The velocity field in a flow is given by V = (x^2)*yi + (x^2)*tj. (a) Plot the streamline through the origin at times t = 0, t = 1, and t = 2. (b) Do the streamlines plotted in part (a) coincide with the path of particles through the origin? Explain.
i&j are directional vectors.
Providing this just in case you guys haven't heard of stream lines. "A streamline is a line everywhere tangent to the velocity vector at a given instant."
The Attempt at a Solution
dx/u=dy/v (equation from streamline from Fluid mechanics textbook)
where u=x^2 * y
After plugging those in and differentiating I get (y^2)/2=tx+C
where C is a constant.
My problem is I don't know how to go about plotting "the streamline through the origin at t=0,1,2."
Do I plug the 3 t's into the equation 3 times and plot those 3 equations I get? If so, how do I get C?