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# Conservation of Mass

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

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

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

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