$u\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}+v\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}=U_0\frac{d{U}_0}{dx}+v\frac{de{l}^{2}u}{del{y}^2}$

This is the Prandtl's Boundary condition. Here v $($the velocity in the y direction$)$ has also been considered. But when we study boundary layer, the y direction is perpendicular to the Surface. The flow we consider is parallel to the Surface and the free stream velocity in the x direction is Uo$.$ Then $,$

$1)$ Is it correct if I say that the flow does not have velocity$($v$)$ in the y direction?

$2)$ If velocity v in the y direction is not present then why do we write v in the Boundary layer equation?