The relation that must hold for the flow to be irrotational

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The relation that must hold for the flow to be irrotational is

1. ∂u − ∂v = 0
  ∂y ∂x
2. ∂u = ∂v
  ∂x ∂y
3. ∂²u + ∂²v = 0
  ∂x² ∂y²
4. ∂u = − ∂v
  ∂y ∂x

Correct Option: A

Let us consider a steady two dimensional flow of an ideal fluid in a rectangular cartesian coordinate system. The velocity field is given by,
V = i^→ u t j^→ v
Hence the condition of irrotationality is

⇒	∂v	−	∂u	= 0
	∂x		∂y

∂²u	+	∂²v	= 0
∂x²		∂y²