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Sign convension in shell momentum balance

Physics Asked by Vishesh Mangla on August 12, 2021

I was trying to understanding the shell momentum balance from https://www.youtube.com/watch?v=sMsw8BPT578. At 26:25 if you see the teacher is saying momentum in – out. Although I have seen the videos previous to this in the series from https://nptel.ac.in/courses/103/105/103105128/ but either I missed or the teacher forgot to tell what is in and what is out. It’s simple to understand the sign of gravity but I ‘m not able to understand the signs of momentum. According to me it should have been opposite of what the teacher is doing i.e., $ tau_{xy}|_{x + Delta x} – tau_{xy}|_{x} $ since momentum should flow from higher velocity to lower velocity. I ‘m talking about conductive momentum in x direction.
Please clarify.

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