The x component of velocity in a two dimensional incompressible

The x component of velocity in a two dimensional incompressible flow is given by u = 1.5 x. At the point (x, y) = (1, 0), the y component of velocity v = 0. The equation for the y component of velocity is

Apply continuity equation (2D, incompressible flow)

∂u	+	∂v	+	∂w	= 0
∂x		∂y		∂z

⇒	∂	(1.5x) +	∂v	+ 0 = 0
	∂x		∂y

⇒ 1.5 +	∂v	= 0
	∂x

∴ ∂v = - 1.5 ∂y
Integrate both sides,
∫ dv = -1.5∫ dy
⇒ v = -1.5y + c
At (x, y), = (1, 0), y component is zero
⇒ 0 = 1.5 × 0 + c
∴ c = 0
∴ v = – 1.5y