The time it takes to start getting warm is due to the distance and flow rate, how much cold water has to be displaced. Plus a bit to warm up the pipes but cooper has a much lower heat capacity than water (1/10) so that is not very great.
How hot it will get eventually will depend on how much heat is lost by the pipes acting like radiators, a combination of the length (surface area) of pipe and how well it’s insulated.
Both. The pipes are full of cold water that has to be flushed out first. The further the pipes are from the water heater the more water to flush out. The pipes also act as a heat sink for the hot water traveling through them. The amount of heat lost to the pipes is a function of material, length, whether or not it is insulated, etc.
Eventually the pipe will heat up to the temperature of the water at which point the air around the pipes becomes a heat sink. This is where insulation helps retain the heat. Not usually a problem for domestic water applications but the pipes in a power plant are insulated to retain as much heat ($$$) as possible.
That’s a good question. Here is my view.
When you first hot water faucet on, the water temperature goes in three phases: First, it is cold. After many seconds or a minute or more, in the second phase, the water rises in temperature over 20 to 30 seconds. In the third phase, the water is hot and continues to flow hot.
In the first phase, the cold water that resides in the pipe is pushed out. The further away, the longer it takes to flush the cold water out.
In the second phase, the water is mixing, Because inside of the pipe is laminar flow, the water in the center of the pipe moves faster then the water close to the pipe wall. It thus take some time for the cold water to get pushed through. During this time, the pipes are getting warmer from the water flowing through them.
In the third phase, the hot water flows in steady state. Yes, some heat is being lost through the pipe, thus the water at the tap will be a tiny bit cooler than when it exits the water heater, but this heat is relatively small.
The reason why I can say that the heat lost is relatively small is because I insulated the hot water pipes in my house, and there was not noticeable difference.
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