Triangular duct flow

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
 

Clausius2

Science Advisor
Gold Member
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jaap de vries said:
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
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.
 
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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