Conservation of Mass for a Control Volume

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The conservation of mass equation for a control volume is analogous to your checking account.  Your balance is what you started with, plus what you deposited, minus what you withdrew.

Conservation of Mass is one of the fundamental equations of fluid dynamics. In its simplest form, this important equation states that there is no change in mass as a function of time. The conservation of mass equation for a control volume is derived using Reynolds Transport Theorem.

 

The extensive property associated with the conservation of mass equation is the mass, m.  The conservation of mass requires that the mass, m, does not change with time.

                                                            

The corresponding intensive property is obtained by dividing the mass by the mass and multiplying by the density, .  This gives

                                                     

The Conservation of Mass equation for a control volume is obtained using the Reynolds Transport Theorem

                          

 

                              

Mass Flux

Mass Flux

The mass flux is the rate at which mass crosses a surface.

Volumetric Flow Rate

Volumetric Flow Rate

This equation states that the net volumetric flow rate is equal to zero.

Average Velocity

Average Velocity