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For a certain two-dimensional incompressible flow, velocity field is given by 2xyi – y² j. The streamlines for this flow are given by the family of curves
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- x²y² = constant
- xy² = constant
- 2xy – y² = constant
- xy – constant
Correct Option: B
v = 2xy i – y²j
| u = | , v = - | δy | δx |
| 2xy = | = 2 | δy |
2xyδy = δψ
on integrating
ψ = xy² + f(x)
= y1 + f'(x)
f'(x) = 0
⇒ f(x)= constant
so ψ= xy² + constant
