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Polar to cartesian coordinates for stream function

  1. Jun 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider a velocity field where the radial and tangenetial components of velocity are V_r=0 and V_theta=cr, respectively, where c is a constant. Obtain the equations of the streamlines.


    2. Relevant equations
    x=rcos(theta)
    y=rsin(theta)


    3. The attempt at a solution
    I know how to obtain the equations of the streamlines. I don't know how to translate the polar coordinates into cartesian. Since V_r=0, wouldn't there be no x-component? But looking at the textbook solution, there is an x component. Any help would be appreciated. Thanks.
     
  2. jcsd
  3. Jun 18, 2011 #2

    tiny-tim

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    hi xzi86! :smile:

    (try using the X2 icon just above the Reply box :wink:)

    Vr = 0 means there is no radial component …

    in which (x,y) direction is the radial direction? :wink:
     
  4. Jun 18, 2011 #3
    x=x(r,[itex]\theta[/itex])=rcos[itex]\theta[/itex]
    y=y(r,[itex]\theta[/itex]=rsin[itex]\theta[/itex]

    You are given

    V[itex]_{r}[/itex]=[itex]\frac{dr}{dt}[/itex]=0

    V[itex]_{\theta}[/itex]=[itex]\frac{d\theta}{dt}[/itex]=cr

    How do you calculate

    V[itex]_{x}[/itex]=[itex]\frac{dx}{dt}[/itex]

    and

    V[itex]_{y}[/itex]=[itex]\frac{dy}{dt}[/itex] ?
     
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