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: Analyze the motion of the water. As a stream of water falls from a faucet, it is accelerated downwards by gravity. This means its speed increases as it descends.
Step 2: Apply the continuity equation for an incompressible fluid. The continuity equation is an expression of the conservation of mass for a fluid. For a steady flow of an incompressible fluid (like water), it takes the form: \[ A_1 v_1 = A_2 v_2 = \text{Constant} \] where \(A\) is the cross-sectional area of the stream and \(v\) is the fluid velocity.
Step 3: Relate the change in velocity to the change in area. Let point 1 be at the faucet and point 2 be some distance below. Due to gravity, \(v_2>v_1\). For the product \(Av\) to remain constant, if the velocity \(v\) increases, the cross-sectional area \(A\) must decrease. A smaller cross-sectional area means the stream becomes narrower. This directly explains the observation. Bernoulli's equation relates pressure, velocity, and height, but the continuity equation is the primary principle explaining the change in shape.