How may gallons of water will flow thru a 1/4 inch valve per minute with 150 psi pushing it

About 1 gallon US per minute

Just a little over 53.3 gallons

The hot side of the faucet is most likely plugged with something that came up thru the water system. The average thankless waterheater requires at least 1/2 to 3/4 gpm flow rate for the unit to sense flow and turn on. If there is not enough flow it will not fire and heat the water. Not sure about this particular unit but a few require at least one full gallon per minute flow. So chances are that if you fix the faucet, you fix the hot water issue at the same time

1) Guesses: Sounds like a bad single-handled faucet cartridge, or low water flow at faucet, or clogged water filter.
Replace faucet cartridge, clean the aerator, and/or clean sediment out of pipes below sink, and clean water filter at tankless unit each month.

2) For exact measure of problem:
Typical faucet can have 2 gallon per minute flow rate.
2 gpm flow rate means faucet fills 1 gallon container in 30 seconds. Test faucet using 1 gallon container and a cooking timer to get flow rate.
Clean aerator to improve flow rate. Compare kitchen flow rate with other faucets in home.
http://waterheatertimer.org/Low-hot-water-pressure.html

Most homes have 1/2" diameter pipe running to kitchen faucet.
100 feet of 1/2" diameter pipe holds 1.2 gallons of water. This assumes no sediment build-up inside pipes.
http://waterheatertimer.org/Water-heater-recirculation-system.html

Assuming only hot is turned on: If faucet is 100 feet away from water heater, and pipe diameter is unobstructed 1/2" diameter, and faucet has 2 gallon per minute water flow, then hot water should arrive in 36 seconds.
50 feet away, and hot water should arrive in 18 seconds.

If kitchen has single handled faucet, and the handle is raised in the middle, then equal amounts of hot and cold water are drawn at same time. This doubles amount of time for hot water to arrive.

If single handle faucet has a bad cartridge, then faucet can have crossover.
Crossover means that cold water can enter the faucet even if faucet is turned to hot.
Bad single-handled faucet cartridge can delay or stop the arrival of hot water.
http://waterheatertimer.org/Crossover.html

Tankless require maintenance including cleaning combustion parts yearly, de-lime heat exchanger frequently, and clean water filter each month.
http://waterheatertimer.org/pdf/Tankless-maintenance.pdf
http://waterheatertimer.org/pdf/Bosch_Overcoming_fluctuating_temps.pdf
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

Add a comment for more help.

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body { background: #FFFFFF; margin: 0px; padding: 4px; font-family: arial, verdana, sans-serif; font-size: 10pt; } p { margin:0px; padding:0px; } .spwrap { background: transparent url(/wysiwyg_rte/misspell.gif) repeat-x scroll center bottom; } You are talking about length of time to get hot water from water heater.What diameter pipe are you talking about? What type of faucet do you have?
1/2" pipe has inside diameter of .54" and holds 1.2 gallons per 100 feet
10 meters is 32 feet and holds .4 gallons
Average faucet puts out 2 gallons per minute, so 30 seconds you should get 1 gallon of water.
Put a bucket under faucet and check amount of water flow.

Assuming you draw just hot water from the faucet, then 30 seconds is slow for receiving hot water.
If you have single-handle faucet and raise handle straight up in middle, then you are drawing half hot and half cold, so it would take 30 seconds for hot to arrive.

If hot water is slow, the problem might be crossover.
http://waterheatertimer.org/Crossover.html
or low water pressure due to clog in water line
http://waterheatertimer.org/Low-hot-water-pressure.html
Other problems could include clogged water filter, clogged water softener, defective pressure valve, and low water pressure.

Sources:
http://waterheatertimer.org/Troubleshoot-Bosch-Tankless-water-heater.html
http://waterheatertimer.org/Water-heater-recirculation-system.html

Can tankless electric water heater be repaired? Sure.
Is it worth the expense if problem is going to happen again? I can't answer, but can offer resources.

New tank-type electric water heater costs $207 and new tank-type gas costs $320 at local box store.
You can install new tank-type electric yourself in a couple hours. DIY repair on tankless is not easy since parts are not at local box store, and what part do you need, and tankless parts can easily cost more than new tank-type water heater.

Open following link for Bosch troubleshooting resources.
http://waterheatertimer.org/Troubleshoot-Bosch-Tankless-water-heater.html

GENERALLY, Tankless require .4 gpm (gallons per minute) water flow to activate heating cycle, and then require .25 gmp flow to keep heating cycle going.
For example .4 gallon per minute means faucet can fill 1 gallon container in 2-1/2 minutes
Some tankless units require more water flow, for example .75 gpm

Tankless water heaters have flow sensor that tells computer chip when enough water is flowing to activate heating cycle.
If the sensor is clogged, or if water filter inside tankless unit become clogged with dirt or sediment from hard water, then the unit does not signal enough water flow and will not activate.
Home filtration system and water softener can also slow the flow of water.
Low water pressure and crossover problem on single-handled faucet and crossover on recirculation system check valve and high thermostat setting can also cause heat cycle to not activate.

Tankless cannot be exposed to water with more than 11 grains hardness or parts inside tankless will coat with sediment and not work. Within 2 years the unit will not work, with diminished efficiency from the beginning.
http://waterheatertimer.org/Battelle_Final_Report.pdf

If water is hard, and you cannot soften the water, or if water is dirty and cannot be cleaned, then the best recommendation is to use tank-type heater instead of tankless.

All costs are energy. For average home: Tankless electric is NOT cheaper to operate than tank-type electric. Tankless gas saves $1-8 per month. However, cost of unit and installation, cost of potential repairs and cost of parts, difficulty of DIY repairs, required yearly-monthly maintenance, etc outweigh expected savings.
http://www.pmengineer.com/Articles/Cover_Story/8cf9e86f7c298010VgnVCM100000f932a8c0____

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A couple of things could be happening.

1. There needs to be more water flow at the faucet, a minimum of .75 gallons per minute. Low flow and pressure balance faucets and aerators will not work well with tank-less water heaters. You need all the flow you can get.

2. The flame sensor in the main control unit is week, this is a common issue with your water heater.

Clean the unit to establish adequate water flow. Remove all faucet aerators and turn the faucets on to activate the unit. If you still get the on and off problem you need to call the company for a new flame sensor and/or control valve.

Hello. let me help you. The water pressure is what it is in the house. In other words, the tankless water heater doesn't increase the pressure of the water, it only heats the water. There is no official minimum pressure but the minimum pressure you would be happy with in any home would be 20 pounds per square inch, PSI.

if the leak is behind the handle take the handle off and tightn the packing nut, do not over tighten, as far as luke warm water is this with just one facucet on, they way these tankless water heaters work they are by gpm, gallons per min, if you have more gallons of water going thru the unit then it is designed for then it won't get hot, if your water pressure is to high going thru it will push it to fast thru the unit and won't get hot, your house pressure should be no higher then 75lbs no lower then 65lbs

no the tub faucet is the only faucet that is wide open you might have to not run full blast on the faucet , your tankless water heater is under sized for the application, to many gallons per min going thru the unit, look at the rating chart for your unit, the r94 is only 9.4 gallons per min, and a tub faucet can be upto 5 gallons per min, depending on the faucet,,