The Law of Mass Conservation states that
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)
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 then the inflow - the change of mass dM is negative -
And obvious - the mass in a system increase if the inflow is higher than the outflow.
Water with density 1000 kg/m3 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/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)
= 2590.5 kg