Equation of Continuity:
The equation of continuity for a flowing fluid is essentially a consequence of the conservation of mass. For appreciate what does conservation of mass mean for fluid in motion, now let us consider a pipe filled fully with an incompressible fluid. If more fluid enters the pipe from one end, an equal amount must leave from the other end, that is, a mass of the fluid within the pipe is conserved.
Figure: Liquid Flowing through a Tube of Different Cross-sectional Areas
To obtain the equation of continuity, consider a tube that has various areas of cross-sections a1 and a2 at points P and Q respectively (Figure 10). Let a liquid flowing through this tube has velocities v1 and v2 respectively at points P and Q. The distance travelled by a particle of the liquid crossing point P in a small time interval δt is v1 δt . Considering all the particles crossing point P in this time interval δt, we can write the volume of liquid crossing point P as a1 v1 δt.