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Conservation of Mass

The Law of Conservation of Mass states that mass can neither be created or destroyed

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The Law of Mass Conservation states that

"mass can neither be created nor destroyed"

The inflows, outflows and change in storage of mass in a system must be in balance.

The mass flow in and out of a control volume (through a physical or virtual boundary) can for an limited increment of time be expressed as:

dM = ρi vi Ai dt - ρo vo Ao dt                            (1)

where

dM = change of storage mass in the system (kg)

ρ = density (kg/m3)

v = speed (m/s)

A = area (m2)

dt = an increment of time (s)

If the outflow is higher than the inflow - the change of mass dM is negative -

  • the mass of the system decreases

And obvious - the mass in a system increase if the inflow is higher than the outflow.

The Law of Mass Conservation is fundamental in fluid mechanics and a basis for the Equation of Continuity and the Bernoulli Equation.

Example - Law of Mass Conservation

Water with density 1000 kg/m3 flows into a tank through a pipe with inside diameter 50 mm. The velocity of the fluid in the pipe is 2 m/s. The water flows out of the tank through a pipe with inside diameter 30 mm with a velocity of 2.5 m/s.

Using equation (1) the change in the tank content after 20 minutes can calculated as:

dM = (1000 kg/m3) (2 m/s) (3.14 (0.05 m)2 / 4) ((20 min) (60 s/min))

                - (1000 kg/m3) (2.5 m/s) (3.14 (0.03 m)2 / 4) ((20 min) (60 s/min))

    = 2591 kg

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