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

2. 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

3. 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

4. 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

5. 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.

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

7. 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

8. 8 Example 1

9. 9 Example 2