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: Are the emergency responders using an Eulerian or Lagrangian approach? Are the engineers are using an Eulerian or Lagrangian approach?

Explanation / Answer

a. Emergency responders are using Eulearian method since they are watching a specific point ( leading edge of the spill ) at a still point.

b. Engineers are using Lagragian apporach as they are visualising the complete flow of gasoline at all points as space and time flows, also they are measuring parameters like velocities at each location.

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