Is a 3d parallel flow necessarily irrotational?

No

Explanation:

We know that

Rationality in 3D flow is given as follows

If ω is equal to zero then flow will be irrotational and if ω is not equal to zero then flow will be rotational .

So if flow is ir-rotational it means that the component of ω in x-direction,in y-direction and in z-direction direction should be zero.

So it is not necessarily that 3D parallel flow will be irrotaional.

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