Consider a non-viscous liquid in streamline flow through a tube AB, of varying cross-section. Let A1 and A2 be the area of cross-section at A and B respectively.
The volume of water entering A per second = A1V1
Volume = Area x distance
where V1 is the velocity of the flow of liquid at A
Assuming there is no loss of liquid in tube and for free steady flow,
Mass of liquid entering per second at A
= Mass of liquid leaving per second at B
or AV = constant.
This is the equation of continuity.
