A flow velocity field V: V (x,y) for a fluid is represented by V = 3 î + (5x) ĵ. In the context of the fluid and the flow, which one of the following statements is CORRECT?

The fluid is incompressible and the flow is rotational.
The fluid is incompressible and the flow is irrotational.
The fluid is compressible and the flow is rotational.
The fluid is compressible and the flow is irrotational.

Correct answer: The fluid is incompressible and the flow is rotational.

Solution

div V = d(3)/dx + d(5x)/dy = 0, so the fluid is incompressible. curl_z = d(5x)/dx - d(3)/dy = 5 != 0, so the flow is rotational. Hence incompressible and rotational, option (a).

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