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: Graph function help - fluid mechanics/streamlines related

  1. Nov 29, 2006 #1
    Graph function help plz - fluid mechanics/streamlines related

    I'm not too sure whether I should have posted this in the Physics section or in the maths :confused: Please move this topic if its in the wrong place!

    this probably seems like a silly question but is it possible to plot x*y + c on a graph where c = a constant? :confused: I'm working on a question on fluid mechanics where I have to find the streamfunction and plot the stream lines. However I'm in doubt whether i have done the question correctly in the first place.

    Please help!

    1. The problem statement, all variables and given/known data

    For the 2D velocity field u = xi - yj find the streamfunction 'psi' (apologises, I'm not too familiar with Latex)

    2. Relevant equations

    given above

    3. The attempt at a solution

    After partially differentiating and using formulas from my notes, i got psi = x*y + c :confused:
  2. jcsd
  3. Nov 29, 2006 #2


    User Avatar
    Science Advisor

    What do you mean by "plot x*y+ c". That's neither a function nor an equation. If you mean xy= c or xy+ c= 0, then, yes, of course, you can plot it- it's a family of hyperbolas.

    Then [itex]\nabla \psi= x\vec{i}- y\vec{j}[/itex], right?
    [tex]\frac{\partial \psi}{\partial x}= x[/tex]
    [tex]\frac{\partial \psi}{\partial y}= -y[/itex]
    That should be easy to integrate.

    Perhaps I am misunderstanding your "stream function". I get the orthogonal family to xy= C which would be the potential function.
  4. Nov 30, 2006 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You are confusing "stream function" with "velocity potential", HallsofIvy!

    A stream function may always be defined if the velocity field is solenoidal, i.e, [tex]\nabla\cdot{\vec{v}}=0[/tex]
    In the 2-D case, we may define: [tex]\vec{v}=\nabla\times\psi\vec{k}[/tex], where [itex]\psi[/itex] is the scalar stream function.

    The analogue in electro-magnetism is called the magnetic vector potential, I believe..
    Last edited: Nov 30, 2006
  5. Nov 30, 2006 #4


    User Avatar
    Science Advisor

    Very likely- it's been a long time since I have looked at fluid dynamics.

    So the equations are
    [tex]\frac{\partial \phi}{\partial x}= y[/tex]
    [tex]\frac{\partial \phi}{\partial x}= x[/tex]

    Yes, that tells us that [itex]\phi(x,y)= xy+ c[/itex].
    Since the stream lines (again, if I remember correctly!) are the lines on which [itex]\phi[/itex] is a constant they are given by xy+ c= c' or xy= C, the hyperbolas that my family, [itex]x^2- y^2= c[/itex] are orthogonal to.

    elle, perhaps your only problem was not realizing that you get an equation to graph by setting your solution for [itex]\phi[/itex] equal to a constant.
  6. Nov 30, 2006 #5

    ohh yeah! I forgot that its equal to a constant :redface: Thanks guys for the help :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook