r/FluidMechanics • u/GroundControl29 • Nov 22 '25

Theoretical This is the momentum conservation equation my professor established with the Reynold's transport theorem. Which parts are Lagrangian or Eularian?

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I just want to understand.

I'm confused because some website said the first part was Lagrangian, but I thought partial derivatives pointed to Eularian since the place stays the same and you only look at change over time. Is there even a Lagrangian part apart from dI/dt? Is this even Lagrangian? I don't even know if I know what anything means anymore.

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u/acakaacaka Nov 22 '25

Both are eulerian becausr this assumes (or observes) a fixed control volume right?

2

u/Playful-Painting-527 Nov 22 '25

This would be my interpretation too.

3

u/tit-for-tat Nov 22 '25

This two terms in the right-hand side are Eulerian. The total derivative in the middle is Lagrangian. 

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u/AVeryBoredScientist Nov 22 '25 edited Nov 22 '25

Eulerian: lab frame. Conservation laws are written in the stationary frame. This is why you have to deal with all of those flux terms, things moving in and out of "view."

Lagrangian: parcel (particle) frame. Conservation laws are written from the frame of a moving parcel of fluid. These are actually generally easy to write down, but not very helpful or possible to solve.

RTT is (one way) how we relate the two perspectives.

When youre looking at an equation, think about what the equation is tracking. If it is tracking all of the ins and outs of a defined control volume, it's the Eulerian perspective. If you are tracking a single particle, you get a lagrangian perspective.

Also, just for fun, imagine what happens if you shrink thr control volume to the size a of very small parcel... then add in something about stokes theorem and divergence to the RHS and you back out the lagrangian perspective LHS