GATE_AE_2027_MOCK_01_Q45 GATE 2027 Aerospace Engineering All-India Master Mock 01 (Foundation & Standard Core Calibration) NAT · 2 Marks
Aerodynamics & Fluid Mechanics • Basic Fluid Mechanics • Incompressible Potential Flow & Stream Functions

A 2D line vortex of strength $\Gamma = 20\pi\text{ m}^2/\text{s}$ is located at the origin in an otherwise quiescent incompressible fluid. What is the induced tangential velocity $v_\theta$ (in m/s) at a radial distance $r = 2.5\text{ m}$?

Answer Key:
4.0

Step-by-Step Verified Solution

### Solution: Induced tangential velocity of a point vortex: $v_\theta = \frac{\Gamma}{2\pi r} = \frac{20\pi}{2\pi \times 2.5} = \frac{20}{5} = 4.0\text{ m/s}$. Correct: 4.0.
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