Combination of cartesian and cylindrical coordinate system

In summary, the conversation discusses solving a numerical problem involving air flow through a porous medium and a narrow channel. Two equations, the Laplace and Reynolds equations, are used to describe the flow in the porous media and gap respectively. These equations must be solved iteratively until the pressure at the boundary is equal, with the question of whether a cartesian coordinate system can be used for the Reynolds equation and a cylindrical coordinate system for the Laplace equation. The exact geometry and dimensions of the problem are also discussed, as well as the type of bearing being used.
  • #1
hermano
41
0
Hi,

I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing).

This problem can be described with the use of two equations namely the Laplace equation describing the flow in the porous media, and the Reynolds equation describing the flow in the gap.

These equations must be solved both separately on an iterative manner until the pressure at the boundary between the porous media and the gap is equal to each other (continuity).

My question is: Can I use a cartesian coordinate system for solving the Reynolds equation (flow in the gap) and a cylindrical coordinate system for solving the Laplace equation (flow in the porous media) if I take care that the nodes where I calculate the pressure at the boundary between the gap and the porous media lie at the same place?
 
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  • #2
What is the exact geometry with the exact dimensions? What kind of bearing is this?
 

1. What is the purpose of using a combination of cartesian and cylindrical coordinate system?

The combination of cartesian and cylindrical coordinate system allows for a more comprehensive and accurate representation of three-dimensional space. It allows for the measurement of both Cartesian coordinates (x, y, z) and cylindrical coordinates (r, θ, z) in a single system, which is useful in many scientific applications.

2. How do I convert from cartesian to cylindrical coordinates?

To convert from cartesian to cylindrical coordinates, use the following equations:
r = √(x^2 + y^2)
θ = tan^-1 (y/x)
z = z.
These equations will give you the cylindrical coordinates for a given point in three-dimensional space.

3. Can you explain the differences between cartesian and cylindrical coordinates?

Cartesian coordinates use a system of three perpendicular axes (x, y, z) to represent a point in three-dimensional space, while cylindrical coordinates use two perpendicular axes (r, θ) and a vertical axis (z). Additionally, in cylindrical coordinates, the distance from the origin is represented by the variable r, and the angle from the positive x-axis is represented by θ.

4. What are some common applications of the combination of cartesian and cylindrical coordinate system?

The combination of cartesian and cylindrical coordinate system is commonly used in fields such as physics, engineering, and mathematics. It is particularly useful in applications involving cylindrical objects, such as pipes, cylinders, and turbines. It is also used in computer graphics and 3D modeling.

5. Are there any limitations to using a combination of cartesian and cylindrical coordinate system?

One limitation of using a combination of cartesian and cylindrical coordinate system is that it can be more complex and difficult to visualize compared to using a single coordinate system. Additionally, it may not be suitable for all types of three-dimensional objects, as some may be better represented using other coordinate systems such as spherical coordinates.

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