Question:
An incompressible fluid flows steadily through a cylindrical pipe having radius R at point A and \(\left(\frac{\mathrm{R}}{3}\right)\) at point B further along the direction of flow of liquid. If the velocity at point A is ' V ' then that at point B is
An incompressible fluid flows steadily through a cylindrical pipe having radius R at point A and \(\left(\frac{\mathrm{R}}{3}\right)\) at point B further along the direction of flow of liquid. If the velocity at point A is ' V ' then that at point B is
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Use the equation of continuity A1 v1 = A2 v2 with area proportional to radius squared.
Updated On: Nov 13, 2026
- \(\frac{\mathrm{V}}{9}\)
- \(\frac{\mathrm{V}}{3}\)
- 3 V
- 9 V
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
For an incompressible steady flow \(A_Av_A=A_Bv_B\).
Step 2: Areas
\(A_A=\pi R^{2}\) and \(A_B=\pi\dfrac{R^{2}}{9}\).
Step 3: Calculation
\(v_B=v_A\dfrac{A_A}{A_B}=V\times9=9V\), option (D).
Final Answer:
The velocity at B is nine times V. \[ \boxed{\text{(D) }9V} \]
For an incompressible steady flow \(A_Av_A=A_Bv_B\).
Step 2: Areas
\(A_A=\pi R^{2}\) and \(A_B=\pi\dfrac{R^{2}}{9}\).
Step 3: Calculation
\(v_B=v_A\dfrac{A_A}{A_B}=V\times9=9V\), option (D).
Final Answer:
The velocity at B is nine times V. \[ \boxed{\text{(D) }9V} \]
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