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Equation 1 · Comparing the Main Approaches to AI Datacenter Power and Cooling

What does this equation mean?

WUEsite=VwaterEIT\mathrm{WUE_{site}} = \frac{V_{\mathrm{water}}}{E_{\mathrm{IT}}}

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Start withV_water
Divide byE_IT
This relates tomathrmWUE_site
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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.

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VwaterV_{\mathrm{water}}

Symbol V_water

total on-site water consumption in litres.

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EITE_{\mathrm{IT}}

Symbol E_IT

the electricity delivered to IT equipment, giving WUE units of litres per kilowatt-hour rather than PUE’s dimensionless ratio [ 4 ].

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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fraction

fraction

Divide the expression above the line by the one below it.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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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, the metric LBNL uses throughout its modeling, is defined analogously to the more familiar Power Usage Effectiveness: WUEsite=VwaterEIT\mathrm{WUE_{site}} = \frac{V_{\mathrm{water}}}{E_{\mathrm{IT}}}. where VwaterV_{\mathrm{water}} is total on-site water consumption in litres and EITE_{\mathrm{IT}} is the electricity delivered to IT equipment, giving WUE units of litres per kilowatt-hour rather than PUE’s dimensionless ratio [ 4 ] . What LBNL’s simulations across roughly 965 US weather stations and multiple facility archetypes show is that this number is driven overwhelmingly by which heat-rejection route a facility uses at the plant level — an economizer decision layered on top of, and largely independent from, the cooling method at…
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Water Usage Effectiveness, the metric LBNL uses throughout its modeling, is defined analogously to the more familiar Power Usage Effectiveness: WUEsite=VwaterEIT\mathrm{WUE_{site}} = \frac{V_{\mathrm{water}}}{E_{\mathrm{IT}}}. where VwaterV_{\mathrm{water}} is total on-site water consumption in litres and EITE_{\mathrm{IT}} is the electricity delivered to IT equipment, giving WUE units of litres per kilowatt-hour rather than PUE’s dimensionless ratio [ 4 ] . What LBNL’s simulations across roughly 965 US weather stations and multiple facility archetypes show is that this number is driven overwhelmingly by which heat-rejection route a facility uses at the plant level — an economizer decision layered on top of, and largely independent from, the cooling method at the rack. Facilities running “water-cooled chiller systems without economizers exhibit the highest WUE, largely attributed to substantial cooling tower water usage,” and this pattern holds for both air-cooled and liquid-cooled IT equipment alike when both sit behind a waterside economizer [ 4 ] . Conversely, facilities using airside economizers “allow for the shutdown of chilled water systems during favorable weather conditions, resulting in substantial water conservation,” regardless of whether the racks behind them are air- or liquid-cooled [ 4 ] .

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