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How is mass flow rate within an annular region of a pipe taken to be an inexact differential?

EDIT:

I read it in Fluid Mechanics textbook by Yunus A. Cengel and John M. Cimbala.

The mass flow rate through the annulus is given to be inexact differential. Why is mass flow through the annulus not equal to $$(m2) ̇-(m1) ̇$$ Given any 2 radius r2 and r1?

Wont the mass flow rate in the annulus be equal to (mass flow in the area with radius r2)-(mass flow in the area with radius r1) ie m2-m1? Also then it goes on to say that the mass flow rate is exact.

Context

GRANZER
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  • I'm wondering if it is not related to the possibility of non-zero curl to the field: https://physics.stackexchange.com/a/75486/520 – dmckee --- ex-moderator kitten Nov 13 '17 at 00:03
  • @GRANZER, Could you provide more context? – stafusa Nov 13 '17 at 00:52
  • @stafusa I read it in Fluid mechanics textbook by Cenge & Cimbala. This is the only book where I could find any resource on it. – GRANZER Nov 13 '17 at 02:00
  • @stafusa You're welcome. Can you help me understand this, please? – GRANZER Nov 13 '17 at 02:19
  • @dmckeeI did go through the link you provided. This question is not related to potential functions and fields. Thank you for your thoughts. – GRANZER Nov 13 '17 at 05:44
  • @GRANZER, This time we'll have to count on the other contributors, as I don't know the answer and I'm too short on time to search for it. Good luck! – stafusa Nov 13 '17 at 07:45
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    Came across the same note on rates dm v. δm The way I had considered it was there is more than one way to get from 10 kg/hr to 20 kg/hr .. running a constant speed pump vs variable speed – ARinLA Aug 11 '18 at 19:08
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    Thus .. a path function where mass rate can vary at constant rate say 10 rpm/min vs . variable rate of 5 rpm/.5min then 15 rpm/.5min. Both paths yield the same mass flow rate – ARinLA Aug 11 '18 at 19:12

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