Residential Energy Use

The industrial sector includes facilities and equipment used for manufacturing, agriculture, mining, and construction.

The transportation sector comprises vehicles that transport people or goods, such as: cars, trucks, buses, motorcycles, trains, subways, aircraft, boats, barges, and even hot air balloons.

The residential sector consists of homes and apartments.

The commercial sector includes buildings such as offices, malls, stores, schools, hospitals, hotels, warehouses, restaurants, places of worship, and more.

How Water Heaters

• Heated water is used in bathing and cleaning periodically throughout the day.

• Energy is required to heat the water.

• If not used immediately, energy is also required to keep the water hot!

Types of Water Heaters: Tank• Water is …

– heated and stored– delivered to user when

needed– replaced in the tank

by municipal connection– Reheated as needed

• Sizes: – 60 – 90 gal. whole home– 3 – 10 gal. point of use

• Energy Use– Electric – Natural gas– Solar– Heat pump

unitedinspection.com

Homedepot.com Heaterdetails.info

Types of Hot Water Heaters: Tankless

• Water is …– run through the heater

when needed– brought up to desired

temperature– delivered to user– not stored

• Energy used– Natural gas– Electric

Heaterinsigt.info

A-archer.net

How to Choose?

• Not an unimportant decision– 22% of US energy use is

residential– 20% of that is heating

water

• Things to consider– Size– Fuel type– Overall cost– First hour rating

Tankless water heat ratings

• Primary consideration: want hot water at a desired flow rate

• Appliances are rated by the maximum temperature rise possible at a given flow rate

• Amperage (amps) : 29 A • Element Wattage (watts) : 7KW • Flow Rate @ 35°F Rise

(gallons/min) : 2.2 gal (US)/min • Flow Rate @ 45°F Rise

(gallons/min) : 1.5 gal (US)/min • Flow Rate @ 77°F Rise

(gallons/min) : 0.5 gal (US)/min • Fuel Type : Electric • Maximum temperature (F) : 125 • Voltage (volts) : 240 V

Rheem Ecosense 7kW

Sizing a tankless water heater• To size one we must estimate

the peak usage flowrate, dV/dt, (usage) in volume/time

• Then, we must determine if the system can heat that amount of water per unit time from the starting to the final temperature.

• Finally total daily usage tells us how much energy is used

• Assume – you live alone and just want a hot

shower.– a low flow 1.5 GPM showerhead

(Federal Regulation from 1992 is 2.2 GPM max)

– 50 F inlet water – You want a 95F shower.

• Is this possible with the 7kW Rheem?

Typical Flow Rates in Gallons per Minute (gpm)

Fixture Type

Bathtub Shower Kitchen Sink

Dish-washer

Flow Rates

2.0 – 4.0 1.5 – 3.0 1.0 – 1.5 1.0 – 3.0

How much energy is required?

• Assume we take a shower at 1.5 gpm• The outlet temperature will be 95F (50F+45F)• How much power (dQ/dt) is required to achieve this change

in water temperature?

kWkJ

F

CF

Ckg

kJ

m

kg

gal

mgal

TcVTct

Vt

TcV

t

Tmc

dt

dTmcQ

1.10sec/1.10

9

5*4519.4

1000

.2.264

1

sec60

min1

min5.1

3

3

Hmmm!! Someone is not telling the truth! Where are their ethics?!

If your luxury shower takes 10 minutes how much energy is used?Q=10,100 J/s * (600 sec) = 6.01 MJ (or 2.5 Big macs)

What about your dorm room or apt.?

• Peak usage– 1 shower at a time– 1 bathroom sink– 1 Kitchen sink (or not?)

• The power required at peak would be the sum required from all sources used at the same time.

• EX: Two 1.5 GPM showers at 95F (from 50F) would require a unit capable of 20.2kW by our calculations.

• Total Daily Usage– # of people bathing– Dishwasher, sink, clothes

washing• The daily energy required is

found by integrating (summing) power usages throughout the day

• If one bather took 5 and the other 10 minute showers, you would use 6MJ +3MJ=9MJ of energy.

...sin21

kshowershower tQtQtQ

dtdt

dQQ

...1sin1 kshowertotal QQQ

What About your parents home?

• Your parent’s home• Peak usage

– ~2 showers concurrently in the morning (possibly multiple sets of two)

– ~2 sinks in the morning (possibly multiple sets of two)

• Total Daily Usage– #of people bathing– Dishwasher, sink, clothes

washing

Peak power tells the size of the unit required.

Total daily use tells the amount of energy used per day.

Worksheet for Estimating Daily Water usage: Say for a family of 4

Use Average gallons of hot water per usage

Times used during day   Gallons used per day

Shower 12 ×3 = 36Bath 9 ×1 = 9Shaving 2 ×1 = 2Hands & face washing 4 ×4 = 16

Hair shampoo 4 ×2 = 8

Hand dishwashing 4 ×0 = 0

Automatic dishwasher 14 ×1 = 14

Food preparation 5 ×3 = 15

Wringer clothes washer 26 ×0 =  0

Automatic clothes washer 32 × 1 =  32

      Total Daily Demand =  100 gallons

How much energy would be required to heat all of this water by 45F?

