This is a part of the proof of the equation of continuity, my professor included in the lecture slides. Here 'rho' denotes the density of the considered mass. Could you please explain how do we derive "the rate of mass flux across any small element dS" , as given in the image? What does the 'underline v' denote here? Thank you so much!
This is a part of the proof of the equation of continuity, my professor included in the lecture slides. Here 'rho' denotes the density of the considered mass. Could you please explain how do we derive "the rate of mass flux across any small element dS" , as given in the image? What does the 'underline v' denote here? Thank you so much!
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This is a part of the proof of the equation of continuity, my professor included in the lecture slides. Here 'rho' denotes the density of the considered mass. Could you please explain how do we derive "the rate of mass flux across any small element dS" , as given in the image? What does the 'underline v' denote here?
Thank you so much!
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)
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