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An1MuS
Jan3-12, 03:24 PM
I'd like to know the result of deriving both sides of the equation in respect to time

v= \frac {V}{m}

\frac {d}{dt}v=( \frac {d}{dt}) \frac {V}{m}

which gives

\dot v = . . . ?

If you want some backup, this is a very common thermodynamics relation, where V = volume, m = mass and v = specific volume [m3/kg]. In open systems, we want to know mass flow and volumetric flow so we get \dot m [kg/s] and \dot V [m3/s]. I'd like to know if there's such a thing about specific volume as well, and that depends on how you do that derivative.

Best wishes and thanks,

An1MuS

mathman
Jan3-12, 03:40 PM
The quotient rule applies: dv/dt = {mdV/dt - Vdm/dt}/m2