Sizing a tank (storage) water heater

• primary consideration: the tank should not run out of hot water; examine the “first our demand”

• Important specifications include– size (gal.) – Energy used (often in BTUs)– Recovery rate: time to reheat

water and “First Hour” rating– energy factor (EF): relative

measure of hot water produced per unit energy

– “R” value of tank insulation (sometimes not given)

• Fuel Type : Gas • Gas Type : Natural Gas • Total BTU : 40000 Btu (per hour)• Maximum temperature (F) : 160 • Minimum Temperature : 60 °F • Recovery Rate at 90F Rise (GPM

GPH) : 40.4 • Tank Capacity (gallons) : 40 gal

(US) • First Hour Rating (GPH):68.0• Tank Diameter (in.) : 20.25 • Tank Height (in.) : 62 • Beware of faulty information

40 gal GE hot water heater

Worksheet for Estimating Peak Hour Demand/First Hour Rating

Use Average gallons of hot water per usage

Times used during 1 hour   Gallons used in 1 hour

Shower 12 × 2 =  24Bath 9 ×  =  Shaving 2 × 1 =  2Hands & face washing 4 × 4 =  16

Hair shampoo 4 ×  =  0

Hand dishwashing 4 ×  =  

Automatic dishwasher 14 ×  =  

Food preparation 5 × 1 =  5

Wringer clothes washer 26 ×  =  

Automatic clothes washer 32 ×  =  

      Total Peak Hour Demand =

 47 gallons!! We are close. Possibly undersized.

How much energy is required to heat the water in the tank?

• Assume the water enters the tank at 50 F.• The energy required to heat 47 gallons to make it

available?

• But if we do not use it immediately, then it will cool off and we will have to heat it again!!

)12(~9.28109.28

9

55012018.4

2.264.471000

3

3

3

BigMacsMJkJ

F

CFF

Ckg

kJ

gal

mgal

m

kg

TVcTmcQ

How much heat is lost by the water in the tank?• Convection will occur at

outer surface of the tank.

•Difference between air temperature and surface temperature drives convection.

• We know Tsurface > Tair so we draw convection leaving tank.

• Since heat is being lost, dQH/dt, we must reheat dQgen/dt, to maintain temperature. Want dT/dt=0

•We set TH20 and we can measure Tair. This is all we need to find heat flux.

Tair

Water heater

tank, @ Th20

generatedQ

HQ

Tsurface

0 Hgenerated QQTmc

Combined convection, conduction problem• Examine control volume (dotted line)

and boundaries. Heat flow is constant.

• Examine Water/insulation surface

• Examine conduction thru insulation

• Examine insulation/air interface

insulationWater

airHQ 20HHQ

kQgeneratedQ

Th20

Tinner

Touter

Tair

QQQQQ airHkHHgenerated _20_

InnerHHinHH

InnerHHinnnerHH

TTRQ

TTHAQ

2020_20_

202020_

*

outerinneroutinsulk

outerinnerouterinsulk

TTRQ

dTTAkQ

_*

/

d

airouterairoutairH

airouterairouterairH

TTRQ

TTHAQ

__

_

*

Conduction+Convection Through multiple thermal “resistances” (R-values)

• If we sum the boxed equations

• In general the thermal resistance for conduction is

• Thermal resistance for convection is

• And for any thermal pathway in 1D, the heat flux from the interior to the exterior is (where a negative sign means a reversal of direction)

airoutoutinsulHin

airH

airHairoutoutinsulHin

RRR

TTQ

TTRRRQ

__20_

20

20__20_*

kAdRk

HARH 1

ii

exteriorerior

R

TTQ int

Note that in our problem, this is the power required to maintain the temperature of a full tank. This is why you insulate your water heater!!! If water is used, then additional heat is required to increase the replacement water’s temperature from ambient, to our set point.

Note: In applications, traditionally “R-values” are given per unit Area,With units of area-temp/power

TARQ A *

Water Heater Heat Loss

• If the water heater is well insulated, k=0.05 W/m-C how much power on average is required to maintain the temperature in the tank for 24 hours assuming worst case natural convections?– Assume the tank has

Ainner~= Aouter=A=2pr*height+2pr2

– Where r~=10.125 inches, height=62 inches

• How much energy is used in that 24 hours?

Costs?

• Energy use cost:– Electricity: 0.18 kW-hr– Gas:

• Installation– Tankless

• Gas: $2200• Electric: 240 V ($2200) or

110V ($1350)

– Tank• Gas:$800 • Electric: 110V ($150) (or

240V ($800)

• Given our average daily usage, we can determine the recurring costs.

• Given the installation costs, we can determine the initial costs.

• Given a prevailing interest rate, we can determine present and future values.