# Hotwater-labs

### From Earlham Cluster Department

## Contents |

## Shower Lab

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?

### Tools

- 6 quart bucket
- Indoor/outdoor digital thermometer
- Plastic bag (to protect thermometer
- Stopwatch

### Procedure

#### 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 temperature, filled the bucket and then made the measurement.

Student | Temperature (F) |
---|---|

Dan | 108.3° |

Ehren | 109.4° |

Kate | 102.0° |

Average temperature: 106° |

#### Average GPM of shower

When filling the bucket for the above experiment, we also recorded the amount of time it took to fill the 6 quart bucket. The average time was: 40 seconds. That's 1.5 gallons / 40 seconds or 2.25 gpm (gallons per minute).

#### Ratio of hot to cold water

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.

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.

#### 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 Renewable Energy Resource Center, 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, etc.)
- 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 (or 28 gallons per person)

### Results

Average shower temperature | 106° |

Shower flow | 2.25 gpm |

Hot/cold water ratio | 4:1 |

Shower usage per day | > 75 gallons |

Total hot water usage per day | 192 gallons |

## Hot Water Heater Monthly Usage

### Data

Element Wattage: | 4500 |

R-rating | 16 |

Storage Capacity | 50 gallons |

Tempeature Setting | 125° Farenheit (as per thermastat) |

Energy Efficiency Factgor | 0.91 |

First Hours Rating | 58-62 gallons |

Recovery Rate | 21 gallons by 90° F in one hour |

### Tools

### Procedure

Watts must be derived from the data we have. One watt is one joule of energy per second. We can get joules from calories (1 calorie = 4.185 J), and a calorie approximates the energy needed to increase the temperature of 1 g of water by 1° C. We can convert the fahrenheit rise to celsius and gallons to grams, to get calories. Calories can then be converted to joules.

In order to convert to watts, we need to figure out the heating duration of our 50 gallon tank. The recovery rate of a hot water heater is the quantity of water that can be heated through a specified temperature rise. The standard seems to be 90° in 1 hour. The AO Smith ProMax is rated at 21 gallons. This relationship can be used to help estimate the heating duration of our 50 gallon tank from a base temperature to the thermostat's setting of 125°. So the input temperature effects the heating duration. Indiana's average inlet water temperature was 43-49° F in 1998. We can also factor in the help from the solar hot water and estimate a higher input temperature. This time can be used in conjunction with joules to get watts.

<math>50 \; gallons \; (tank \; capacity) \over 21 \; gallons \; (recovery \; rate)</math> <math>\times</math> <math>80 \deg \; (fahrenheit \; rise) \over 90 \deg \; (recovery \; rate)</math> <math>= 126.98</math> minutes to heat 50 gallons by 80°

In the previous part of the lab, we estimated the house would use around 192 gallons of hot water per day. With a 50 gallon tank, that's about 4 heatings a day.

Now we have kilowatt hours!

### Script to do the math for us

The data above can be plugged into our little script, ENPR: Sustainable Systems - Electric Hot Water Efficiency.

### Results

In Temp. | Thermostat | Degree Rise | kWh | Cost |
---|---|---|---|---|

45° (avg. inlet) | 125° | 80° | 1140 | $74.10 |

80° | 125° | 45° | 642 | $41.73 |

100° | 125° | 25° | 356.4 | $23.17 |