Question

Water flows at $3~ms^{-1}$ in a horizontal pipe under a pressure of $2\times10^{5}~Nm^{-2}$. The pipe narrows to half its original diameter at one end. The speed of water (in $ms^{-1}$) in this narrow section is ________.

• A. 3
• B. 4
• C. 6
• D. 12
• E. 24

Hint:

When diameter is halved, speed increases by a factor of 4.

Answer 1

The Correct Option is D

Step 1: Concept
Use the equation of continuity: $A_1v_1 = A_2v_2$.

Step 2: Meaning
Area $A$ is proportional to the square of the diameter ($d^2$).

Step 3: Analysis
If diameter is halved ($d_2 = d_1/2$), the area becomes one-fourth ($A_2 = A_1/4$). Substituting into continuity: $A_1 \times 3 = (A_1/4) \times v_2$.

Step 4: Conclusion
$v_2 = 3 \times 4 = 12~ms^{-1}$. Final Answer: (D)