Calculate Numbers of Pipe Earthing

Quick corrected formulas 

1. BS 7430 (metal rod/pipe, SI units)

2. IS (as you quoted — formula expressed using cm)

Important: in this IS form $L$ and $d$ must be in centimetres (cm). The factor 100 converts units — this is why unit consistency is vital.

3. Max allowable current density (per IS 3043 style expression you used)

4. Lateral surface area (pipe) (m²)

$$\mathrm{<span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span>A}=2\pi rL\text{(use meters)}$$

5. Parallel rods total resistance (approx, identical rods, well spaced):

Examples

Example A — BS 7430 rod calculation (you gave: 4 m, 12.2 mm, ρ = 500 Ω·m)

• 

• 
  

If you (incorrectly) use d = 0.0125 m, R ≈ 136.23 Ω.
So R ≈ 136.7 Ω (not 156.19 Ω as in your example) — the difference comes from either a unit slip or arithmetic error in the original worked example.

---

Example B — Number of CI earthing pipes and resistance

• Pipe dia = 100 mm → d = 0.10 m (i.e. 10 cm).

• Pipe length = 3.0 m → 300 cm for the IS formula.

• Soil resistivity $\rho = 72.44\ \Omega\!\cdot\!m$.

• Fault current = 50 kA for t = 1 s.

1) Max allowable current density

$$$$

2) Surface area of one 100 mm × 3 m pipe (lateral area)

$$\mathrm{<span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span>A}=2\pi rL=2\pi (0.05)\cdot 3\approx 0.94248{\text{m}}^2$$

3) Max current dissipated by one pipe

$${\mathrm{<span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> \; </span><span> </span>I}}_{\max \mathrm{\_}pipe}=I_{\text{dens}}\times A\approx 889.4195\times 0.94248\approx 838.26\text{ A}$$

4) Number of pipes required (purely by current dissipation argument)

5) Resistance per isolated pipe using IS formula (L,d in cm)

• $$

6) Overall resistance for 60 identical, well-spaced pipes (approx)

$$$$

Note: your example showed 7.99 Ω per pipe and 0.133 Ω overall — that looks like a decimal/units slip (factor ≈10). Using the proper unit handling (L, d in cm for the IS expression) gives ≈0.803 Ω per pipe and ≈0.0134 Ω total for 60 pipes.

---

Key practical points & common pitfalls 

1. Unit consistency is everything. IS formula uses cm (hence the mysterious factor 100) — mixing m and cm gives big errors (×10 or ×100). Always state units beside formula and variable.

2. Which formula to use? BS 7430 (SI units, m) is common in international texts; IS versions sometimes use cm. Make that clear in the article with both forms and an example conversion table.

3. Surface area: use lateral area for pipes. Don’t forget top/bottom caps are negligible compared to lateral surface for long rods.

4. Spacing of multiple rods: the simple $R/N$ parallel approximation is valid only when rods are sufficiently spaced (rule of thumb ≥ 3×L). If closer, mutual resistance means less benefit — use empirical correction factors or soil modelling.

5. Soil layering & resistivity tests: real sites often have layered soils — use Wenner/Terzaghi tests to measure. Single ρ value is an approximation.

6. Chemical backfills and strips: a buried strip or chemical backfill changes both dissipating surface and effective resistance; include these in designs to reduce number of rods.

7. Testing after installation: measure step & touch potentials and take 4-point (or fall-of-potential) measurements to confirm results on site.

8. Safety & standards: reference the correct standard (IS 3043, BS 7430, or the latest national standard) and ensure protective clearances and signage.

---