Integral form of momentum equation

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Discussion Overview

The discussion revolves around the derivation of the integral form of the momentum equation, focusing on the interpretation of terms within the equation and the notation used by a teacher in a fluid dynamics class. Participants explore the implications of different derivatives and the logic behind the teacher's approach.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants propose that the first term in the momentum equation should be a partial derivative with respect to time, indicating the rate of accumulation of x-momentum within the control volume.
  • Others argue that the second term represents the net rate of x-momentum leaving the control volume.
  • There is a question regarding the teacher's consistent use of a specific form of the equation, with participants expressing uncertainty about the reasoning behind it.
  • One participant questions how the teacher's equation accounts for the time rate of accumulation of x-momentum and whether it aligns with the conservation of mass equation.
  • Another participant inquires about the units of the term as written by the teacher and whether those units correspond to force.
  • Clarifications are made regarding the notation, with one participant acknowledging a mistake in writing the derivative as partial with respect to x instead of t, based on the teacher's explanation.

Areas of Agreement / Disagreement

Participants express differing views on the correct interpretation of the momentum equation's terms and the notation used. There is no consensus on the reasoning behind the teacher's approach or the implications of the terms in the equation.

Contextual Notes

Participants note that the discussion is influenced by the teacher's unique writing style and the potential for misinterpretation of the notation. There are unresolved questions regarding the units of the terms and their physical significance.

Ali Durrani
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Hello guys!
can i get the derivation for this equation ?

upload_2016-6-25_16-1-0.png
 
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I think the first term should be a partial derivative with respect to time t (not x), and represents the rate of accumulation of x-momentum within the control volume. The second term represents the net rate of x-momentum leaving the control volume.
 
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Chestermiller said:
I think the first term should be a partial derivative with respect to time t (not x), and represents the rate of accumulation of x-momentum within the control volume. The second term represents the net rate of x-momentum leaving the control volume.
yes sir as you said the 1st term should be the partial derivative with respect to time but i don't know why our teacher in the fluid class wrote the equation in this form, and it was not a mistake because he used it again and again, can you explain the logic behind it as he is a very senior teacher and he wouldn't make such a silly mistake
 
Ali Durrani said:
yes sir as you said the 1st term should be the partial derivative with respect to time but i don't know why our teacher in the fluid class wrote the equation in this form, and it was not a mistake because he used it again and again, can you explain the logic behind it as he is a very senior teacher and he wouldn't make such a silly mistake
I stand by what I said. I can't account for what your teacher does. All I can do is confidence in what I am saying.

My questions for you are:

1. How does his equation account for the time rate of accumulation of x momentum within the control volume?

2. When he writes the corresponding equation for the conservation of mass within the control volume, does his equation have a partial derivative with respect to x or a partial derivative with respect to t?
 
Here's a couple of more questions for you:

1. What are the units of the term as your teacher has written it?

2. Are those units of force?
 
So... What are your answers to my questions?
 
sorry i asked him and he said its partial by partial t and not x his writing style is different so i mistakenly wrote it as partial by partial x
 
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Ali Durrani said:
sorry i asked him and he said its partial by partial t and not x his writing style is different so i mistakenly wrote it as partial by partial x
No problem.
 

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