Where long distances are covered by impressed current systems, voltage drops occur along the structure in a reduction fashion of voltages and currents.
Reductions can be significant depending on the current demand and voltage drops. This may require additional cathodic protection for the pipeline system.
𝑅𝐿 — Linear Electrical Resistance of the Section of the Pipeline(ohm/m)
𝑅𝑇 — Leakage or Transverse Resistance of the Section of the Pipeline(ohm/m)
𝑅𝐾 — Characteristic Resistance of the Section of the Pipeline(Ohms)
𝛼 — Attenuation Constant of the Section of the Pipeline(Ohms)
𝑅0 — Pipe to Electrolyte Insulation Resistance(Ohms)
𝜌 — Specific Resistance of the Pipeline Material(Ohms)
𝐿 — Half Distance between Drain Points(anodes)(m)
𝐷𝑜 — External Diameter of the Pipeline(m)
𝐷𝑖 — Internal Diameter of the Pipeline(m)
𝐴𝑤 — Pipe Cross Sectional Area(,in-2.)
𝐸0 — Pipe to Electrolyte Potential at the Drain Point(Anode)(V)
𝐸𝑥 — Pipe to Electrolyte Potential at the Distance of X from the Drain Point(V)
𝐼0 — Current Flowing onto the Pipe at the Drain Point(Anode)(amp)
𝐼𝑥 — Current Flowing onto the Pipe at Distance X from the Drain Point(Anode)(amp)
For typical pipeline with multiple drain points (anodes) with uniform spacing of 2L the potential and current are given: