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 = 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.
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.