Faraday's Law and Corrosion Rates

You’re back at the two tanks.

Last module, they were a problem to solve — the two-tank problem in EC-011’s Apply lesson, if you need the refresher. Two bare-steel water tanks, same design, different dirt. The hilltop sits in dry silty loam around 8,000 Ω·cm, and it got magnesium — the strong pusher, roughly six-tenths of a volt of drive, because high-resistance ground swallows gentle voltages. The creek bottom sits in wet gray clay around 400 Ω·cm, and it got zinc — a quarter-volt of steady push, plenty for soil that barely fights back. You made the call, you gave the reasoning, and it held up.

Then the operator asked the question that ends most tailgate meetings: “So how many years does each anode last?”

And we told the truth: that’s arithmetic we haven’t done yet — but it is arithmetic. Not judgment, not experience. Arithmetic. Today we do it — and by the end of this lesson, the operator’s question is one you can answer on the tailgate with a phone calculator and a straight face.

Why this module sits where it does

You’ve already held every piece of this lesson in your hands. Two modules ago you counted the electrons — two per iron atom, no exceptions. Last module you ranked the metals and sized the push; you even watched a spent 17-pound bar come out of the ground along the way. This is where the counting and the ranking turn into pounds and years — the exchange rate of the whole trade.

From counting electrons to weighing metal

You already have the bookkeeping. Every iron atom that leaves the wall leaves as Fe²⁺, and every one of them hands off exactly two electrons. Two electrons per atom — no exceptions, no partial credit. At the time, that looked like chemistry trivia. It’s actually the foundation of corrosion accounting, because if every atom ships with a fixed number of electrons, then counting charge is counting metal.

That’s Faraday’s Law. The mass of metal consumed at an anode is directly proportional to the electric charge that passed. Not roughly proportional. Proportional the way a scale ticket is proportional to what’s on the truck.

Here it is in its chemistry clothes — the only time in this module you’ll see it fully dressed:

Faraday’s constant is the same number for every metal, every couple, every soil, every job. It never changes and you never solve for it. It’s the posted conversion rate between electrons and amp-seconds, and the rest of this lesson is about spending it.

Here’s the good news. You’ll run that full equation exactly once, in the next section — and then never again in this module. The industry ran it decades ago for every metal a corrosion crew will ever meet and wrote the answers down as constants. We work the equation once so the constants aren’t magic. After that, we use the constants like everyone else in this trade does.

The twenty-pound year

Sit with that number. A single amp of stray current leaving a pipeline at one spot is twenty pounds of pipe wall, every year, until somebody finds it. Half an amp is ten pounds. A hundred milliamps is two pounds — which sounds small until you remember it doesn’t take pounds to make a leak.

Because here’s what the law doesn’t tell you: where the metal comes from. Faraday counts the pounds; the current distribution picks the address. Spread one amp evenly across an entire bare tank bottom and it’s a haze of surface rust nobody will ever measure. Concentrate that same amp at three coating holidays the size of quarters, and the law delivers the same twenty pounds to three spots — and now you’re cutting out pipe. The law says how much. The circuit says where.

Run the equation for other metals and the answers land close enough to remember as a short list — the consumption rates, in pounds per amp-year, at 100% theoretical spending:

The field form of the law is just this list with the algebra pre-chewed: pounds = rate × amps × years. When a report or a design sheet writes W = K × I × T, that K is a row from the table above. Nothing new is happening — someone already did the Faraday math and folded it into one constant per metal.

Amp-hours per pound: the anode’s fuel gauge

For sacrificial anodes, the same constant is friendlier flipped upside down. Instead of asking how many pounds an amp consumes in a year, ask how many amp-hours of charge live inside one pound of metal. That’s a capacity — a battery rating for a bar of metal — and it’s how anode suppliers publish their numbers.

Theoretical capacity comes straight off Faraday’s Law: about 1,000 amp-hours per pound for magnesium, about 372 for zinc.

But a buried anode doesn’t spend every electron on your structure. Some of its surface runs little corrosion cells of its own — metal dissolving locally, electrons round-tripping right there on the bar, doing nothing for the tank at the end of the wire. The trade calls the honest fraction current efficiency, and the difference between theoretical and actual is the tax the anode pays for being active enough to do the job at all.

Magnesium gives you half of what the chemistry promises. Zinc gives you ninety cents on the dollar. Neither number is a defect — it’s a property of each metal, and it’s already folded into every honest anode-life estimate in the industry.

Back at the hilltop: the arithmetic, start to finish

Now the operator gets an answer.

The hilltop tank’s magnesium string is built from standard 17-pound bars — the same size bar you’ve already watched come out of the ground, eaten down to a stub around its steel core. At the test station, put your multimeter across the bar’s shunt and let Ohm’s Law do the rest: 5.0 mV across a 0.1-Ω shunt is 50 milliamps, and the polarity tells you which way it’s flowing. (An amp clamp gets you the same number when there’s one on the truck.) Fifty milliamps is a modest output, and modest is the point: that dry 8,000 Ω·cm loam is exactly why the strong pusher got this job, and even magnesium only moves a trickle through it.

Three honest footnotes come with that answer. First — run the same chain on theoretical capacity and you’d promise 39 years. That’s the efficiency tax in one comparison: the difference between an estimate and an apology is one factor of two, applied up front.

Second — the bar doesn’t die on schedule at 19.4 years. Output wanders with soil moisture and season; the draw you measure in April isn’t the draw in August. The number is a design estimate, not an expiration date. It tells you which decade to plan the replacement in, and that’s its job.

Third — crews don’t wait for zero. As an anode gets down toward its last stretch — a common planning figure is around 85% consumed — the remaining stub can’t hold dependable output, and replacement gets scheduled. Design sheets carry that as a utilization factor. For now it’s enough to recognize the idea: the last bite of the bar never gets spent.

And the creek-bottom zinc? Same chain, different numbers — 335 amp-hours per pound in the bank, and a bigger draw, because wet clay at 400 Ω·cm barely resists and zinc runs steadier and harder there. We could work it right here, but you’d learn more running it yourself. It’s waiting in Lesson 3 with fresh numbers — and this time, you’re the one at the tailgate.

Running the law in reverse: rates and current density

Everything so far ran forward: current in, pounds out. The law runs backward just as well — grams of metal lost convert to the current that must have carried them out. The industry uses both directions, and which one you meet depends on which side of the pipe wall you work.

The backward direction is a lab move. Weigh a coupon before and after exposure, walk the mass loss through density, area, and time, and out comes a corrosion rate in mils per year. That workflow belongs to internal corrosion work, where coupons ride inside the line and come out on a schedule with retrieval tools. If your career runs down the IC path, you’ll meet it properly there.

External corrosion coupons live a different life. They go in the ground beside the pipe, wired to it through the test station — and they stay buried. Nobody’s mailing them to a lab. What they give you, they give you alive: a bare piece of steel with one property no real holiday ever has — a known surface area. Read the current on the coupon’s shunt, divide by that area, and you’re holding current density — the number CP design speaks in — measured, not assumed. The same coupon gives you honest potentials too, one reason we’ve called coupons the closest thing to asking the steel directly.

Now the block above has a job. Say the coupon is 10 square centimeters and its shunt works out to 22 microamps: that’s 2.2 µA/cm² — call it a mil a year in steel language. On a freely corroding bare spot, that’s the wall it would lose. On a protected coupon, that’s the bill your anodes are paying on its behalf. Same number, read as a threat or as a receipt — and Faraday’s Law is what makes the translation honest.

The full coupon procedures — retrieval tools, lab reports, pitting rates — live where they belong, later in the catalog and over on the internal side. What matters now is smaller and sturdier: a corrosion rate is a current, a current density is a rate-in-waiting, and every mil of wall that ever leaves is carried out by electrons somebody could have metered.

Why cathodic protection works, by the pound

Which brings us to the quiet idea underneath this whole trade.

If a structure’s corrosion cells are drawing current off it — pounds leaving on schedule, per the exchange rate — then supplying that current from somewhere else means the structure stops paying. The pounds don’t vanish. They move. Faraday’s Law keeps the books balanced either way.

With galvanic anodes, the payer is magnesium or zinc, budgeted in advance — that’s literally what the “expected life” line on a galvanic CP quote is: Faraday’s Law, worked out the way we just did, priced by the pound. With impressed current systems, a rectifier drives the circuit and the anodes are materials picked because they spend almost nothing — high-silicon cast iron, mixed metal oxide, graphite — each with its own small published consumption rate. Same law, different bill structure. The design details of both live in later modules; the accounting principle is yours today.

And that principle is why this module matters more than its four formula blocks suggest. Every galvanic-anode quote our office writes ends in a Faraday line item — anode count, anode size, expected life. Every internal-corrosion coupon report our lab produces converts mass to rate with the same law. The tech who can run the chain reads those documents instead of taking them on faith — checks them, catches the theoretical-capacity mistake before it ships, answers the operator without calling the office. That’s the difference between running the survey and understanding the system. It’s the first step from technician thinking toward designer thinking, and it costs four lines of arithmetic.