Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2010
Medium
Velocity vector of a flow field is given as V = 2xy î - x²z ĵ. The vorticity vector at (1,1,1) is
- A4î-ĵ
- B4î-k̂
- Cî-4ĵ
- î-4k̂
Explanation
ω=∇×V. ωx=∂Vz/∂y-∂Vy/∂z=0-∂(-x²z)/∂z=x². ωy=∂Vx/∂z-∂Vz/∂x=0. ωz=∂Vy/∂x-∂Vx/∂y=-2xz-2x. At (1,1,1): ωx=1, ωy=0, ωz=-2-2=-4. So ω=î-4k̂.
Source: GATE ME 2010 (2010)
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