Velocity of two-dimensional flow

[glebovg]

If the velocity in a two-dimensional flow is given as $\vec u = \left\langle {u(y),v(y),0} \right\rangle$. Why must $v$ be constant? I am not sure where to start. Can anyone help?

 

[Dick]

If the velocity in a two-dimensional flow is given as $\vec u = \left\langle {u(y),v(y),0} \right\rangle$. Why must $v$ be constant? I am not sure where to start. Can anyone help?

What kind of fluid is it? Is it maybe incompressible? What kind of properties do you know that apply to the velocity field of that kind of fluid?