Module 5: Reynolds Transport Theorem
  Lecture 12: Conservation of mass and examples
 
 
Example 1: Consider a closed tank partially filled with water. In such case air is trapped at the top. Tank is filled with water at the rate of 1m/s through a nozzle of 10 cm inside-diameter and drained from the bottom at the rate of 0.5m/s through a nozzle of 5 cm diameter. Determine the rate of change in the height of water. The diameter of the tank is 5 m.
(Fig. 12b)
Ans: Consider the drawn above. Note that is chosen in such a way that the CS is perpendicular to the inlet and outlet nozzles of the tank.
The LHS term of the Reynolds transport theorem or conservation of mass: