N
Nick Pine
- Jan 1, 1970
- 0
NREL says an average June day in Phoenix is 88.2 F, with an average daily
max of 103.5 and a humidity ratio w = 0.0056, so the vapor pressure of water
in air is P = 14.696/(0.62198/w+1) = 0.1311 psi, and Y = 0.135T+1.92P-11.122
= 3.1, ie it's "hot," on one ASHRAE comfort scale (0 is comfy, +1 is warm,
and -1 is cool.) Can we evaporate water indoors to make 0.135T+1.92P-11.122
= 0, ie T+14.22P = 82.39? Say the house thermal conductance is 200 Btu/h-F,
and it uses 600 kWh/mo of electricity indoors, and windows are well-shaded.
P = 29.921/(0.62198/w+1) = 0.2670 "Hg makes Tdp = 9621/(17.863-ln(P)) = 502 R
or 42 F, less than the 55 F said to be needed for swamp cooler effectiveness.
With indoor temp T, airflow of say, 1000 cfm brings in about (103.5-T)1000
Btu/h of sensible heat. The house conductance adds (103.5-T)200. Electrical
use adds 2841 Btu/h, so the peak cooling load is (103.5-T)1200+2841 Btu/h.
It takes about 1000 Btu to evaporate a pound of water, and air weighs about
0.075 lb/ft^3. With an indoor humidity ratio w, 1000 cfm of air can move
about 1000x60x0.075(w-0.0056) = 4500(w-0.0056) pounds of water per hour or
4.5x10^6w-25200 Btu/h of heat... (103.5-T)1200+2841 = 4.5x10^6w-25200 makes
T = 126.87-3750w. P = 14.696/(0.62198/w+1), so 126.87-3750w+14.22P = 82.39
makes 44.48-3750w+208.98w/(0.62198+w) = 0, ie 84.31w^2+46.74w-0.62198 = 0,
which makes w = 0.0130 pounds of water per pound of dry air.
T = 78.1 F and P = 0.3009 psi (0.613 "Hg) makes Y = -0.001, ie "comfortable."
Adding 4500(0.0130-0.0056) = 33.3 lb/h of water (4 gph) would raise the RH
from 100x0.267/e^(17.863-9621/(103.5+460)) = 12% outdoors to 62% indoors. We
might use 12 40 psi 0.5 gph indoor misters, eg 2 $26.96 Mister Cool kits from
http://www.hydropool.com/cgi-bin/hydro/pool_supplies/accessories/az-pro.htm,
with a 67% duty cycle.
But that's 103.5 F peak of an average June day, and houses have mass.
At the average 88.2 temp, (88.2-T)1200+2841 = 4.5x10^6w-25200 Btu/h makes
T = 111.57-3750w, and 128.5w^2+71.77w-0.62198 = 0 makes w = 0.008536, so
T = 79.6 and P = 0.199 psi, as we evaporate 4500(0.008536-0.0056) = 13.2
pounds per hour of water.
And why 1000 cfm? It looks like an intelligent swamp cooler might use less
air and water flow for lower outdoor temps, eg 200 cfm and 6.9 pounds of
water per hour at 88.2 F and 300 cfm and 16.3 pounds at 103.5. Does this
comfort equation apply all the up to 100% RH? At that point, we can't
evaporate any water indoors...
A 120 V solenoid valve dug out of an old washing machine might control misters
with a $5 humidistat or a PIC microchip with a $15 Honeywell humidity sensor
and a $5 temp sensor, and maybe a moisture sensor on the floor.
Alternatively, we might build an air-air heat exchanger into the ceiling so
outgoing cooler air near the ceiling cools incoming warmer air before it
absorbs water indoors. Or trickle water over the roof at night or use a
rock-filled pond or gabion to make water near the dew point, with an indoor
fan-coil unit or ceiling radiator, without adding any warm air or humidity
to the house.
Nick
10 WA=.0056'humidity ratio (#H20/#dryair)
20 GH=200'house conductance (Btu/h-F)
30 E=2841'internal energy use (Btu/h)
40 FOR TA= 88.2 TO 103.5 STEP 15.3'outdoor temp (F)
50 FOR CFM=100 TO 500 STEP 100'vent fan airflow (cfm)
60 G=GH+CFM'effective house conductance (Btu/h-F)
70 A2=(TA*G+E+4500*CFM*WA)/G
80 A5=(82.39-A2)/(14.22*14.696)
90 B2=4500*CFM/G/(14.22*14.696)
100 A=-B2
110 B=-.62198*B2+1-A5
120 C=-.62198*A5
130 W=(-B-SQR(B^2-4*A*C))/(2*A)
140 PHG=29.921/(.62198/W+1)'indoor vapor pressure ("Hg)
150 T=82.39-14.22*14.696/(.62198/W+1)
160 PSAT=EXP(17.863-9621/(460+T))'vapor pressure at 100% RH ("Hg)
170 RH=100*PHG/PSAT
180 PRINT TA;CFM;TAB(15);T;TAB(26);RH;60*CFM*.075*(W-WA)
190 NEXT CFM
200 PRINT
210 NEXT TA
outdoor indoor indoor lb H20
temp (F) cfm temp (F) RH (%) per hour
88.2 100 75.82893 103.0296 6.552321
88.2 200 78.02118 63.76435 6.912526 <--
88.2 300 78.68417 52.91046 7.598912
88.2 400 79.00403 47.83385 8.358578
88.2 500 79.19236 44.89248 9.146326
103.5 100 71.8588 189.0924 12.33336
103.5 200 75.50176 109.3604 14.04029
103.5 300 76.62033 88.23434 16.28082 <--
103.5 400 77.16261 78.50755 18.64345
103.5 500 77.48267 72.91886 21.05314
max of 103.5 and a humidity ratio w = 0.0056, so the vapor pressure of water
in air is P = 14.696/(0.62198/w+1) = 0.1311 psi, and Y = 0.135T+1.92P-11.122
= 3.1, ie it's "hot," on one ASHRAE comfort scale (0 is comfy, +1 is warm,
and -1 is cool.) Can we evaporate water indoors to make 0.135T+1.92P-11.122
= 0, ie T+14.22P = 82.39? Say the house thermal conductance is 200 Btu/h-F,
and it uses 600 kWh/mo of electricity indoors, and windows are well-shaded.
