Continuity Equation

Let consider an elementary control volume, whose edges are dx, dy and dz. Let the fluid enter across ABCD with velocity u & density ρ and leaves through EFGH with velocity & density   respectively. Therefore mass entering and leaving to the control volume can be calculated as follows.

• Mass entering = ρu dy dz.
• Mass entering 
• Rate of accumulation = Rate of influx - Rate of Efflux ( or in simple word entring rate – outgoing rate)
• Therefore Rate of accumulation for a point in a flow field =
• Or Using, Rate of influx = Rate of Accumulation + Rate of Efflux 
  Writing the differential equation in all there direction in Rectangular Cartesian Coordinate System. 
  
  
  
  After rearranging the terms