the proof of "the equation of continuity",
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Can you can explain the proof of "the equation of continuity", in an easy-to-understand manner?
Attached images are the proof my professor gave. I really do not understand all the simple v's , capital v's and all?
Can you kindly explain it in an easy-to-understand manner?
Thank you!

Transcribed Image Text:The equation of continuity - Proof cont...
The rate of outward mass flux across any small element dS of S is
PY •dS
; where the magnitude of dS is equal to the element's area and
we take dS along the outward normal.
Integrating over the whole surface we have:
ev. ds = v. (ov)dV
Rate of mass flux out of V =
pv. dS =
2
(Here, we used Green's formula to convert to a volume integral)

Transcribed Image Text:The equation of continuity - Proof
Consider a volume V bounded by a surface S that is fixed in space.
Then mass inside is given by J„ pdv
a
Rate of decrease of mass in V
a l, pdV = - | CP dv.
1
If mass is conserved, Eqn. 1 must equal to the total rate of mass
flux out of V.
How do we calculate this?
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