# Hot-h2o-ked

### From Earlham Cluster Department

Estimating the energy cost and hot water usage for Miller Farm turned out to be an involved process. In attempting to produce a reasonable estimate, we used multiple online hot water cost and energy usage resources, online manufacturer provided equipment model information, experimental data collection, and our best guesses.

We began with a list of hot water considerations:

- What fixtures use hot water at Miller Farm?
- How often are these fixtures used?
- What is the averge hot water consumption for each use?
- What is the daily peak hot water use?
- Can the current water heater accomidate the peak use (i.e. is all hot water used fully heated)?
- How much energy is needed to provide the averge daily hot water used?
- What is the monthly cost of heating water at Miller Farm?

The next logical step is data collection. This proceeded in a piecemeal fasion as we worked. Special thanks to Kate for finding the online model information for the hot water heater and to Dan for the online Washing Machine model info.

Miller Farm Water Fixtures (w/ hot water):

- (2) Showers
- (3) Bathroom Sinks
- (1) Kitchen Sink
- (1) Washing Machine

Appliance Information:

- Water Heater AO Smith ProMax ECT-52
- Element Wattage: 4500 Watts
- R-rating: 16
- Storage Capcity: 50 gal.
- Tempeature Setting: 125 degrees Farenheit (as per thermastat)
- Energy Efficiency Factor: .91
- First Hours Rating: 58-62 gallons
- Recovery Rate: 21 gallons by 90 degees F in one hour

- Clothes Washer Maytag model MAT12PDBAW
- Total Average Water Used per Load: 31.5 gal.
- Average Hot Water Used per Load: 6.5 gal.

Armed with the hard data on the water heater and the washer, we proceeded to address the question of how much hot water is used at Miller Farm. Unfortunatly, without installing a water meter on the hot water line (might not be a bad idea), the hot water usage data will be approximate at best. We began with online hot water heater sizing tables to get an idea of the average hot water use of everyday activities.

Average Hot Water Usage Sources:

All three sources have different hot water use estimates for given activities (even the two tables from the same DOE department). The averages of the three tables were calculated and are as follows

Hot Water Usage Estimates from Online Sources:

- Showering: 20 gal. (only the GRU table listed their number based on a 10 min. shower at 2.5 gal./min)
- Shaving: 2 gal.
- Washing Hands and Face: 2.6 gal.
- Shampooing Hair: 4 gal.
- Hand Dishwashing: 3.6 gal. (seems low)
- Clothes Washing: 25 gal. (only GRU listed usage for various washer settings, note that this number does not corrolate to the model information)
- Food Preparation: 5 gal. (DOE listings)

Given the limited time that our group had to work together, we decided to focus our efforts on finding our own shower hot water usage data. Some questions that came to mind:

- What is the average shower temperature?
- How many gallons per minute are used on average?
- How long is the average shower?

We answered the first two questions as best we could by conducting the following experiments:

Tools

- 6 quart bucket
- indoor/outdoor digital thermometer
- plastic bag (to protect thermometer
- stopwatch

Finding Average Shower Temperature: How do know what temperature the average Miller Farm dweller likes for a shower? Well, we used ourselves as a typical sample of EC students. We each set the shower to the desired temp., filled the bucket and then made the measurement.

Results:

- Dan prefered 108.3F
- Ehren 109.4F
- Kate 102F

Average temp.: 106.3 degrees F.

Finding Average Gal./Min. Hot Water Use: When filling the bucket for the above experiment, we also recorded the amount of time it took to fill the 6 quart bucket. Average: 40 seconds. That's 1.5 gal./40 seconds or 2.25 gal./min. total water use. But, how much of that water came from the water heater? The answer to this question would have been easy to find if only the shower fixtures had separate hot and cold handles, but no dice. So, we played with the sink water temperature until it was close to 106 degrees. We measured the flow of this mixture over a 40 second period, then shut off the hot water and measured the amount of cold water over a 40 second period. The ratio of hot to cold turned out to be about 4:1. That means that on average 1.8 gallons of hot water are used for every minute in the shower.

How long is the typical Miller Farm shower? Who knows... but if we assume the average shower to be ten minutes (as the GRU website does) then a typical Miller Farm Shower would use 18 gallons of hot water, which is only a 10% difference from the online average shower use estimation. Not bad.

We can check to see if the 4:1 ratio makes sense by finding the temperature of four gallons of 125 degree water and 1 gallon of 46 degree water: (125x4+46)/5 = 109 degrees. Since the 4:1 ratio was approximate this result seems reasonable.

**Inlet Temperature:**
Additionally in order to calculate the cost of heating our hot water we needed to know the average inlet water temperature. The below study on residential hot water in the US shows regional averages for inlet temperature, average daily draw and more!

- According to this source Indiana's average inlet water temperature ( in 1998) was 43-49F
- It is also nice to see that the regional set point average is between 134- 136F and our setpoint is 125F

**Estimating Household Usage:**

- With the hot water heater, shower, and washing machine information we can use the hot water usage estimates to estimate the daily hot water use at Miller Farm. To check our estimates we are using the below site which estimates hot water consumption per household occupants.

The RERC says that five occupants will use 75+ gallons of hot water in a day. Our average occupancy is 7 adults, so we expect our daily usage to be a good bit higher.

The Estimate (figured on a weekly basis and divided by 7):

- 42 showers per week ( Figuring some take more than one shower a day, some not every day, visitors may shower also. )
- 12 shavees per week ( maybe 4 occupants shave 3x a week)
- 100 hand and face washings ( about 2 per person per day)
- 7 dish doings per week (one per day but figure 7.2 gallons as there are more occupants than what the above average assumes)
- 5 food prep (does it really take 5 gallons of
**hot**water?) - 6 loads of laundry ( with some doing multiple loads, others using warm water setting, etc.)

The average daily usage is therefore: 192 gallons of hot water

- per person: 28 gallons of hot water per day

**Questions that still need to be resolved**

- What is the daily peak hot water use?
- Can the current water heater accomidate the peak use (i.e. is all hot water used fully heated)?
- Ehren has found two websites that will help answer this question:

http://home.inu.net/davidstua/wh_cal.htm and http://www.hydroquebec.com/residential/energywise/calcul_consom.html

- What is the monthly cost of heating water at Miller Farm?

- 225 minutes to heat 100 gal by 71 degrees from 46 to 125 degrees.
- 100 gal water ~ 833 pound
- 833 ~ 377,842.4 grams
- temp rise 71 F ~ 21.6 C
- calories: 8161387.2
- 34,147,244 joules
- total 2529.4 watts
- 225 minutes = 3.75 hours
- hot water energy output: 9,485.25 watt-hours or ~9.5 KWH
- elec. energy input = 4500 watts * 3.75 hours = 16.9 KWH
- Which would make our efficiency 0.56