P = 29.921/(0.62198/w+1) = 0.2670 "Hg makes Tdp = 9621/(17.863-ln(P)) = 502 R
or 42 F, less than the 55 F said to be needed for swamp cooler effectiveness.
With indoor temp T, airflow of say, 1000 cfm brings in about (103.5-T)1000
Btu/h of sensible heat. The house conductance adds (103.5-T)200. Electrical
use adds 2841 Btu/h, so the peak cooling load is (103.5-T)1200+2841 Btu/h.
It takes about 1000 Btu to evaporate a pound of water, and air weighs about
0.075 lb/ft^3. With an indoor humidity ratio w, 1000 cfm of air can move
about 1000x60x0.075(w-0.0056) = 4500(w-0.0056) pounds of water per hour or
4.5x10^6w-25200 Btu/h of heat... (103.5-T)1200+2841 = 4.5x10^6w-25200 makes
T = 126.87-3750w. P = 14.696/(0.62198/w+1), so 126.87-3750w+14.22P = 82.39
makes 44.48-3750w+208.98w/(0.62198+w) = 0, ie 84.31w^2+46.74w-0.62198 = 0,
which makes w = 0.0130 pounds of water per pound of dry air.
T = 78.1 F and P = 0.3009 psi (0.613 "Hg) makes Y = -0.001, ie "comfortable."
Adding 4500(0.0130-0.0056) = 33.3 lb/h of water (4 gph) would raise the RH
from 100x0.267/e^(17.863-9621/(103.5+460)) = 12% outdoors to 62% indoors. We
might use 12 40 psi 0.5 gph indoor misters, eg 2 $26.96 Mister Cool kits from
http://www.hydropool.com/cgi-bin/hydro/pool_supplies/accessories/az-pro.htm,
with a 67% duty cycle.
But that's 103.5 F peak of an average June day, and houses have mass.
At the average 88.2 temp, (88.2-T)1200+2841 = 4.5x10^6w-25200 Btu/h makes
T = 111.57-3750w, and 128.5w^2+71.77w-0.62198 = 0 makes w = 0.008536, so
T = 79.6 and P = 0.199 psi, as we evaporate 4500(0.008536-0.0056) = 13.2
pounds per hour of water.
And why 1000 cfm? It looks like an intelligent swamp cooler might use less
air and water flow for lower outdoor temps, eg 200 cfm and 6.9 pounds of
water per hour at 88.2 F and 300 cfm and 16.3 pounds at 103.5. Does this
comfort equation apply all the up to 100% RH? At that point, we can't
evaporate any water indoors...
A 120 V solenoid valve dug out of an old washing machine might control misters
with a $5 humidistat or a PIC microchip with a $15 Honeywell humidity sensor
and a $5 temp sensor, and maybe a moisture sensor on the floor.
Alternatively, we might build an air-air heat exchanger into the ceiling so
outgoing cooler air near the ceiling cools incoming warmer air before it
absorbs water indoors. Or trickle water over the roof at night or use a
rock-filled pond or gabion to make water near the dew point, with an indoor
fan-coil unit or ceiling radiator, without adding any warm air or humidity
to the house.
Nick
10 WA=.0056'humidity ratio (#H20/#dryair)
20 GH=200'house conductance (Btu/h-F)
30 E=2841'internal energy use (Btu/h)
40 FOR TA= 88.2 TO 103.5 STEP 15.3'outdoor temp (F)
50 FOR CFM=100 TO 500 STEP 100'vent fan airflow (cfm)
60 G=GH+CFM'effective house conductance (Btu/h-F)
70 A2=(TA*G+E+4500*CFM*WA)/G
80 A5=(82.39-A2)/(14.22*14.696)
90 B2=4500*CFM/G/(14.22*14.696)
100 A=-B2
110 B=-.62198*B2+1-A5
120 C=-.62198*A5
130 W=(-B-SQR(B^2-4*A*C))/(2*A)
140 PHG=29.921/(.62198/W+1)'indoor vapor pressure ("Hg)
150 T=82.39-14.22*14.696/(.62198/W+1)
160 PSAT=EXP(17.863-9621/(460+T))'vapor pressure at 100% RH ("Hg)
170 RH=100*PHG/PSAT
180 PRINT TA;CFM;TAB(15);T;TAB(26);RH;60*CFM*.075*(W-WA)
190 NEXT CFM
200 PRINT
210 NEXT TA
outdoor indoor indoor lb H20
temp (F) cfm temp (F) RH (%) per hour
88.2 100 75.82893 103.0296 6.552321
88.2 200 78.02118 63.76435 6.912526 <--
88.2 300 78.68417 52.91046 7.598912
88.2 400 79.00403 47.83385 8.358578
88.2 500 79.19236 44.89248 9.146326
103.5 100 71.8588 189.0924 12.33336
103.5 200 75.50176 109.3604 14.04029
103.5 300 76.62033 88.23434 16.28082 <--
103.5 400 77.16261 78.50755 18.64345
103.5 500 77.48267 72.91886 21.05314
