Equation 11 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter
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the temperature rise. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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change
Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.
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What the article says around this equation
The following is my own worked calculation, using standard property values rather than any cited source. At around 27 °C and atmospheric pressure, air has 1.17\ ; liquid water has 4180\ . The ratio is roughly 3,600 to one. Rejecting 100 kW at a 15 K rise therefore requires about 5.7\ of air — near 12,000 cubic feet per minute, through a single rack aperture — or about 1.6\ of water, which is a garden hose. There is no engineering cleverness that closes a factor of 3,600; the only levers are a larger T or a larger duct, and both run out.
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