Module 5: Reynolds Transport Theorem
  Lecture 12: Conservation of mass and examples
 
 
Conservation of mass
N = property =M; Therefore,  
Apply Reynold’s Transport Theorem:
(Fig. 12a)
  (Particle-mass cannot be created or destroyed)
The 1st term of the right-hand-side is zero:  particle-mass cannot be created or destroyed.
Therefore,  : conservation of mass equation
  • Note that  of a fluid in a CV may change with time, for example, in a tank filled with air and water. If water is drained out,  of the mixture (air + water) will vary with time. Message: Be careful while evaluating the integral, whether  under evaluation refers to the density of a pure fluid or fluids-mixture.