Deriving Equation for Triangular Duct Flow

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SUMMARY

The discussion focuses on deriving the equation for flow in a triangular duct under specific assumptions: laminar, steady, constant properties, no slip at walls, and incompressible flow. The Navier-Stokes equations are referenced, particularly the term for viscous and incompressible flow, which simplifies to 0 = -∇P + μ∇²u. The conversation highlights the importance of establishing an appropriate coordinate system, suggesting cylindrical coordinates and the calculation of hydraulic diameter as effective methods for solving the problem.

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jaap de vries
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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
 
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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.[/tex]
 
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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