Conservation of Mass - The Continuity Equation

Law of conservation of mass

The law states that mass can neither be created nor be destroyed. Conservation of mass is inherent to a control mass system (closed system).

• The mathematical expression for the above law is stated as:

∆m/∆t = 0,    where m = mass of the system

• For a control volume (Fig.9.5), the principle of conservation of mass is stated as

Rate at which mass enters = Rate at which mass leaves the region + Rate of accumulation of mass in the region

OR

Rate of accumulation of mass in the control volume
                                                        + Net rate of mass efflux from the control volume = 0      (9.1)

Continuity equation

The above statement  expressed analytically in terms of velocity and density field of a flow is known as the equation of continuity.

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Fig 9.5    A Control Volume in a Flow Field