What's the rate of change dm/dt of the mass m(t)?

Gas moves out of a pipe at a rate of v m/s which has a cross-sectional area of A .The density of the gas is p.


Our task is to prove that dm/dt=pAv

 OK lets begin with enthusiasm:


p(density) =mass/volume (we learnes this equation in a lower class)


therefore mass=density x volume


ie m = pV


we already know that volume= area x height 


we already know that height= velocity x time




therefore mass   = density x volume
                           =density x area x height
                           =density x area x velocity x time
                           = p x A x v x t


Therefore dm/dt =p x A x v


THE RATE OF CHANGE IN MASS IS EQUAL TO THE DENSITY TIMES THE CROSS SECTIIONAL AREA TIMES THE VELOCITY .