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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

    HallsofIvy

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    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?
    So
    [tex]\frac{\partial \psi}{\partial x}= x[/tex]
    and
    [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

    arildno

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    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

    HallsofIvy

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    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]
    and
    [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:
     
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