Verify if the vector ~u = 6xˆ i+(2y−y2)ˆ j+(6z−x3)ˆ k is (a) incompressible or (b) conservative

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Answer 1

Answer #1

Given

PART A:

This vector field is incompressible only and only if the divergence is equal to zero everywhere.

So, let us calculate the divergence of this vector field.

So, this vector field is not incompressible.

PART B:

This vector field is conservative if the curl is zero.

Now let us calculate the curl of this vector field.

So, this vector field is not conservative.

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Answer 2

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