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For a certain two-dimensional incompressible flow, velocity field is given by 2xy î − y² ĵ. The streamlines for this flow are given by the family of curves

1. x²y² = constant
2. xy² = constant
3. 2xy − y² = constant
4. xy = constant

Correct answer: xy² = constant

Solution

The streamlines of a flow are determined by the relationship between the velocity components. In this case, the velocity field indicates that the change in y with respect to x is proportional to y², leading to the conclusion that the product xy² remains constant along the streamlines.

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