I’m happy to hear you got it sorted out! I know the mixing definitely causes more water than the pipe volume to come out, figured some quick mathematical musing on it would be fun. I’m glad to hear your estimates are around the range of varience I’d have expected. Thank you for the thought provoking articles.

Josef: My estimate is that the pipes from the water heater to my kitchen sink are about 80 feet long and 3/4″ in diameter until the last few feet. I wrote in the article above, though, that the amount of water that comes out of the tap while you’re waiting for the hot water to arrive is greater than the water in the pipe. Near the end of the pipe diameter section, I wrote:

“With low flow, the hot water doesn’t come rushing through the pipe, pushing everything in front of it all at once. That kind of displacement flow, or plug flow, doesn’t happen with low flow rates in larger pipes. The velocity is low enough that mixing occurs, which increases the time it takes to get hot water and the amount of wasted water.”

My pipes were both too long and too big. I just finished a retrofit and get much better performance now. Here’s my article on the improvement in my bathroom shower and lavatory:

How I Got Faster Hot Water

I did the kitchen last weekend and now get warm water in less than 20 seconds and hot by 30 seconds. The amount of water that comes out in the meanwhile is about 9 cups, a little more than half a gallon.

David, we’ve had years of experience using a POU 4-gal 120V 1800W water heater for our master bath, which is at the opposite end of the house from our water heater. The hot water line comes zig-zagging from the WH to the laundry, then the kitchen, then the wet bar, then the guest bath, and finally to the master shower, followed by the master vanities. A really stupid layout, but it is what it is. The original owner or the plumber or builder must have realized that it was going to be problematic, and seemingly last-minute, added a loop and 120V outlet in a closet near the master shower to allow the installation of a small POU water heater.

When we bought the house, no POU WH was installed, so I bought a good-quality new one (Bosch). The 4 gallons routinely required up to 30 min to come up to the set-point heat, which I set on the hot side (135F) to reduce the amount of hot water coming from this small reservoir that was required for a comfortable shower. It would barely last through my wife’s hot showers, at which point the incoming water to the mini-tank from our main WH would be “warm” not “hot.” Being 85 ft from the main WH, with uninsulated 3/4″ copper pipes buried in the soil under the slab (cold and hot close to each other), it is no wonder. But here’s the kicker: I was also using a recirculator with a hot/cold return crossover in the guest bath, which meant that the water in the line up to that point was generally “warm” already. We also originally were using an outlet timer to automatically turn on the minitank so that hot water would be ready when needed for a morning or evening use, but the hard water killed the heating element and anode in only 3 years. So, after installing a new element and anode, we changed to just turning it in for shower use, and had to wait for the tank to heat. When both of us showered, we had to wait again for the re-heat. If there was an event for which we needed to shower, we had to plan ahead and start the process about 1.5 hours in advance.

The only realistic solution was to run a new power cable to the closet from the nearby service entrance (just outside of the master bath), and install a 12 kW tankless water heater in place of the mini-tank. Set for the usual 120F output level, it works like a charm, with hot water in seconds. And the electrical power (kWh) used for a shower is now LESS than the power required for the mini-tank WH for the same length of showering, although the kW spike is significant (but drops rapidly as the shower proceeds). This also resolved the problem of the drop in temperature of the incoming hot water to the shower valve during the shower, since it is now quick and constant. A win-win, especially since we do not find it necessary to take showers every day, and only use a master bath vanity’s hot water perhaps 10 times a week.

To elaborate further on my last comment, the concept you raised has been realized a couple of ways. Potable water ECM circulators are available for domestic recirculation lines with one or more “hot buttons” where the user pushes the button prior to using the fixture. The cool water in the branch(es) is flushed back into the water heater as hot water is advanced to the fixture. Also, some on-demand heaters (Navien comes to mind) have integral circulators and optional “hot buttons” to do exactly the same thing. Retrofit can be fairly easy in many cases if plumbing is accessible in basements or crawl spaces.