Rate of Flow of Liquid:
For streamlining the flow of a perfectly incompressible liquid, the amount of liquid flowing through any cross-section of a tube in a given time interval remains constant.
The rate of flow of a liquid through a tube means the volume of liquid flowing through any cross-section of the tube per second.
Suppose a liquid flows through a tube of the cross-sectional area a with a uniform velocity v. The volume of liquid flowing through any cross-section of the tube per second is equal to the volume of a cylinder of length v and cross-sectional area α.
∴ The volume of liquid flowing per second
= the rate of flow of the liquid
= velocity of flow x area of cross-section of the tube
= vα
Therefore, the mass of liquid flowing per second
= velocity of flow x area of cross-section of the tube x density of the liquid
= vαρ [ρ = density of the liquid]
Equation of Continuity:
For a streamline flow of a fluid (liquid or gas) through a tube, the mass of the fluid flowing per second through any cross-section of the tube remains constant. This is known as the equation of continuity.