# impedance of a pipe (equivalent circuit)

#### aaballe

Joined Dec 10, 2003
1
I am trying to use PSPICE to model the behaviour of a electrified and buried pipe.
Specifically, I wish to know the impedance of the steel pipe (ferromagnetic, hollow conductor). There is a rectifier which connects the pipe a grounding system: so a 120Hz rectified current is going through the ground to different points of the pipe and coming back to the rectifier.

I understand that I should not considered the system as a transmission line because is too short (10 miles) compared to the current frequency (120Hz).

Is the impedance the same for a pipe as for a cylindrical conductor (no hollow)? That is; is the Z= (1+j)/(sd); s=conductance, d=skin depth. Can I apply this equation even for low frequencies such as 120Hz?

Z= (1+j)/(sd) applies for the internal inductance and the surface resistance..Are there any other factor to consider (external inductance, coupled inductace)?

#### PRR

Joined Dec 16, 2003
5
> Is the impedance the same for a pipe as for a cylindrical conductor (no hollow)? That is; is the Z= (1+j)/(sd); s=conductance, d=skin depth. Can I apply this equation even for low frequencies such as 120Hz?

What is the skin depth for 120Hz?

If it is less than the wall thickness, it is probably valid.

If it is greater than the wall thickness (and I suspect it is), use the wall thickness and conductivity of iron.

Note that the "space" outside the pipe is damp dirt of uncertain conductivity and permeability. The free-space value of inductance won't be valid under those conditions. In fact I bet you can not KNOW the impedance except by testing. You may find general rules of thumb if you research pipe corrosion control.

A very important point: the damp soil is a shunt resistance. A couple-foot pipe may be 100 ohms, but 10 miles of pipe may bleed more current into the soil than to the far end.

Don't forget that the pipe joints may be imperfect (though very well screwed or welded joints will be nearly perfect).