Fluids doubt water falling from a tap

[rishicomplex]

Fluids doubt...water falling from a tap

When water falls from a tap its area of cross-section is supposed to decrease progressively in accordance with the equation of continuity
A₁V₁=A₂V₂
in order to maintain the conservation of mass.

But using another line of thought, every particle in a cross-section that has just left the tap should undergo identical motion (as they are all subject to the same forces and have identical velocities), so each layer of water should fall down uniformly (without shrinking). Considering a differential cross-sectional element, can anyone explain how it got compressed, ie why some of its molecules decided to become slower and others decided to become faster?

 

[rl.bhat]

Hi rishicpmlex, welcome to PF.

When the water leaves the tap, every particle in the drop accelerates in the downward direction. Due to that its velocity increases causing decreasing the area of cross section.