The velocity components in the x and y directions of a

The velocity components in the x and y directions of a two dimensional potential flow are u and v, respectively.
Then , ∂u is equal to
∂x

	∂²φ	+	∂²φ	= 0 ...(i) (Laplace Equation should be satisfied)
	∂x²		∂y²

∴ u = -	∂φ	and v = -	∂φ
	∂x		∂y

⇒	∂u	= -	∂²φ	and	∂v	= -	∂²φ
	∂x		∂x²		∂y		∂y²

Putting values in equation (i), we get

	-∂u		+		-∂v		= 0
	∂x				∂y

⇒	∂u	= -	∂v
	∂x		∂y

Then ,	∂u	is equal to
	∂x