Navier-Stokes equations for unique flow through a rectangular diverging pipe

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SUMMARY

The discussion focuses on developing a mathematical model for fluid flow through a diverging square pipe, specifically addressing the Navier-Stokes equations. The scenario involves a uniform, laminar flow entering a section of the pipe that expands in a 1:4 ratio. Key assumptions include steady state, incompressibility, and uniform flow, although the user expresses uncertainty about handling flow separation at the divergence. The need for validation of these assumptions is emphasized, highlighting the complexities of modeling such flow dynamics.

PREREQUISITES
  • Understanding of Navier-Stokes equations
  • Knowledge of fluid dynamics principles
  • Familiarity with laminar flow characteristics
  • Concept of flow separation in fluid mechanics
NEXT STEPS
  • Research techniques for simplifying Navier-Stokes equations in fluid dynamics
  • Study flow separation phenomena in diverging pipes
  • Explore mathematical modeling of incompressible flow
  • Learn about computational fluid dynamics (CFD) tools for simulating flow scenarios
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Fluid dynamics researchers, mechanical engineers, and students studying advanced fluid mechanics who are interested in mathematical modeling of flow in diverging geometries.

stevie1990
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I am currently trying to provide a mathematical model that describes the flow through a diverging square pipe. I am trying to simplyfy the navier stokes equations by usings assumptions but am unsure if my current progress is correct.
The problem is as follows:
Fluid enters a section of a square cross sectioned pipe which undergoes an area expansion of 1:4. The flow is uniform and laminar at the inlet and fully developed before entering the expansion and at the outlet. Provide a mathimatical model which describes the unique flow through the pipe.
By assuming steady state, incompressible, uniform flow with no body force in the direction of motion I can simplyfy considerably however I do not know how to take into account flow separation at the divergance nor how to justify properly my assumptions :S
anyone help pleaseee
 
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hi, classmate

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