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GATE 2022 MT – Question 45

Transport Phenomena and Rate Processes · Fluid flow and momentum transfer · 2 marks · Multiple select

A fixed nonrotating smooth sphere is in a horizontal, slow, steady inviscid incompressible stream of density $\rho$. Far-field flow near O is fully developed, as shown. B is the sphere centre; line OAB intersects its surface at A. Select all true statements.

Diagram for GATE 2022 MT question 45
  1. Fluid velocity at A is zero
  2. Pressure at A exceeds that at O by $\rho v^2/2$, where $v$ is velocity at O
  3. Fluid moving precisely along OA turns perpendicular to OA to circumvent the sphere
  4. Flow on each side of the central streamline OA is deflected around the sphere

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Show answer and explanation

Correct answer: (A) Fluid velocity at A is zero; (B) Pressure at A exceeds that at O by $\rho v^2/2$, where $v$ is velocity at O; (D) Flow on each side of the central streamline OA is deflected around the sphere

Explanation

A is the upstream stagnation point, so its velocity is zero. Bernoulli between O and A gives $p_A-p_O=\rho v^2/2$. Adjacent streamlines deflect around the sphere. The exact central streamline ends at stagnation and does not make a finite-speed perpendicular turn. Correct choices: **A, B, D**.