Everything so far has been a prediction from water chemistry. A coupon is different: a flat piece of the actual alloy, weighed, hung in the actual stream, pulled, cleaned to a written procedure and weighed again. The mass that has gone is not an opinion.

This lesson is authored in mils per year on purpose. Every fixed-equipment inspector on this continent writes mpy, coupon racks are logged in square inches and hours, and the packed constant below exists only in that dialect. A metric twin is coming; the mil is not going anywhere.

$P = \dfrac{534\,m}{\rho\,A\,t}$ — P equals five three four m, over rho A t. $P$ is the uniform penetration rate in mils per year, a mil being one thousandth of an inch. $m$ is the coupon weight loss in milligrams. $\rho$ — rho — is the alloy density in g/cm³: mild steel 7.85, copper 8.94. $A$ is the coupon's total exposed area in square inches, both faces and the edges. $t$ is the exposure in hours. Solve it forward for the rate, or backwards for the weight loss an acceptance limit corresponds to.

The 534 is not a fudge factor. It is every one of those units bundled together — milligrams into grams, cubic centimetres into cubic inches, inches into mils, hours into a year. Change any unit in the list and the constant changes with it, which is why the commonest error on this calculation is entering the exposure in days.

Then what the rate is for. $L = \dfrac{T - T_r}{P}$ — L equals T minus T-sub-r, over P. $L$ is the remaining life in years. $T$ is the present wall thickness, measured today, usually by ultrasonic. $T_r$ is the retirement thickness — the minimum the fitness-for-service assessment permits, below which the component comes out. $P$ is the penetration rate. Watch the subtraction: the metal you may SPEND is what sits above retirement, not the whole wall, and forgetting it is the most flattering mistake available here.

Two cautions, both worth more than the arithmetic. First, this is uniform-attack arithmetic and it is worthless where the attack is localised. A pit perforates at its own depth, and pitting rates run five to fifty times the general rate on the same coupon. If the surface comes back with pits or tubercles, the remaining life is set by the deepest one, and finding it is an inspection problem rather than a calculation. Second, a rate from one short exposure carries the uncertainty of two weighings divided by very little metal. Three coupons over a long baseline are worth far more than two close together, and 90 days is the usual compromise. Typical cooling-water acceptance: mild steel under 3 mpy good, 3 to 5 fair, above 5 poor; copper alloys under 0.3 mpy good, above 1 poor.