Continuity of velocity at the interface

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Discussion Overview

The discussion revolves around the continuity of velocity at the interface of two fluids in the context of wave transmission, specifically for acoustic waves. Participants explore the implications of velocity discontinuity and seek physical insights into the boundary conditions governing fluid particle motion.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Rahul questions the requirement for velocity continuity at the interface and seeks a physical understanding of the consequences of a discontinuity.
  • One participant argues that a velocity discontinuity would necessitate an impulse to change momentum, which is not available, suggesting that momentum cannot change at the interface.
  • Rahul later requests a practical example of a scenario where velocity discontinuity might occur, indicating curiosity about exceptions to the stated principle.
  • A participant expresses frustration at the request for a practical example after explaining why discontinuity cannot occur, yet acknowledges Rahul's understanding of the concept.
  • Rahul clarifies that he is interested in hypothetical cases where an impulse could lead to a velocity discontinuity, indicating a desire for deeper exploration of the topic.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the possibility of velocity discontinuity at the interface, with some asserting it cannot happen and others exploring hypothetical scenarios where it might occur.

Contextual Notes

The discussion does not resolve the conditions under which velocity discontinuity might occur, nor does it clarify the assumptions behind the boundary conditions being discussed.

SDRK
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Dear experts,

While solving the wave transmission at an interface for an acoustic wave problem, a boundary condition states that the "velocity of a fluid particle at the surface must be continuous". Could you please let me know why is it required, and a physical insight of what would happen if the velocity was discontinuous at the interface.

Thanks,
Rahul
 
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A velocity discontinuity at the interface would imply that a particle moving toward the interface would have a sudden change in momentum at the interface. Where is the necessary impulse going to come from? The required impulse is absent, therefore there can be no change in momentum at the interface
 
Thanks Dr.D for your reply. Could you also give me an example (in practical) of a case where there would be a velocity discontinuity at the interface?

Thanks a lot!
 
After I just explain you why it cannot happen, you now ask for a practical example where it does happen. I give up.
 
Dr.D said:
After I just explain you why it cannot happen, you now ask for a practical example where it does happen. I give up.

Oh, I clearly understood the concept you mentioned...However,I was just curious to know if there would be a case of an impulse at the interface to create discontinuity of velocity.
 

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