The equation of continuity leads to

Explanation

Consider a liquid flowing through a tube AB of variable area of cross-section as shown in figure
Let ` A_1 , A _ 2 ` be the cross-sectional areas of the tube at A and B and ` v_1 , v_2 ` be the velocities of flow of liquid at A and B respectively. Volume of the liquid flowing per second through ` A= A_1 v_1 `
Mass of liquid flowing per second through ` A = A _ 1 v _ 1 rho _1 `
Where ` rho _1 ` is the density of the liquid at A.
Similarly, mass of the liquid flowing per second through ` B = A _ 2 v_2 rho _ 2 `
where ` rho _ 2 ` is the density of the liquid at B.
According to the law of conservation of mass, mass of liquid entering A per second = mass of liquid leaving B per second
or ` A_1 v _ 1 rho _1 = A_2 v_2 rho _2 ` ...(i)
In case the liquid is incompressible, ` rho _1 = rho _ 2 ` and in that case
` A _ 1 v_1 = A_2 v _ 2 or Av ` = constant ...(ii)
This is known as the Equation of continuity of flow of an incompressible liquid and is a statement of conservation of mass.