Derivation of Potential Change along a Cathodically Protected Pipeline

4 DERIVATION OF POTENTIAL CHANGE ALONG A CATHODICALLY PROTECTED PIPELINE 

Assume that current enters a pipe from the soil side through a porous insulating coating, returning to the anode by way of the pipe (Fig. 29.6). Then the change of current, /, in the pipe per unit length at x is equal to the total current entering the pipe at x, or 

At small values of 4, polarization of the pipe surface is a linear function of the true current density at the base of pores in the coating, or 

Assuming that the resistance z per unit area of coating is inversely proportional to the total cross-sectional area of pores per unit area, true current density increases with z, or 

For an infinite pipeline, this differential equation has the solution 

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