Corrosion & Protection formulas — 12 solvers

Anode Current Output

I = \frac{\Delta E}{R}

Corrosion & ProtectionWhat a galvanic anode actually delivers: the driving voltage between the anode and the polarized structure, divided by the total resistance of the circuit. Ohm's law doing the whole of cathodic protection design.

Cathodic Protection Current Demand

I = A \, i \, f

Corrosion & ProtectionThe total current a cathodic protection system has to supply: the structure's surface area times the current density its environment demands, times the fraction of that surface actually exposed through the coating.

Dissolved Oxygen Saturation with Temperature

\ln C_s = -139.34411 + \frac{1.575701 \times 10^5}{T} - \frac{6.642308 \times 10^7}{T^2} + \frac{1.243800 \times 10^{10}}{T^3} - \frac{8.621949 \times 10^{11}}{T^4}

Corrosion & ProtectionHow much oxygen fresh water can hold at saturation, falling from about 14.6 mg/L at freezing to 7.6 at 30 °C. The Benson and Krause fit adopted by Standard Methods, and the reason deaerators and hot systems corrode differently from cold ones.

Dwight's Equation for Anode Resistance to Earth

R = \frac{\rho}{2 \pi L} \left[ \ln\!\left(\frac{8L}{d}\right) - 1 \right]

Corrosion & ProtectionH. B. Dwight's 1936 result for a vertical rod in uniform soil: the resistance between a buried anode and remote earth, from the soil resistivity and the anode's length and diameter. Almost the whole resistance of a cathodic protection circuit.

Galvanic Driving Voltage

\Delta E = E_c - E_a

Corrosion & ProtectionThe potential difference between two metals coupled in the same electrolyte: the noble one's potential less the active one's. The voltage that drives every galvanic cell, wanted or otherwise.

Penetration Rate from Corrosion Current Density

P = \frac{i \, M}{n \, F \, \rho}

Corrosion & ProtectionFaraday's law applied to a corroding metal: a corrosion current density converted into the thickness of metal it removes per year, through the equivalent weight and the density.

Pitting Resistance Equivalent Number (PREN)

PREN = \%Cr + 3.3\,\%Mo + 16\,\%N

Corrosion & ProtectionThe single index that ranks stainless steels for resistance to pitting and crevice attack in chloride: chromium, plus molybdenum weighted 3.3, plus nitrogen weighted 16. A composition arithmetic, not a measurement.

Polarization Resistance

R_p = \frac{\Delta E}{\Delta I}

Corrosion & ProtectionThe slope of potential against current at the corrosion potential: apply a few millivolts, measure the current that flows, divide. The measurement that feeds the Stern-Geary equation.

Sacrificial Anode Mass for a Required Life

W = \frac{I \, t}{C \, u}

Corrosion & ProtectionHow much anode metal a cathodic protection system has to carry to supply its current for the design life, given the anode alloy's current capacity and the fraction of it that can be consumed before the anode stops working.

Stern-Geary Corrosion Current

I_{corr} = \frac{\beta_a \beta_c}{2.303 \, (\beta_a + \beta_c) \, R_p}

Corrosion & ProtectionStern and Geary's 1957 result: the corrosion current is the Stern-Geary constant divided by the polarization resistance. The equation that made an instantaneous corrosion rate a field measurement rather than a laboratory exercise.

Tafel Equation for Overpotential

\eta = a + b \log_{10} i

Corrosion & ProtectionJulius Tafel's 1905 observation, still the backbone of electrode kinetics: the overpotential driving an electrode reaction rises with the logarithm of the current density, in a straight line whose slope is the Tafel slope.

Wall Penetration and Remaining Life

L = \frac{T - T_r}{P}

Corrosion & ProtectionHow many years of wall are left: the metal above the retirement thickness divided by the penetration rate. The number that turns a corrosion rate into an inspection interval.