Waiting for the water to heat up after you've turned on the hot water tap at a sink or a tub wastes a lot of water. As Gary Klein writes in his JLC article Architectural Compactness and Hot-Water Delivery,

'When you turn on a hot-water tap, all the standing water in the pipe serving the tap has to flow out before you see hot water at the tap. In fact, it’s even worse than that: It turns out that because of mixing in the pipe, you actually have to flush double the volume of the standing water out of the pipe before fully heated water reaches the tap. In a modern house, that wait is often two minutes or more.

In practice, that adds up to a waste of water, energy, and of course, time. If the person using the tap actually decides to wait for the hot water, then several gallons of water can go down the drain before hot water arrives. If they don’t wait, but instead go ahead and wash or rinse using cold water from the hot-water pipe, then there’s a waste of energy: Water from the water heater ends up stranded in the pipe where it cools down, letting the energy dissipate without being used.'

In his recent Energy Vanguard blog post How I Got Faster Hot Water, Allison Bailes explains how he applied Klein's principles of smaller diameter-piping and shorter distances between the source of the hot water and the fixtures while tackling the problem in his own home. His solution involved a plumbing retrofit with a site-built hot water distribution manifold, smaller-diameter PEX tubing, and insulation. Bailes reports that before the retrofit he had to wait 80 seconds for 1.5 gallons of cold water to run out of his bathroom faucet before hot water arrived. After the retrofit, it only took 23 seconds before the water was hot at the faucet, wasting about a half-gallon of cold water first.

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