# 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 = ρ_{i}v_{i}A_{i}dt - ρ_{o}v_{o}A_{o}dt(1)

where

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

ρ= density (kg/m^{3})

v= speed (m/s)

A= area (m^{2})

dt= an increment of time (s)

If the outflow is higher then 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/m ^{3}* flows into a tank through a pipe of

*50 mm*inside diameter. The velocity 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/m^{3}) (2 m/s) (3.14 (0.05 m)^{2 }/ 4) ((20 min) (60 s/min))

- (1000 kg/m^{3}) (2.5 m/s) (3.14 (0.03 m)^{2 }/ 4) ((20 min) (60 s/min))

= 2590.5 kg

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