# Boundary Conditions for an infinite rectangular pipe

• guyvsdcsniper
In summary, setting up the problem symmetrically on this axis and the boundary conditions applied makes sense.
guyvsdcsniper
Homework Statement
An infinite rectangular pipe with sides a, has two opposite sides at voltage V
(front and back) and at voltage V=0 (top and bottom).

Find the potential inside the pipe.
Relevant Equations
Fourier Sine Trick
Does setting up the problem symmetrically on this axis and the boundary conditions applied make sense? I don't believe I will have a problem solving for the potential inside, but i just want to make sure I have my B.C and axis correct before proceeding.

EDIT:

Or should this be a 2-D lapace equation since the pipe is infinitely long, making this independent of the z axis?

Last edited:
I'm a bit confused about how you are assigning the axes.
I'll call the left right axis X, the vertical axis Z and the lower left/ upper right axis in the picture Y. From that and the text description, I would say the pipe is infinite in the X axis and width a in the other two. The voltage is V on the faces normal to the Y axis and 0 on those normal to the Z axis.

haruspex said:
I'm a bit confused about how you are assigning the axes.
I'll call the left right axis X, the vertical axis Z and the lower left/ upper right axis in the picture Y. From that and the text description, I would say the pipe is infinite in the X axis and width a in the other two. The voltage is V on the faces normal to the Y axis and 0 on those normal to the Z axis.
Sorry I missed that. y is the vertical axis.z is the axis coming out of the page. X is horizontal.

But I think it should be independent of Z since it is infinitely long. It mirrors an example straight out my textbook.

quittingthecult said:
z is the axis coming out of the page.
quittingthecult said:
independent of Z since it is infinitely long.
Looking at the diagram, the infinitely long direction is horizontal.

## 1. What are boundary conditions for an infinite rectangular pipe?

Boundary conditions for an infinite rectangular pipe refer to the constraints or limitations on the flow of fluid within the pipe. These conditions are typically defined at the inlet and outlet of the pipe and can include factors such as pressure, velocity, and temperature.

## 2. Why are boundary conditions important in fluid mechanics?

Boundary conditions are important because they help to define the behavior of fluid flow within a system. They allow us to accurately model and predict the movement of fluid, and can also help us to understand and control the flow in practical applications.

## 3. What are the different types of boundary conditions for an infinite rectangular pipe?

There are several types of boundary conditions that can be applied to an infinite rectangular pipe, including: no-slip condition (fluid velocity is zero at the pipe walls), constant pressure condition, constant velocity condition, and temperature boundary conditions (such as adiabatic or isothermal).

## 4. How do boundary conditions affect the flow of fluid in a pipe?

Boundary conditions can greatly influence the behavior of fluid flow in a pipe. For example, a no-slip condition at the walls of the pipe can cause a decrease in velocity near the walls, while a constant pressure condition can result in a uniform flow throughout the pipe.

## 5. Can boundary conditions be changed during a fluid flow simulation?

Yes, boundary conditions can be changed during a fluid flow simulation in order to study the effects of different conditions on the flow. However, it is important to carefully consider the implications of changing boundary conditions and to ensure that the changes are physically realistic.

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