Question

As water flows from a faucet, stream of water becomes narrower as it descends. The guiding principle for this observation is:

• A. Bernoulli's equation in fluid dynamics
• B. Pascal's law
• C. Continuity equation in fluid dynamics
• D. Archimedes's principle

Hint:

The continuity equation \(Av = \text{constant}\) is a very intuitive principle of fluid flow. It simply means that "what goes in must come out." If you squeeze a hose to make the opening smaller (decrease A), the water must speed up (increase v).

Answer 1

The Correct Option is C

Step 1: Examine water's movement. When water falls from a faucet, gravity accelerates it downward, increasing its speed as it descends.
Step 2: Implement the continuity equation for incompressible fluids. This equation represents mass conservation in a fluid. For steady flow of an incompressible fluid like water, it is expressed as: \[ A_1 v_1 = A_2 v_2 = \text{Constant} \] Here, \(A\) denotes the stream's cross-sectional area, and \(v\) represents the fluid velocity.
Step 3: Connect velocity changes to area changes. Consider point 1 at the faucet and point 2 at a lower position. Due to gravity, \(v_2>v_1\). For the product \(Av\) to remain constant, an increase in velocity \(v\) necessitates a decrease in cross-sectional area \(A\). A reduced cross-sectional area results in a narrower stream, thus directly explaining the observed phenomenon. While Bernoulli's equation relates pressure, velocity, and height, the continuity equation is the fundamental principle explaining the change in shape.