In a two-dimensional steady flow field, in a certain region

In a two-dimensional steady flow field, in a certain region of the x-y plane, the velocity component in the x-direction is given by
v_x = x² and the density varies as ρ = 1 .
x

Which of the following is a valid expression for the velocity component in the y-direction, v_y?

Continuity equation

∂	(ρv_x)	∂	(ρv_y) = 0
∂x		∂y

⇒	∂	(x) +	∂		1	.v_y		= 0
	∂x		∂y		x

⇒ 1 +	∂		v_y		= 0
	∂y		x

⇒	∂		v_y		= −1
	∂y		x

⇒ v_y = – xy

v_x = x² and the density varies as ρ =	1	.
	x