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/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

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm