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Is water heater supplying correct amount of hot water?

Check for crossover before starting test:
Test for crossover

"Read all steps prior to beginning.
STEP 1 At faucet nearest to water heater, time (in seconds) how long it takes to fill a 1 gallon bucket (flow rate).
Gallon per minute (gpm) = 60 seconds / seconds to fill a 1 gallon bucket
If the bucket fills in: 10 sec = 6 gpm
12 sec = 5 gpm
15 sec = 4 gpm
20 sec = 3 gpm
24 sec = 2.5 gpm

STEP 2 Turn thermostat dial on the water heater so the arrow points to approximately 130°F  How to adjust thermostat
STEP 3 Run about 15 gallons of hot water from the nearest faucet. Shut water off.
STEP 4 Water heater should complete heating 15 gallons in approximately 20-35 minutes.
STEP 5 At a nearby faucet using a thermometer or heat sensor, measure the hot water temperature.
STEP 6 The temperature should fall between 120°F to 140°F.
STEP 7 Continue running the hot water until 60% of the tank capacity is depleted:
CAPACITY DEPLETE
30 gallons tank, run 18 gallons
40 gallons, 24 gallons
50 gallons, 30 gallons

STEP 8 At the same faucet using a thermometer or heat sensor, measure the water temperature after 60% is emptied.
STEP 9 The temperature should be about 30°F below the temperature in step 6.

What to do to FIX
If the temperature was not within range at step 6, check or replace the thermostat.  How to replace thermostat on electric heater    Replace thermostat gas heater
If more than 30 °F was lost after step 9, check the dip tube."  How to replace dip tube

Resources:
Test amount-of-hot-water.pdf
Test-hot-water-Volume.pdf
Look at yellow label on side of tank for first hour delivery: this will be the average expected amount of hot water the heater should provide before water turns cold.
The average will decrease in winter with colder incoming water.
Ways to increase amount of hot water
What is first hour delivery?
First hour delivery is amount of hot water a fully heated water heater can deliver in the first hour period. 
Start with a water heater that is fully heated (has recovered to its thermostat setting) and someone begins to use hot water such as a shower or bath. 
It does not mean the hot water will last for one full hour.

First Hour Rating
"The calculated amount of hot water a fully heated water heater can deliver in the first hour period. The output of a water heater is normally given in gallons per hour at a 100°F temperature rise.  It is the quantity of water that the heater will deliver at 140°F, when the cold start temperature is 40°F." Footnote: typical bath-shower is 104-110°F and not dangerously high 140°F. Resources: Average temperature shallow groundwater   How to calculate cost of running gas water heater
First hour is based on initial storage (gallonage of tank) plus the ability to heat water as it is being drawn (recovery). 

ENERGYGUIDE label sometimes shows first hour rating.
The number is approximation.
Part I: Tank capacity x .70
"Residential water heater can deliver 70% of tank capacity at the thermostat setting minus 20 degrees.  What does this mean?  If the thermostat is set on 120 degrees, the unit should deliver 70% of tank volume at a temperature between 100 degrees and 120 degrees."
What does 70% of tank capacity mean?  It means 70% of the gallon capacity listed on the rating plate.  For example 30 gallon x .7 = 21 gallons as seen on chart.
Why 70% of the tank capacity? 
Cold water enters heater as the hot water is being used. The cold water mixes with hot water in the tank, causing the water inside tank to cool, just like adding cold water to a hot cup of tea.
As hot water is used, the dip tube, attached to the cold water inlet on water heater, delivers cold to the bottom of the tank.  The pressure of incoming cold
water pushes hot water out of the tank. Once cold water has mixed with the hot water, the water turns warm, then tepid, then cold.
Once cold reaches 30% of tank capacity, the available hot is 70% and the water will quickly become cold.

Check your heater with Draw-down test:

Is the tank producing enough hot water to match size of tank?
"Residential water heater can deliver 70% of tank capacity at the thermostat setting minus 20 degrees.  What does this mean?  If the thermostat is set on 120 degrees, the unit should deliver 70% of tank volume at a temperature between 100 degrees and 120 degrees."

