[SI-LIST] Re: impedance for 10-mile pipe at 120Hz, skin effect
- From: "George Tang" <gtang@xxxxxxxx>
- To: <aballe73@xxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Mon, 15 Dec 2003 20:00:34 -0800
This problem is a little vague, since the complete circuit is not given. To
model this as a transmission line, I would need to know the signal path and
the return current path. But the only info given is the grounding steel
pipe carrying the 120Hz current from the rectifier. But with some
assumptions, it is still possible to approximate the impedance of the steel
pipe.
1. Assume that the steel pipes are not routed next to other conductors.
This may be a good assumption since the pipe is 10 miles long, so other
conducting objects may seem small compared to the size of the pipe. At 120
Hz low frequency and with the absence of other conductors, the capacitance
parameter can be ignored for now.
2. Assume that the soil is dry. At 120 Hz, dry soil is an insulator (10^-5
mhos/m). Since there is no conductor within miles radius of this pipe, the
conductance, G, can be ignored.
3. The exact composition of this steel is unknown, but it is assumed that
its electrical properties are similar to iron, (relative permeability =
5000, conductivity = 10^7). External inductance can be ignored for this
approximate calculation.
4. The rectified current usually have harmonics going up to hundreds of
KHz, but for now, higher order harmonics are ignored. Only the 120 Hz
current is considered.
In this case, all we have left is the internal impedance Zs.
Zs = Rs + jwLi = (1+j) Rs = (1 + j) * 4.9E-4 (ohms)
You can model this with just resistor and inductor for Rs and Li.
Best regards,
George
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of aballe73
Sent: Friday, December 12, 2003 12:51 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] impedance for 10-mile pipe at 120Hz, skin effect
Dear SI experts,
First of all, I should say that I am a chemist (no familiar with SI
or very complex circuits). However, I think you can help me a lot.
I am trying to use PSPICE to model the behaviour of an electrified
and buried pipeline (for natural gas or oil). Specifically, I wish
to know the impedance of the steel pipe (ferromagnetic, hollow
(0.375 inches thick) conductor). There is a rectifier having one of
these leads connected to the pipe, and the other lead connected to a
grounding system: so a 120Hz rectified current is going through the
ground into different points of the pipe and coming back to the
rectifier through the pipe.
I understand that I should not considered the system as a
transmission line because is too short (10 miles or so) compared to
the current frequency (120Hz).
Is the impedance for a pipeline the same as for a cylindrical
conductor (no hollow)? That is; is the Z=3D (1+j)/(s=95d);
s=3Dconductance, d=3Dskin depth. Can I apply this equation even for low
frequencies such as 120Hz?
From Z=3D (1+j)/(s=95d), I can obtain the internal inductance and the
surface resistance..Are there any other factors to consider
(external inductance, coupled inductance)?
Thanks a lot.
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