Hot Water Flow Rates in Residential Plumbing Systems with Tank Type and Tankless Water Heaters
I'd like to take a look at water flow rates through residential hot water plumbing systems with and without a tankless water heater.
Humans don't like to wait for anything including the hot water at the fixture. I read one study that concluded that in 80% of the bathroom sink uses where the hot water was turned on the user did not wait for the hot water to arrive and actually finished using the water before the hot water arrived at the fixture.
The flow rate of the water, (the gallons per minute), and the diameter of the piping are the determining factors in the velocity of the water in the pipes, and thus the waiting time to get hot water at the fixture. The flow rate is determined by the pressure difference driving the flow; the higher the pressure the higher the flow.
High Flow Rates – Pros and Cons
Flow rates that are too high can produce humming and vibration in the piping, and can cause water hammer problems with fast closing valves. High flow rates over long periods of time can cause pipe erosion in the piping and especially in elbows and T fittings. Typically building codes limit the water velocity in hot water piping to 5 to 8 feet per second to prevent erosion of the pipe and fittings.
Five feet per second is moving right along. At that velocity the hot water should reach a fixture connected to the water heater with a 100 foot pipe in about 20 seconds. But how many gallons per minute Is that? It depends upon the size of the pipes.
The table below gives the flow velocity in feet/second for a number of flows in gpm with typical pipe sizes.
Water velocity in inches per second at given flow rates for various pipe sizes  
Size  Gal/Min  0.5  1  1.5  2  2.5  3  3.5  4  4.5  5 
3/8  Feet/sec  1.11  2.21  3.32  4.42  5.53  6.63  7.74  8.84  9.95  11.06 
1/2  Feet/sec  0.69  1.37  2.06  2.75  3.44  4.12  4.81  5.5  6.18  6.87 
3/4  Feet/sec  0.33  0.66  0.99  1.32  1.64  1.97  2.3  2.63  2.96  3.29 
1  Feet/sec  0.2  0.39  0.58  0.77  0.97  1.16  1.35  1.55  1.74  1.93 
If your pipe is ¾", then at 5 gallons per minute the flow rate would be 3.29 feet per second, so a 100 foot long pipe would require about 30 seconds. If the pipe was 1/2"", then it would only take about 15 seconds to get the hot water through the 100 foot long pipe.
As you can see the smaller the pipe the higher the water velocity for a given gpm flow rate. However, it is much harder to push 5 gallons per minute through a 1/2"" pipe than a ¾" pipe, requiring more pressure.
Pressure Drop Affects Flow Rate
psi drop at various flow rates and pipe sizes per foot of pipe 


. 3/8  1/2  3/4 
1 g/m  .023  .008  .001 
2 g/m  .084  .030  .004 
3 g/m  .177  .062  .009 
4 g/m  .106  .015  
5 g/m  .161  .023 
To push for instance, 4 gallons per minute through a 100 foot long 1/2"" 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 5 gallons per minute the pressure drop would be 16.1 psi.
At 1 gallon per minute the drop would be less than 1 psi but the wait would be about 112 seconds.
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.) Therefore: 10.6 psi = 24.45 feet of head and 16.1 psi = 37.1 feet of head.
That 10.6 psi required to cause a 4 gallon per minute flow is 24.45 feet of head, which most of the pumps in the above chart won't reach. Interestingly, none of the pumps could push 5 gallons per minute through the pipe.
The 100 feet of 1/2" inch pipe is the only significant obstacle to high flow rates other than of course the fixture itself. Most if not all residential fixtures have low maximum flow rates to promote water conservation. Typically most showers are limited to 2.2 gallons per minute or less, bathroom sink fixtures often to 1 gallon per minute.
If however you are using a circulating pump then the flow does not pass through the fixtures, just the pipe and the return line.
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 ondemand 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
There is a substantial difference in the hot water flow rate for a specific plumbing layout when a tankless water heater is substituted for a tank type water heater. The reason for this difference is the tankless unit has a heat exchanger, and heat exchangers have pressure drops across them which can be quite significant and affect the flow rate accordingly.
Storage water heaters (Tank type heater) typically have a very small pressure drop when water flows through them. In a hydraulic system, such as a residential plumbing system, there are no pressure differences anywhere in the system unless water is flowing. Flowing water produces pressure drops and the pressure drop is related to the flow rate. Larger flows produce higher pressure drops.
Below is a graph showing the pressure drop through various models of Rinnai tankless water heaters.
From the graph it can be seen that the larger the heater the lower the pressure
drop at any given flow rate. In our previous example we had a 100 foot long hot
water supply pipe with a 1/2"" diameter and with a 4 gallon per minute flow our
pressure drop was 10.6 psi.
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.