GATE_AE_2027_MOCK_04_Q45
GATE 2027 Aerospace Engineering All-India Master Mock 04 (Aerospace Structures, Thin-Walled Beams & Aeroelasticity)
NAT · 2 Marks
Aerodynamics & Fluid Mechanics • Basic Fluid Mechanics • Navier-Stokes Equations & Vorticity Dynamics
A flow field has stream function \psi(x, y) = 3x^2 y - y^3. What is the u-velocity component at the point (x, y) = (2, 1)?
Answer Key:
9
Step-by-Step Verified Solution
### Solution: u = d\psi / dy = d(3x^2 y - y^3)/dy = 3x^2 - 3y^2. At (2, 1): u = 3(2^2) - 3(1^2) = 3(4) - 3(1) = 12 - 3 = 9. Correct: 9.