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Euler-Lagrange Description Click here for Reynolds Transport Theorem

Key Concept: You have two main options to study fluid motion. In one you follow each

individual fluid particle ˗ the Langrangian Method. The other approach is to investigate what

happens to the fluid at a given location ˗ the Eulerian Method.

In a Nutshell: Both methods of description can be used to characterize fluid dynamics ( includes

linear momentum, angular momentum, mass, and energy). The figures below depict the Lagrangian

method of description on the left, and the Eulerian method of description in the middle. Picture an intersection with cars representing “fluid particles” passing thru the intersection.

In the Lagrangian method you characterize motion of the fluid by following individual fluid

particles such as fluid particles “a” and “c” shown above. Fluid particle “a” enters the

intersection from the right and continues straight through whereas fluid particle “c” enters the

same intersection but exits to the right.

In the Eulerian method you observe fluid particles at a fixed location and view all of them entering

and leaving that location. You will use the Eulerian description to study the dynamics of fluid motion in elementary fluid mechanics.

The Eulerian description gives rise to the definition of a “control surface” (CS) and a “control

volume” (CV) used in finite volume analysis of fluid dynamics. Mass, momentum, and energy

may enter the control volume by passing through the control surface.

Click here to move on to a discussion of the Reynolds Transport Theorem.

Return to Notes on Fluid Mechanics