# How is mass flow an inexact differential

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1. Nov 13, 2017 at 2:18 AM

### granzer

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

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?
Won't the mass flow rate in the annulus be equal to (mass flow through the area with radius r2)-(mass flow through the area with radius r1) ie m2-m1?
Also later it goes on to say that the mass flow rate is exact.
Thank you.

2. Nov 13, 2017 at 9:04 AM

### Staff: Mentor

I have no idea why they are making this distinction. Just keep moving on and see if it makes any kind of sense later.

3. Nov 13, 2017 at 9:13 AM

### granzer

@Chestermiller Yes sir, that's what I have been doing. Heat and work are easy to be understood as inexact. But this particular example is difficult to grasp.

4. Nov 13, 2017 at 9:24 AM

### Staff: Mentor

They are trying to say that the three transport quantities heat flux, momentum flux, and mass flux are path-dependent. But, in the case of mass flux, it is usually thought of in terms of diffusion. Heat flux (conductive) is proportional to the temperature gradient, mass flux is proportional to the velocity gradient, and mass flux (diffusion) is proportional to the concentration gradient. This is the analogy they are trying to establish.

Their description here does not work for me either.

5. Nov 13, 2017 at 5:41 PM