Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2009
Medium
Three two-dimensional velocity fields in the xy-plane are given: P. u=2y, v=-3x; Q. u=3xy, v=0; R. u=-2x, v=2y. Which flow(s) should be recommended when the application requires the flow to be incompressible and irrotational?
- AP and R
- BQ
- CQ and R
- R
Explanation
Incompressibility requires ∂u/∂x+∂v/∂y=0: P gives 0+0=0 ✓, Q gives 3y+0≠0 (fails generally), R gives -2+2=0 ✓. Irrotationality requires ∂v/∂x-∂u/∂y=0: P gives -3-2=-5≠0 (fails), R gives 0-0=0 ✓. Only R satisfies both.
Source: GATE ME 2009 (2009)
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