Question

In a horizontal pipe of non-uniform cross-section, water flows with a velocity of \( 1 \text{ m s}^{-1} \) at a point where the diameter of the pipe is 20 cm. The velocity of water (in m s\(^{-1}\)) at a point where the diameter of the pipe is 5 cm is

• A. 64
• B. 24
• C. 8
• D. 32
• E. 16

Hint:

Velocity increases when cross-sectional area decreases — inverse square relation with diameter.

Answer 1

Answer: (E)

Concept: Continuity equation: \[ A_1 v_1 = A_2 v_2 \] Since $A \propto d^2$, we use: \[ d_1^2 v_1 = d_2^2 v_2 \]

Step 1: Given: \[ d_1 = 20 \text{ cm}, \quad v_1 = 1 \] \[ d_2 = 5 \text{ cm} \]

Step 2: Apply formula: \[ (20)^2 \cdot 1 = (5)^2 \cdot v_2 \] \[ 400 = 25 v_2 \]

Step 3: Solve: \[ v_2 = \frac{400}{25} = 16 \] Final Answer: \[ v_2 = 16 \text{ m/s} \]