The flow rate of the water in a pipe, and the diameter of the pipe determine the velocity of the water
traveling in the pipe, and thus the amount of waiting time for hot water to arrive at the fixture.
Increasing the flow rate and decreasing the pipe diameter have the same affect; increasing the velocity of the water in the pipe. Flow rates that are too high can produce noise and vibration in the piping, and can cause water hammer problems. High flow rates can cause pipe erosion especially in the elbows and T fittings.
Often building codes limit the water velocity in hot water piping to 5 feet per second. At five feet per second the hot water should reach a fixture connected to the water heater with a 100 foot pipe in about 20 seconds.
The table below gives the flow velocity in feet/second for a number of flows in g/m with typical pipe sizes.
Pressure Drop Affects Flow Rate
To push for instance, 4 gallons per minute through a 100 foot long ½” diameter Type L copper tubing would require a pressure of 10.6 psi. No problem if your source of water is more than 10.6 psi, but if you are circulating water with a hot water circulating pump then you have more of a challenge.
At 1 gallon per minute the drop would be less than 1 psi but the wait would be about 112 seconds.
At 5 gallons per minute the pressure drop would be 16.1 psi. (37.1 feet of head)
Hot Water Circulating Pumps
Here is a graph showing the pump curves for TACO hot water circulating pumps and are virtually the same as all the other brands. (1 psi = 2.3 feet of head and 1 foot of head = .434 psi.)
From the graph it is easy to see that none of the pumps will be able to create a 5 g/m flow and only two a 4g/m flow.
Hot Water Return Line
If you have a hot water circulating system then you need a return line from the furthest end of the hot water supply pipe back to the pump and water heater. If you are using a hot water demand system then the cold water piping is typically used as the return line. When calculating the wait time for the hot water the return line isn’t included, but for purposes figuring pressure drop and flow rates it will need to be included.
Tankless Water Heater Pressure Drops
Storage water heaters (Tank type heater) typically have insignificant pressure drops when water flows through them. Below is a graph showing the pressure drop through various models of Rinnai tankless water heaters. Tankless hot water heaters do have significant pressure drops. 
From the graph it can be seen that the larger the heater the lower the pressure drop at any given flow rate.
To find the pressure required to push a certain flow through the piping system requires one to add the pressure drops from the piping and from the water heater.
Reading from the graph with the largest model (lowest pressure drop) we find that at 4 gallons per minute the pressure drop will be approximately 5 psi, and at 5 g/m the drop will be about 8 psi. On the other end of the scale, the smallest tankless water heater has a pressure drop at 4 g/m of about 9psi and at 5 g/m it’s close to 12 psi.
Armed with the above charts and graphs it should be fairly easy for you to get a good idea of how long the wait for hot water will be for any given plumbing layout and pump combination. Basically you want to minimize pipe diameters and lengths to minimize the total volume contained in the hot water piping to have
the most efficient hot water plumbing system.
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