Take the entire tank as the control volume
(red dashed lines). Applying the conservation of mass equation for this
fixed and nondeforming control volume yields:
The chosen control volume includes both air and water. Note that the
rate of change of the mass of air inside the control volume should
balance the mass of air flowing out, hence the conservation of mass can
be written separately for air and water. For this problem, only the conservation
of mass for water is needed.
For water:
The mass of water within the control volume is given by (assuming constant
ρ)
