Transcript Slide 1

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:
Homedepot.com
Heaterdetails.info
– 60 – 90 gal. whole home
– 3 – 10 gal. point of use
• Energy Use
–
–
–
–
Electric
Natural gas
Solar
Heat pump
unitedinspection.com
Types of Hot Water Heaters: Tankless
Heaterinsigt.info
• Water is …
– run through the heater
when needed
– brought up to desired
temperature
– delivered to user
– not stored
• Energy used
– Natural gas
– Electric
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
• Amperage (amps) : 29 A
• Element Wattage (watts) : 7KW
• Flow Rate @ 35°F Rise
Rheem Ecosense 7kW
(gallons/min) : 2.2 gal (US)/min
• Flow Rate @ 45°F Rise
• Primary consideration: want
(gallons/min) : 1.5 gal (US)/min
hot water at a desired flow • Flow Rate @ 77°F Rise
rate
(gallons/min) : 0.5 gal (US)/min
• Appliances are rated by the • Fuel Type : Electric
maximum temperature rise • Maximum temperature (F) : 125
possible at a given flow rate
• Voltage (volts) : 240 V
Sizing a tankless water heater
• Assume
– you live alone and just want a hot
• To size one we must estimate
shower.
the peak usage flowrate,
– a low flow 1.5 GPM showerhead
dV/dt, (usage) in volume/time
(Federal Regulation from 1992 is 2.2
• Then, we must determine if
GPM max)
the system can heat that
– 50 F inlet water
amount of water per unit time
– You want a 95F shower.
from the starting to the final
• Is this possible with the 7kW Rheem?
temperature.
• Finally total daily usage tells us
how much energy is used
Typical Flow Rates in Gallons per Minute
(gpm)
Fixture
Type
Bathtub
Shower
Kitchen
Sink
Dishwasher
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?
dT
T
T
Q  mc
 mc
 V c
dt
t
t
V 
   cT  V cT
 t 
gal  1 min  1m3  1000kg 
kJ 
5C 



 1.5
4
.
19
45
F
*





3


min  60 sec  264.2 gal.  m 
kg  C 
9F 
Hmmm!! Someone is not telling the truth!
 10.1kJ / sec  10.1kW
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.
Q total  Q shower1  Q sin k1  ...
• 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
 dQ 
Q  
dt
 dt 
 Q t shower1  Q t shower 2  Q t sin k  ...
• If one bather took 5 and the
other 10 minute showers, you
would use 6MJ +3MJ=9MJ of
energy.
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
Total daily use tells the amount of energy
used per day.
Peak power tells the size of the unit required.
Worksheet for Estimating Daily Water usage: Say for a family of 4
Use
Average gallons of
hot water per usage
Times used
during day
Shower
Bath
Shaving
Hands & face
washing
12
9
2
×3
×1
×1
=
=
=
36
9
2
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
=
100 gallons
Total Daily
Demand
Gallons used per day
How much energy would be required to heat all of this water by 45F?
Sizing a tank (storage) water heater
40 gal GE hot 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
Worksheet for Estimating Peak Hour Demand/First Hour Rating
Use
Average gallons of
hot water per usage
Times used
during 1 hour
Shower
Bath
Shaving
Hands & face
washing
12
9
2
×2
×
×1
=
=
=
24
4
×4
=
16
Hair shampoo
4
×
=
0
Hand dishwashing
4
×
=
Automatic
dishwasher
14
×
=
Food preparation
5
×1
=
Wringer clothes
washer
26
×
=
Automatic clothes
washer
32
×
=
Gallons used in 1 hour
Total Peak
Hour Demand =
2
5
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?
Q  mcT  VcT

kg 
m3
kJ 
5C 
 4.18
 120 F  50 F 
 1000 3  47 gal.

m 
264.2 gal 
kg  C 
9F 
 28.9  103 kJ  28.9 MJ (~ 12 BigMacs )
• But if we do not use it immediately, then it will cool
off and we will have to heat it again!!
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
Tsurface
Q H
Water
heater
tank, @
Th20
Q generated
mcT  Q generated  Q H  0
Combined convection, conduction
problem
• Examine control volume (dotted line)
and boundaries. Heat flow is constant.
Q generated  Q H _ H 20  Q k  Q H _ air  Q
• Examine Water/insulation surface
Th20

QH _ H 20  Ainnner H H 20 TH 20  TInner 
Water
insulation
Tair
Q H _ H 20 * Rin _ H 20  TH 20  TInner 
Tinner
• Examine conduction thru insulation
Q k  kinsul Aouter Tinner  Touter  / d
Q * R
 T
T 
k
insul _ out
inner
outer
• Examine insulation/air interface
Q H _ air  Aouter H air Touter  Tair 
Q H _ air * Rout _ air  Touter  Tair 
Q generated
Q H  H 20
d
Touter
Q k
Q H  air
Conduction+Convection Through
multiple thermal “resistances” (R-values)
• If we sum the boxed equations
Q * Rin _ H 20  Rinsul_ out  Rout _ air   TH 20  Tair 
Q 
R
TH 20  Tair 
 Rinsul_ out  Rout _ air 
• In general the thermal resistance for conduction is
in _ H 20
Rk  d
kA
• Thermal resistance for convection is
RH  1
HA
Note: In applications,
traditionally “R-values” are
given per unit Area, Q * R A  T
With units of area-temp/power
A
• 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)
T
T
Q  int erior exterior
i Ri
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.
Water Heater Heat Loss
• If the water heater is well insulated, k=0.05 W/mC 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.