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GATE 2021 CE (CE1) – Question 42

Fluid Mechanics · Potential flow, laminar and turbulent flow · 2 marks · Multiple choice

A circular pipe of radius R has axial velocity $V_r=U(1-r^2/R^2)$, with U the centreline maximum. Find the average velocity.

  1. $U/2$
  2. $U/3$
  3. $U/4$
  4. $5U/6$

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Correct answer: (A) $U/2$

Explanation

Average over the cross-section using annular area $2\pi r\,dr$: $\bar V=(2/R^2)\int_0^R U(1-r^2/R^2)r\,dr$. The integral is UR²/4, giving **U/2 (A)**. An unweighted arithmetic average along the radius would be incorrect.