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Finding the stream function given velocity components

  1. Apr 12, 2017 #1
    1. The problem statement, all variables and given/known data
    The velocity components in a steady, incompressible, 2-D flow field are

    u = 2y
    v = 4x

    Find the corresponding stream function.

    2. Relevant equations

    u = ∂Ψ/∂y
    v = -∂Ψ/∂x

    3. The attempt at a solution
    I can verify that a stream function exists for this problem because conservation of mass is satisfied. (∂u/∂x + ∂v/∂y = 0)

    After plugging in my values for u and v, I get that Ψ = y2 + f(x) and Ψ = -2x2 + f(y).

    I then equate the 2 equations to give me f(x) + y2 = -2x2 + f(y).

    I then set f(y) to 0, to give me that f(x) = -2x2 - y2.

    I then put f(x) back into my original Ψ equation to give me that Ψ = -2x2 and this is the function that I get for my stream function.

    However, my book is telling me that Ψ = -2x2 + y2 should be my stream function.

    Am I doing something wrong?
    Thanks in advance.
     
  2. jcsd
  3. Apr 13, 2017 #2
    If you take the partial derivatives of your stream function, do you get the correct velocities?
     
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