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Velocity vector of a flow field is given as = 2xyî - x²zĵ. The vorticity vector at (1, 1, 1) is
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- 4î - ĵ
- 4î - k̂
- î - 4ĵ
- î - 4k̂
Correct Option: D
v = 2xyi – x 2zj
Velocity of a vector = ∇ × v
= î | 0 - | ( - x²z) | - î | 0 - | (2xy) | - k̂ | 0 - | (-x²z) - | (2xy) | ||||||||||
δz | δz | δx | δy |
= î(-x²) + k̂(-2 × z - 2X)
At(1 , 1 , 1),
∇ × v = î + k̂ (-2 -2) = i - 4k