Deriving Equation for Triangular Duct Flow

[jaap de vries]

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]

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: $$0=-\nabla P +\mu\nabla^2\overline{u}$$. 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.

 

[jaap de vries]

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