# Conservation of Mass

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 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/m ^{3}* 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/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))

= 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.

## Related Documents

### Equations in Fluid Mechanics

Equations used in fluid mechanics - like Bernoulli, conservation of energy, conservation of mass, pressure, Navier-Stokes, ideal gas law, Euler equations, Laplace equations, Darcy-Weisbach Equation and more.

### Fluid Flow - Equation of Continuity

The Equation of Continuity is a statement of mass conservation.

### Technical Terms in Fluid Mechanics

Some commonly used technical terms in fluid mechanics.