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

Mass flux is defined as the rate of mass flow per unit area Let the rate of mass flow be…

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!