Part of the mechanics course I'm taking this semester are also fluids, but the material our teacher gave us to this topic is very poor (but unfortunately I haven't found a better source). The problem is that there are many "magic formulas", which come just out of nowhere - without any explanation.(adsbygoogle = window.adsbygoogle || []).push({});

I have a problem with the very first chapter and that is the mass conservation in fluids.

So if we have a fluid in a pipe with constant area S,

fluid has density [tex]\varrho(x,t)[/tex] (depending on time and location), and velocity v(x,t) then the mass of the fluid in volume [tex]V = S*\Delta x[/tex] is [tex]m = S*\Delta x * \varrho[/tex]

And now the formula I don't understand occurs:

[tex]\frac{\partial (\varrho*S*\Delta x)}{\partial t} = \varrho(x,t)*v(x,t)*S - \varrho(x+ \Delta x,t)*v(x+ \Delta x,t)*S[/tex]

Could someone plaese explain me how can we come to that equation?

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# Homework Help: Mass conservation in fluid mechanics

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