1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Plotting steamlines?

  1. Aug 28, 2012 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations

    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."

    3. 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?
  2. jcsd
  3. Aug 28, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Different values of C correspond go different streamlines. You have to choose C so that the equation holds for x=0, y=0.
  4. Aug 28, 2012 #3
    Oh I see since the question is through the original that would make C=0 right for this equation?

    Which would give me (y^2)/2=tx. Then I just plug in t=0,1,2 into this equation and plot the 3 equations?
  5. Aug 29, 2012 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

  6. Aug 29, 2012 #5
    That would give me
    the equations

    The solutions seem to only have the streamlines plotted in the first quadrant. But doesn't the 2 square root functions exist in both the 1st and 4th quadrant? The first equation y=0 would also exist in all 4 quadrants.
  7. Aug 29, 2012 #6
    In fluid mechanics, the concept of streamlines only applies to steady state flow. This is a non-steadystate problem. In such problems, you can solve for the pathlines of particles, but the pathlines change with time. For your problem, the pathlines are determined by:

    dx/dt = vx = x2y

    dy/dt = vy= x2t

    You need to solve this coupled set of ODEs for sets of initial values of x, y, and t.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook