Question

An in-compressible fluid flows steadily through a horizontal cylindrical pipe. The pipe has radius '\(3R\)' at point A and '\(1.5R\)' at point B, further along the flow direction at the same level. If the velocity at point A is '\(v\)', then that at point B is

• A. \(v\)
• B. \(2v\)
• C. \(3v\)
• D. \(4v\)

Hint:

Use the equation of continuity A1 v1 = A2 v2.

Answer 1

The Correct Option is D

Step 1: Flow Rate:
The volume per second through any cross section is constant: $\pi r_A^2v=\pi r_B^2v_B$.

Step 2: Ratio:
$v_B=v\left(\dfrac{r_A}{r_B}\right)^2=v\left(\dfrac{3R}{1.5R}\right)^2=4v$.

Step 3: Answer:
Option (D).

Final Answer:
Option (D). \[ \boxed{\text{(D) } 4v} \]