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Triangular duct flow

  1. Dec 11, 2005 #1
    Dear friends,

    Does anybody now how I derive the equation that describes the flow in a triangular duct.
    making the assumptions
    Laminar
    steady
    constant properties
    no slip at walls
    incompressible

    Jaap
     
  2. jcsd
  3. Dec 11, 2005 #2

    Clausius2

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    Science Advisor
    Gold Member

    The equation you shl

    Neglect unsteady term of N-S equations: [tex]0=-\nabla P +\mu\nabla^2\overline{u}[/tex]. This is the equation for viscous and incompressible flow. The main problem you have is to establish a coordinate system. Solving this problem in cylindrical or cartesian coordinates may be a little bit difficult. A nice engineering approach is to calculate the Hydraulic Diameter of the pipe (which holds [tex]\dot {m}=\rho UA[ /tex] assuming a round pipe), and work in cylindrical coordinates with that average diameter.
     
  4. Jan 11, 2006 #3
    Thank you Claussius,

    That is a possibility however, I know there is a closed form analytical solution to this problem the initial N-S equation is correct but the boundary conditions are not so easely defined.

    Jaap
     
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