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

• stevie1990
In summary, the conversation is about creating a mathematical model for the flow through a diverging square pipe. The speaker is trying to simplify the Navier-Stokes equations by making certain assumptions, but is unsure if their progress is correct. They need help in accounting for flow separation at the divergence and justifying their assumptions.
stevie1990
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

hi, classmate

lol

Anyone has some suggestion ?

## 1. What are the Navier-Stokes equations for unique flow through a rectangular diverging pipe?

The Navier-Stokes equations are a set of partial differential equations that describe the motion of a fluid. In the case of a rectangular diverging pipe, the equations can be written in terms of the velocity and pressure of the fluid.

## 2. How are the Navier-Stokes equations used to analyze flow through a rectangular diverging pipe?

The Navier-Stokes equations can be solved numerically to determine the velocity and pressure distribution within the pipe. This information can then be used to understand the behavior of the fluid and make predictions about its flow.

## 3. What factors influence the flow behavior in a rectangular diverging pipe according to the Navier-Stokes equations?

The Navier-Stokes equations take into account factors such as the fluid's viscosity, density, and velocity, as well as the geometry of the pipe. These factors all play a role in determining the flow behavior and can be adjusted to observe their effects.

## 4. Can the Navier-Stokes equations be applied to any type of fluid flow?

The Navier-Stokes equations can be applied to a wide range of fluid flows, including both laminar and turbulent flows. However, they are not always accurate for highly complex or non-Newtonian fluids.

## 5. What are the limitations of using the Navier-Stokes equations for analyzing flow in a rectangular diverging pipe?

The Navier-Stokes equations assume that the fluid is incompressible, and that there are no external forces acting on it. In reality, these assumptions may not hold true, and the equations may not accurately predict the behavior of the fluid. Additionally, solving the equations for complex geometries can be computationally challenging.

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