Path Lines

What is a path line?

A path traversed by a given fluid parcel. It is analogous to parcel trajectory.

Path lines are defined like this: $\frac{dx}{dt}=U\left(x,y,t\right)$

$\frac{dy}{dt}=V\left(x,y,t\right)$

For steady flow, $V\ne f\left(t\right)$ or V is not a function of time