Boundary Conditions for an infinite rectangular pipe

AI Thread Summary
The discussion centers on the appropriate boundary conditions and axis assignments for modeling an infinite rectangular pipe. Participants clarify their axis definitions, agreeing that the pipe is infinite along the X-axis, with the Y-axis representing width and Z-axis being vertical. There is consensus that the problem can be treated as a 2-D Laplace equation, as the infinite length along the Z-axis makes it independent of that dimension. The voltage conditions are specified, with V on the Y-axis faces and 0 on the Z-axis faces. Overall, the focus is on ensuring correct boundary conditions and axis orientation before proceeding with the solution.
guyvsdcsniper
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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.

IMG_0381.jpg


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:
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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.
 
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