. Eulerian description on the car velocity is to observe each car velocity on the different position of the road In this case, we use Lagrangian description on our car velocity is simpler than Eulerian description one

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4 Eulerian Description Example When I am teaching series lectures inside the same classroom, I am interested on students behaviour inside each position of classroom only. I am not interested in each student behaviour outside the classroom, e.g. canteen, street or their house Lagrangian description on the student behaviour is to follow and observe each student at the different position inside the classroom in different lectures at different time instant In this case, we use Eulerian description on our car velocity is simpler than Lagrangian description one

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5 Fluid Flow Description When we are interested on some properties of a group objects in certain domain, Eulerian description is more simple and convenient to express our interest information In fluid mechanics it is usually easier to use the Eulerian method to describe a flow in either experimental or analytical investigation. Except that we are required to know how do each fluid particle interaction with each other. At that time, Lagrangian description is required.

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6 Fluid Flow Video http://web.mit.edu/fluids/www/Shapiro/ncfmf.html

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7 Relation Between Lagrangian and Eulerian Description Under different situation, the given information may be in Lagrangian or in Eulerian forms, we need to know how to transform the given information into our interested one. By chain rule of calculus, these two descriptions have such mathematical relationship: Lagrangian Eulerian

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8 Example 1

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9 Example 2

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