Water either wants to put calcium carbonate down or wants to take it up, and which of those it wants decides a great deal about the inside of a pipe. Wilfrid Langelier's index is the oldest and most used way of asking, and it is one subtraction.

$\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}$, read aloud L-S-I equals p-H minus p-H-sub-s. $\mathrm{LSI}$ is the Langelier saturation index, a bare number with no units. $\mathrm{pH}$ is the measured pH of the water — what a probe reads at the sample point. $\mathrm{pH_s}$ — say p-H-s, or saturation p-H — is the pH at which THIS water, with the calcium, alkalinity, dissolved solids and temperature it actually has, would be exactly saturated with calcium carbonate. You are solving for the index; either pH can be recovered from the other two.

Read the sign, not the size. Positive is supersaturated and the water tends to deposit carbonate. Negative is undersaturated and it tends to dissolve it. Zero is the tightrope. Roughly: below −2 strongly aggressive, −0.5 to +0.5 balanced and where most treated systems are held, above +2 heavily scaling.

Now the saturation pH itself, in the closed form every plant uses: $\mathrm{pH_s} = (9.3 + A + B) - (C + D)$ — p-H-s equals nine point three, plus A, plus B, all less C plus D. The 9.3 is a constant of the fit. $A$ is the dissolved-solids factor, $(\log_{10}\mathrm{TDS} - 1)/10$, typically 0.1 to 0.2. $B$ is the temperature factor, $34.55 - 13.12\log_{10}T$ with $T$ in kelvin — it falls as the water warms, which is why a hot service scales when the same water cold does not. $C$ is the calcium factor, $\log_{10}\mathrm{Ca} - 0.4$, with calcium hardness as CaCO₃. $D$ is the alkalinity factor, $\log_{10}\mathrm{Alk}$, alkalinity as CaCO₃. All four are bare numbers: every unit was spent inside the logarithm that made them.

Which pair does what is worth memorising. TDS and temperature push pHs UP; calcium and alkalinity pull it DOWN, because a water already rich in both is much closer to holding all the carbonate it can. More calcium means the water saturates at a lower pH, so it takes less pH to be scaling.

And now the honest limit, which is the spine of this whole chapter. The Langelier index predicts a scaling TENDENCY. It is not a corrosion rate. A negative index says no protective calcium carbonate film will lay down — nothing more. It contains no time, no surface area and no metal, so it cannot possibly tell you how many mils a year are leaving a wall. It also has no idea whether there is any oxygen in the water, and oxygen is what does most of the corroding. Rates come from a coupon on a balance or a current on a probe, and those are lessons four and five.