The circulation ‘Γ’ around a circle of radius

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The circulation ‘Γ’ around a circle of radius 2 units for the velocity field u = 2x + 3y and v = 2y is

1. – 6π units
2. – 12π units
3. – 18π units
4. – 24π units

Correct Option: B

^{^→}V = ui + vj
u = 2x + 3y , v = -2y

	∂u	= 3 ,	∂v	= 0
	∂y		∂x

circulation =		∂v	-	∂u		× Area
		∂x		∂y

= (0 - 3) × πR²
= (-3)π × 2²
= – 12π units