There is a gasoline spill in a major river. The mayor of a large downstream city

Question

There is a gasoline spill in a major river. The mayor of a large downstream city demands an estimate of how many hours it will take for the spill to get to the water supply plant intake. The emergency responders measure the speed of the leading edge of the spill. Meanwhile, environmental engineers at the local university employ a computer model, which simulates the velocity field for any stage of the river and for all locations (including steep narrow canyon sections with fast velocities and an extremely wide reach with slow velocities). Compare these two mathematical approaches and explain: a. Are the emergency responders using an Eulerian or Lagrangian approach? Are the engineers are using an Eulerian or Lagrangian approach?

Explanation / Answer

Here is the difference between Lagrangian and Eulerian Approaches:

Since emergency responders measure the speed of leading edge of the spill (i.e. they are focusing on the motion of fluid as the spill passes through space in time) hence they are using Lagrangian Approach.

Since environmental engineers at the university observe the the velocity at different locations as the time passes, therefore, they are using Eulerian approach.

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