Equation 6 · AI Datacenter Power and Cooling: A First-Principles Introduction
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →Numerator: Annual Site Water Usage
The complete quantity above the fraction bar.
Denominator: IT Equipment Energy
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Water usage effectiveness fills that second gap, introduced by the same organization a few years before this decade’s AI buildout made it urgent: . reported in litres per kilowatt-hour and deliberately built to use “the same value… as the denominator for this new metric” as PUE, “to both ensure the metrics stay linked and speed their adoption” [ 6 ] . WUE exists because the cheapest way to reject a given amount of heat is very often evaporative — cooling towers and adiabatic assistance work against the wet-bulb temperature rather than the dry-bulb temperature, so they can reach a lower effective cooling temperature for less fan and compressor energy than a fully dry system…
Read the full surrounding passage
Water usage effectiveness fills that second gap, introduced by the same organization a few years before this decade’s AI buildout made it urgent: . reported in litres per kilowatt-hour and deliberately built to use “the same value… as the denominator for this new metric” as PUE, “to both ensure the metrics stay linked and speed their adoption” [ 6 ] . WUE exists because the cheapest way to reject a given amount of heat is very often evaporative — cooling towers and adiabatic assistance work against the wet-bulb temperature rather than the dry-bulb temperature, so they can reach a lower effective cooling temperature for less fan and compressor energy than a fully dry system — and that efficiency is paid for in water rather than electricity. A facility can improve its PUE by switching from dry to evaporative rejection while its WUE gets worse in the same stroke, which is exactly why the two ratios are reported together rather than treated as substitutes for one another.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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