Streamline flow of a liquid:

Now, according to the law of conservation of mass, the mass of liquid entering at point P must be equal to the mass leaving the point Q because there is no accumulation of mass between the points P and Q in the tube. Therefore, we can write:

ρ a₁ v₁ δt = ρ a₂  v₂  δt

 or, a₁ v₁ = a₂ v₂

or,       a v = constant.

Eq. (1.9) is called the equation of continuity for streamline flow of a liquid. One of the important consequences of the equation of continuity can be obtained if we write Eq. (1.9) as:

v₂   = v₁   a₁/a₂

This implies that if a₂ < a₁ then v₂ > v₁. That is, the velocity of liquid flow increases if the tube becomes narrower and vice-versa. This explains why water from a tube falls at a larger distance if its outlet is made narrower.

An important advancement in the understanding of fluid dynamics was made by Bernoulli. In view of the fact that, like mechanical particles, fluid particles also obey the Newton's laws of motion and Bernoulli employed work-energy principles to investigate behaviour of fluid in motion. This gave rise to the Bernoulli's equation which you will study now.