Total surface area would be ,"(2(3.14)(h)(r+R))+(2(3.14)(r+R)/2)(t))", where 't' is the thickness of pipe, If thickness is considerable. First formula is good, if thickness is neglected.

In case we have neglected the thickness, can we assume that the current flows both along outer and inner surface area of the cylindrical pipe??

Yes, if diameter is not, too small.

Thank you for your response sir. In my case it is diameter d = 40mm and length of the pipe electrode is L = 3.5m long. So can I assume the same for my case. Or please let me know if there is any criteria say "L/d" ratio which determines the current flow ability.

Thanks in advance.

Inside the pipe the electrical field will be zero so no current actually flow through the inside surface of the pipe rather current will flow from pipe to outer side where the electrical potential has a gradient depending on the soil characteristics. Now when there is a potential difference between the earth electrode and surrounding soil( this potential difference will not be uniform along the length of the pipe but it is expected to be symmetrical in radial planes vertical to the length of the pipe ) a radially divergent current will flow from pipe to surrounding soil through the outer surface of the pipe electrode. Now we see whether the thickness of pipe is important? The thickness of pipe matters due to the fact that current flows vertically along the length of the pipe and diverge to outer soil through outer periphery of the pipe. So outer peripheral surface is to be considered so far as divergent current to earth through pipe is considered

@Arijit Basuray ...... Thank you sir. In general an earth electrode is clamped to an earth strip only at the outer surface. Now in case if we weld or bolt the same earth strip inside the electrode also and fill the inner area with soil then is there a chance for the current to flow along the inner surface area. This may look odd but I just want to give a try.

Thanks in advance.

Your question has two possibilities firstly we will have to see whether the copper strip electrode is directly connected to pipe or it is just placed co-axially with the pipe.

If the strip is directly connected to the pipe at upper end my old answer will stand as the field inside the pipe will then be zero and will remain at same potential as the copper strip. If the strip remains inside the pipe along it's length without any direct connection the pipe will have at different potential and a field will exist between strip and inner side of the cylinder and between outer surface of cylinder and rest of the ground. In this situation the divergent current from strip to global ground will cut both the inner and outer surface of the pipe as the pipe will barely serve as a equipotential cylindrical surface in electric field.

Dear Srikanth. I agree with the comments from Mr. Basuray. To make the picture easier for you, imagine that your pipe electrode is filled with metal (no soil material inside). It becomes like a solid rod electrode, just thicker than usual. Note (for the solid rod) that the surface area that makes most contact with soil is the round surface along the rod lenght. The contact area at the bottom of the rod is too small and does not contribute much with current dispersion to soil. In practice, a pipe can be treated as a rod electrode (unless it is too wide compared to its length... I have never seen any L/d criterion for this case in literature). The current to soil inside the pipe is negligible (some longitudinal current may flow but, perhaps, if compared to the current along the pipe, in a proportion as small as the soil versus metal pipe conductivities). Earthing resistance formula for a vertical rod is applicable for pipes, taking the external radius of the pipe of course. Note that the internal surface of a pipe is wasted when used as earthing electrode. Take a look on paper "A comparison between the performance of strips and round conductors as grounding electrodes". It is available in ResearchGate.

@Basuray and @ Silva ....... Thank you very much for your valuable inputs. Now I'm almost clear with respect to the current flow through a rod.

Now advancing a bit in our discussion I would like to ask one more question. According to BS:7430 and IS:3043, the number of electrodes shall be calculated to withstand the Short circuit current. Here, the current density "J" is calculated initially and then it is multiplied by the surface area "2*pi*R*h" . This gives the current carrying capacity of one electrode. Now if we could increase the surface area (like considering the inner surface area) then the overall current capacity of the electrode increases thereby reducing the number of pits. So, if there could be any condition for say L/R ratio (or a condition for L/R ratio is framed), we can start using such electrode, fill it with low resistivity material and therefore number of electrodes can be reduced. Is there any possibility of such practice?

Srikanth, the inner surface area of the pipe isn't going to do anything for you. Rod spacing has to be factored in. As current flows, the voltage gradient in the surrounding soil will change, affecting the ability of other nearby rods to sink current to ground. Multiple closely spaced rods will not be as effective as spacing the rods across a larger area. How far apart they need to be spaced so you can consider them independent of each other, i.e. the ground voltage gradient from current flow in one rod does not impact a nearby rod, will depend on the soil conductivity.

If you are having difficulty obtaining the required ground resistance, chemical grounds are an option (sometimes used in rocky environments, mountaintop radio sites, etc.). Chemical grounds come with their own set of problem though, like more frequent inspection and maintenance of the grounding system. Generally, if site conditions permit you'll be much better off in the long term by driving more conventional grounding electrodes.

For d

@Mr. Arijit Basuray

Electric field inside the pipe IS NOT zero, because there is not electrostatic problem...

Dear Mr. Celic, In our present problem if the length of the pipe >> the diameter of the pipe(Long Cylindrical earth electrode filled with conducting soil) the field inside the pipe can be assumed as zero whether an electrostatic or flow of current is considered and we should not forget that even if it is not an electrostatic problem flow of current here is due to electric field only. I hope that I could clarify the mode of flow of current in my previous discussions, you may also go through the explanation given by Mr. José Claudio Oliveira Silva.

Dear Mr. Basuray SC current is transient so field inside the cylinder IS NOT zero...

The confusion here may be due to language. If "inside the pipe" refers to the hollow, nonconducting (free space) region, then I would have to agree with Mr. Basuray. Gauss's Law applies for both static and transient charge. Since there is no charge within a Gaussian cylindrical surface defined by the inner wall of the pipe, no field can exist there. If "inside the pipe" refers to the region within the conducting walls of the pipe, then I would have to agree with Mr. Celic. The field and, hence, the current density there is certainly not zero. In the case of a fast transient (as in a SC fault), the initial electromagnetic field would tend to concentrate the current near the outer surface of the conductor due to the skin effect. However as the current reaches steady-state (until circuit protection activates) the field and current would become more uniformly distributed within the conducting walls of the pipe. Regardless of how the current is distributed in the pipe above ground, it will flow predominantly radially outward into the soil. The comments offered by Mr. Hainzl and Mr. Silva are correct. The goal is to minimize the ground system impedance (L and R) via proper design of the number, spacing and diameters of the ground rods.

Dear All, 

Thank you for your contribution. In continuation to this I would like to add one more query. In case if I make the earthing strip to insert and pass through the rod across the diameter and I weld the inner joining surface, will there be a chance for the current to flow on the inner surface of the rod ??

Srikanth,

The inner surface of a hollow grounding electrode (a pipe) isn't going to help dissipate current into the surrounding ground, no matter how you connect it. If you assume the grounding electrode can be filled with earth, it could, in theory, conduct a tiny amount of energy out the ends of the pipe. But in a practical application, the fraction of current out the ends of the pipe from the inner surface would be so small, it's not even worth your time to try and calculate the result.

All that being said, I went back to the original post and it appears this is a textbook question, so making practical approximations for real applications might cost you in this case. Perhaps the objective of the problem is to demonstrate how little current would flow from the inner surface of the pipe?