Steps:  Turn off heater. Connect hose to drain. Run hose into 5 gallon bucket.
With a 50 gallon tank. Expect minimum 70% or 35 gallons of hot water before it starts to cool.  Run water fast before it cools.
If result shows correct amount of hot, then tank is functioning.
Part II: Recovery
Offsetting loss of heat, the water heater thermostat responds to cold water and turns on the burner or element. The tank is heating the water even while hot water is being used. This means the tank is recovering.
Water heater recovery must be factored with the 70% rule to determine first hour delivery. To determine the 'ballpark' first hour delivery use the following formula:
(tank capacity) x .70 + (recovery) = first hour delivery
Resource:How to calculate recovery

Larger image
Part III:  Calculate first hour:
(tank capacity) x .70 + (recovery) = first hour delivery

Use chart on left for recovery.  Check the rating plate of your water heater for the input in watts (electrical) or BTUs (gas). Resource:How to calculate recovery

Example first hour calculations:
Summertime: Assume 60° incoming temperature and thermostat set at 120° resulting in 60° rise in temperature.
 40 gallon, 30,000 BTU gas water heater
(40 x .7) + 61 = 89 gallons first hour delivery

Winter: Assume 40° incoming temperature and thermostat set at 120° resulting in 80° rise in temperature.
40 gallon, 30,000 BTU gas water heater
(40 x .7) + 46 = 74 gallons first hour delivery
More first hour calculations
40 gallon electric water heater with 4500 watt elements:
Summertime: Assume 60° incoming temperature and thermostat set at 120° resulting in 60° rise in temperature.
(40 gallon x .7) + 31 gallon recovery = 59 gallons

40 gallon electric water heater with 5500 watt elements:
(40 gallon x .7) + 38 gallon recovery = 66 gallons
40 gallon electric water heater with 4500 watt elements:
Winter: Assume 40° incoming temperature and thermostat set at 120° resulting in 80° rise in temperature
(40 gallon x .7) + 23 gallon recovery = 51 gallons

40 gallon electric water heater with 5500 watt elements:
(40 gallon x .7) + 28 recovery = 56 gallons
What is peak hour demand?
Peak hour demand is the busiest one-hour of hot water usage period.
This may be in the morning, evening or some other time during the day.
Accurate calculation of demand is essential to proper water heater sizing.
Resources:
How to calculate recovery
How to calculate first hour delivery
Figure peak demand
Peak hour demand for family of three.
Illustration shows 3 showers using 20 gallons hot water per shower.
This amount of hot water seems very high.
Dishwasher and clothes washer manufactured after 2015 are designed to consume much less water.
There are many ways to conserve hot water. If peak hour can be reduced, then smaller size water heater can be installed.
Generally: cost to operate 40 gallon water heater can be $9 per year less over 50 gallon. 40 gallon heaters have 2% higher efficiency vs 50 gallon.
Caution: buying gas water heater that is too small can overwork the heater and shorten lifespan. Overuse has no effect on electric heater since parts are generic and easily replaced DIY.

Resource:
9 ways to save with water heater
Two water heaters
How much does it cost to fun gas water heater
How to repair electric water heater
How much hot water does your shower consume?
Typical shower or bath is 104-110°F. Typical water heater thermostat is set at 120°F. Divide 104-110° by 120° to find the ratio of hot and cold. This example shows the ratio of Hot-cold is 85-90%.
For more accurate percentage, use cooking thermometer to measure water temperature with full Hot water coming out of faucet, and then test again at bath or shower temperature.

To find the total for your shower habits, plug drain, take ordinary shower, remove water using measuring cup, then multiply by 85-90% hot-cold ratio.
Similar calculations can be made for laundry by filling empty laundry tub then use measuring cup to manually empty tub. Estimations can be made for other hot water usage like washing hands. Of course toilets and outdoor faucets are not connected to Hot water and should have no effect.giving a ratio of 85-90% hot and 10-15% cold if thermostat is not out of calibration, and single handle faucet cartridges are not leaking Read about crossover.
Recovery Capacity
... is the maximum amount of water that can be heated by a water heater with a given temperature rise in one hour.
Recovery is typically measured in gallons per hour (GPH).
Generally, more BTUs or higher wattage input means faster recovery rate. 
Recovery rates are also a component of the First Hour Rating which is basis for water heater sizing. Resource: How to calculate first hour
GPH gallon per hour recovery for ELECTRIC water heater
= Watts divided by [2.42 x temperature rise in F°]
Requirements:
You need incoming water temperature and actual temperature of water inside tank.
Note: thermostat calibration is approximate so actual temperature of water inside tank is unknown without measuring.
Install temperature gauge
Buy: temperature-pressure gauge
Winters Temperature gauge<
Note: Seasonal fluctuations in local incoming water temperature vary year-round.
Other variables such as efficiency are not considered in the formula.
Resources:
Water heater formulas .pdf
Ways to increase amount of hot water
Recovery calculations for Electric water heater/ summer and winter:

A) Typical residential non-simultaneous water heater with 4500 watt elements.
Summer: 65° incoming water temperature. Resource: Average temperature shallow ground water
Thermostat set to 125°F:
4500 watt divided by [2.42 x 60° rise in temperature] = 31 GPH recovery in summer
Winter: 40° incoming water temperature.
Thermostat set to 125°F:
4500 watt divided by [2.42 x 85° rise in temperature] = 21 GPH recovery in winter

B) Residential water heater converted to simultaneous wiring where both elements can heat at same time
Install 2 - 5550 watt elements each connected to a separate 30 amp breaker. Resource: How to wire simultaneous water heater
Summer: 65° incoming water temperature.
Thermostat set to 125°F. Resource: How to adjust water heater temperature
11000 watts divided by [2.42 x 60° rise in temperature] = 75 GPH recovery for simultaneous water heater in summer
Winter: 40° incoming water temperature.
Thermostat set to 125°F:
11000 watt divided by [2.42 x 85° rise in temperature] = 53 GPH recovery for simultaneous water heater in winter

Increase recovery by raising thermostat
Raise recovery by changing thermostat setting. Resource: How to adjust water heater temperature
Upper and lower thermostat can be set differently.
A timer can be used to control temperature differences, and save money by toggling the water heating capacity depending on peak usage times. Resource: Use timer to control thermostats
 

Increase recovery by installing tempering tank to passively preheat incoming cold water
Tempering tank

Increase recovery by installing 2 water heaters
2 water heaters mean higher volume of hot water is available, and user is less likely to run short of hot water
Resource: Two water heaters

Opinion:
Raising thermostat to 130°F is easiest way to increase recovery. Installing tempering tank is extra work but effective for increasing temperature of cold incoming water.

If very high recovery is needed, then wiring extra breaker and running another 10 gauge wire for simultaneous operation is best way to increase recovery.
Resource:   How to wire simultaneous water heater
Converting to simultaneous is more work, but safer than increasing water temperature to 140-150°F.
Temperature gauge
Permanent install on hot pipe leaving water heater.

Buy:
Winters Temperature gauge
Temperature-pressure gauge for boiler
GPH gallon per hour recovery for Gas water heater
= BTUs per hour divided by [11.0 x temperature rise in F°]
GPH gallon per hour recovery for GAS water heater =
BTUs per hour divided by [11.0 x temperature rise in F°]

To accurately calculate temperature rise, you need incoming water temperature and actual temperature setting
Note: thermostat calibration is approximate and actual temperature of hot water is not known without measuring.
Note: Seasonal fluctuations in local incoming water temperature vary year-round.
Other variables such as efficiency are not considered in the formula.
Gas water heaters recover faster than electric.
Resource:s
Water heater formulas .pdf
Water heater efficiency calculation
Ways to increase amount of hot water
Recovery calculations for Gas water heater/ summer and winter:

A) Typical gas heater with 40,000 BTU heater
Summer: 65° incoming water temperature.
Thermostat set to 125°F.
40,000 BTU divided by [11 x 60° rise in temperature] = 60 GPH recovery in summer.

B) Typical gas heater with 40,000 BTU heater
Winter: 40° incoming water temperature.
Thermostat set to 125°F.
40,000 BTU divided by [11 x 85° rise in temperature] = 42 GPH recovery in winter.
Problems with setting thermostat too high:
Very hot water poses extreme risk of scalding. 140-150°F is extremely dangerous
Hotter water heater temperatures increase pressures inside the tank, shortening life of tank that is rusted. Prevent tank from rusting
Very hot water can cause leaks or drizzling TP valve.
A tank that is connected to pipes in a closed system where expansion of water is confined by a check valve or pressure-reducing valve, can experience damaging/dangerous pressure increases when thermostat temperatures are set very high.
Resources:
Closed system .pdf
Install pressure tank to prevent closed system
Very hot water poses risk of scalding.
Temperatures above 135° are extremely dangerous and will scald the skin in seconds.
Average bath-shower temperatures are 104-110° and rarely much higher.
120° F thermostat setting is considered best for optimal savings, 140F is for killing bacteria .

Hotter water heater temperatures increase pressures inside the tank, possibly shortening life-span of tank, causing rupture or drizzling TP valve.
Prevent rusted tank by replacing anode rod:
Resource: How to replace anode rod

A tank that is connected to pipes in a closed system where expansion of water is confined by a check valve or pressure-reducing valve, can experience dangerous pressure increases when thermostat temperatures are set very high.
Resource: Prevent damage from closed system
gas meter on gas water heater Install meter on Gas water heater
Record exact usage of BTU of gas appliances.
3/4" pipe thread connections. Use yellow teflon tape or gas-approved sealant.
No excess tape or sealant inside pipe. Use black pipe or yellow flex line. Keep pipes clean during assembly.
Install in vertical position with inlets pointing up as illustrated.
12.2" Tall x 8.5" Wide x 11.2" Deep
No power source required
Digital readout in cubic feet
Remote Readable option (pulse output) using EKM-25IDS

Buy:
EKM gas meter
Approved gas pipe sealant
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EKM gas meter
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