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

1
MECH 221 FLUID MECHANICS(Fall 06/07)Tutorial 4
FLUID IN MOTIONS
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
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
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
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
Fluid Flow Video
http//web.mit.edu/fluids/www/Shapiro/ncfmf.html
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
Example 1
9
Example 2