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How to decide what is in momentum and what is out momentum in using shell momentum balance? My main motive is to understand why at 25:26 in the balance equation at https://www.youtube.com/watch?v=sMsw8BPT578 the professor is doing $\tau_{xy}|_{x} - \tau_{xy}|_{x+\Delta x} $ and not the other way round?

Even on wikipedia, https://en.wikipedia.org/wiki/Shell_balance it isn't written what is in and what is out. If you consider always that the ground/wall kind of releases momentum then consider this https://www.youtube.com/watch?v=2DHR96x21GY at 17:26 where in is taken as being released from the center of the circular pipe and not the walls.

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  • $\begingroup$ I 'm a 3th year chemical eng, student taking a transport phenomena course.Already done fluid mechanics and heat transfer last year. $\endgroup$ – Vishesh Mangla Sep 12 '20 at 19:42
  • $\begingroup$ will it depend on how the analysis is started? $\endgroup$ – Solar Mike Sep 12 '20 at 20:13
  • $\begingroup$ If you see nptel.ac.in/courses/103/105/103105128 at 22:59 , here the prof is considering in as the region of highest velocity which experiences least viscous force. $\endgroup$ – Vishesh Mangla Sep 12 '20 at 21:13
  • $\begingroup$ On the other hand in the posted question by me, the professor is taking in as where the region of min velocity is there, i.e., near the wall. The concept that I have is momentum flows from a region of high velocity to a region of low velocity. So I 'm confused that if it is like U is the higher velocity in this case than the air-water interface like in other cases. $\endgroup$ – Vishesh Mangla Sep 12 '20 at 21:17
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    $\begingroup$ Please post the whole question here. People who answer your question should not be required to watch an entire lecture video to understand what you are asking about. $\endgroup$ – hazzey Sep 25 '20 at 21:12
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We made an assumption at the start that $ \tau_{xy} $ means momentum flows in x direction which means the "in" is in the x direction. So as long as "in" is taken in the positive x, y, z direction for appropriate coordinates the analysis w'd be right.

Reference Book:

Transport Phenomena

Textbook by Edwin N. Lightfoot, Robert Byron Bird, and Warren E. Stewart

Page 43 enter image description here

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