Why does cross sectional area of a liquid stream reduces while falling vertically??
The cross-sectional area of a liquid stream decreases while falling vertically due to a phenomenon known as the "Bernoulli's principle." According to Bernoulli's principle, as the speed of a fluid (such as a liquid) increases, its pressure decreases.
When a liquid falls vertically, it gains kinetic energy due to gravitational acceleration. As a result, its velocity increases, and according to Bernoulli's principle, the pressure decreases. To understand why the cross-sectional area decreases, we need to consider the conservation of mass.
The mass flow rate (the amount of liquid passing through a given area per unit of time) must be conserved in a streamline flow. Since the liquid is falling vertically without getting any additional mass, the mass flow rate should remain constant along its path.
As the liquid stream falls and its velocity increases, it needs to pass through a smaller area to keep the mass flow rate constant. This is known as the principle of continuity. According to this principle, the product of the fluid's cross-sectional area and its velocity remains constant in an incompressible fluid.
So, as the liquid stream falls and gains velocity, it must decrease its cross-sectional area to maintain a constant mass flow rate. This reduction in cross-sectional area is a result of the conservation of mass and the principles of Bernoulli and continuity.