If an incompressible, non-viscous fluid flows through a tube of non-uniform cross section, the product of the area of cross section and the fluid speed at any point in the tube is constant for a streamline flow.
Let A1 and A2 denote the areas of cross section of the tube where the fluid is entering and leaving. If v1 and v2 are the speeds of the fluid at the ends A and B respectively, and ρ is the density of the fluid, then the liquid entering the tube at A covers a distance v1 in one second.
So volume of the liquid entering per second = A1 × v1
Mass of the liquid entering per second at point A = A1 v1 ρ
Mass of the liquid leaving per second at point B = A2 v2 ρ
Since there is no accumulation of fluid inside the tube, the mass of the liquid crossing any section of the tube must be same. Therefore,
A1 v1 ρ = A2 v2 ρ
A1 v1 = A2 v2
This expression is called equation of continuity.