Chapter 10: PSYCHROMETRIC APPLICATIONS

Example 10.01, page: 250

In [1]:
from __future__ import division
import math

# Initialization  of  Variable
m = 1 #lb
T1 = 70 #degF
phi = 0.7
T2 = 40 #degR
P = 14.7 #lbf/in2

#calculations:
#from Table T-2E
Pg1 = 0.3632 #lbf/in2
Pv1 = phi*Pg1
w1 = 0.622*Pv1/(P - Pv1)
#dew point Temp
Td = 60 #degF
#
mv1 = 1/(1 + 1/w1)
ma = 1 - mv1
#
Pg2 = 0.1217 #lbf/in2
w2 = 0.622*Pg2/(P - Pg2)
#mass of the water vapor present at the final state
mv2 = w2*ma
#amount of water vapor that condenses is
mw = mv1 - mv2

#Results
print  "a)the initial humidity ratio is", round(w1,3),"lb(vapor)/lb(dry)"
print  "b) dew point temp is", Td,"degF"
print  "c)mass  of  water  vapor  that  condenses is", round(mw,4),"lb(condensate)"

a)the initial humidity ratio is 0.011 lb(vapor)/lb(dry)
b) dew point temp is 60 degF
c)mass  of  water  vapor  that  condenses is 0.0057 lb(condensate)

Example 10.02, page: 250

In [2]:
from __future__ import division
import math

# Initialization  of  Variable
AV1 = 150 #m3/min
T1 = 10 #degC
phi1 = 0.8
T2 = 30 #degC
P = 1 #bar
R = 8314/28.97 #J/kg-K

#calculations:
#from Table T-9
ha1 = 283.1 #kJ/kg
ha2 = 303.2 #kJ/kg
hg1 = 2519.8 #kJ/kg
hg2 = 2556.3 #kJ/kg
#From Table T-2
Pg1 = 0.01228 #bar
Pv1 = phi1*Pg1
Pa1 = 0.9902
#specific volume of the dry air
va1 = R*(T1 + 273)/(Pa1*1E5)
#mass flow rate of the dry air
madot = AV1/va1
#humidity ratio
w = 0.622*(Pv1/(P - Pv1))
Qcvdot = madot*((ha2 - ha1) + w*(hg2 - hg1))
# From Table T-2
Pv2 = Pv1
Pg2 = 0.04246
#relative humidity
phi2 = Pv2/Pg2

#Results
print  "a)heat  flow  rate is", round(Qcvdot,0),"kJ/min"
print  "b)relative humidity  is", round(phi2*100,1),"%"

a)heat  flow  rate is 3717.0 kJ/min
b)relative humidity  is 23.1 %

Example 10.03, page: 250

In [3]:
from __future__ import division
import math

# Initialization  of  Variable
AV1 = 280 #m3/min
T1 = 30 #degC
phi1 = 0.5
T2 = 10 #degC
Tsat = 10 #degC
P1 = 1.013 #bar
R = 8314/28.97 #J/kg-K

#calculations:
#from Table T-2
Pg1 = 0.04246 #bar
Pv1 = phi1*Pg1
Pa1 = P1 - Pv1
#mass flow rate
madot = AV1*(Pa1*1E5)/(R*(T1+ 273))
#
w1 = 0.622*Pv1/(P1 - Pv1)
#from Table T-2
Pg2 = 0.01228 #bar
w2 = 0.0076 #kg(vapor)/kg(dry air)
#ratio
mwmadot = w1 - w2
#from Table T-2 and T-9
ha2 = 283.1 #kJ/kg
ha1 = 303.2 #kJ/kg
hg2 = 2519.8 #kJ/kg
hg1 = 2556.3 #kJ/kg
hf2 = 42.01 #kJ/kg
#heat transfer rate
Qcvdot = madot*(ha2 - ha1 - w1*hg1 + w2*hg2 + (w1 - w2)*hf2)/211

#Results
print  "a) mass  flow  rate  is", round(madot,2),"kg/min"
print  "b) the rate at which water is condensed is", round(mwmadot,4),"kg(vapor)/kg(dry air)"
print  "required refrigerating capacity is", round(-1*Qcvdot,1),"tons"

a) mass  flow  rate  is 319.35 kg/min
b) the rate at which water is condensed is 0.0057 kg(vapor)/kg(dry air)
required refrigerating capacity is 52.6 tons

Example 10.04, page: 250

In [4]:
from __future__ import division
import math

# Initialization  of  Variable
madot = 90 #kg/min
T1 = 22 #degC
Twb = 9 #degC
mstdot = 52 #kg/h
Tsat = 110 #degC

#calculations:
#From Table T-4
w1 = 0.002 #kg(vapor)/kg(dry air)
#
w2 = w1 + (mstdot/60)/madot
#from table T-2 and T-9
T2 = 23.5 #degC

#Results
print "a) humidity  ratio  is", round(w2,4),"kg(vapor)/kg(dry air)"
print "b) Temperature T2 is", T2,"degC"

a) humidity  ratio  is 0.0116 kg(vapor)/kg(dry air)
b) Temperature T2 is 23.5 degC

Example 10.05, page: 250

In [5]:
from __future__ import division
import math

# Initialization  of  Variable
T1 = 100 #degF
phi1 = 0.10
AV1 = 5000 #ft3/min
Tw = 70 #degF
T2 = 70 #degF
P = 14.696 #lbf/in2
Cpa = 0.24 #Btu/lb-degR

#calculations:
#From Table T-2E
Pg1 = 0.95 #lbf/in2
#partial pressure of the moist air
Pv1 = phi1*Pg1
#humidity at 1
w1 = 0.622*Pv1/(P- Pv1)
#specific vol of dry air
va1 = 14.2 #ft3/lb(dry air)
#mass flow rate of dry air
madot = AV1/va1
#from Table T-2E
hf = 38.1 #Btu/lb
hg1 = 1105 #Btu/lb
hg2 = 1092 #Btu/lb
#w2
w2 = (Cpa*(T1 - T2) + w1*(hg1 - hf))/(hg2 - hf)
#
mwdot = madot*60*(w2 - w1)
#
Pv2 = w2*P/(w2 + 0.622)
#saturation Pressure at 70 degF
Psat = 0.3632 #lbf/in2
#relative humidity at exit
phi2 = Pv2/Psat

#Results
print  "a) mass  flow  rate  is", round(mwdot,1),"lb(water)/h"
print  "b) relative  humidity  is",round(phi2*100,1),"%"
#answer slightly varies with book

a) mass  flow  rate  is 145.4 lb(water)/h
b) relative  humidity  is 69.9 %

Example 10.06, page: 250

In [6]:
from __future__ import division
import math

# Initialization  of  Variable
AV1 = 142 #m3/min
T1 = 5 #degC
w1 = 0.002 #kg(vapor)/(kg(dry air)
AV2 = 425 #m3/min
T2 = 24 #degC
phi2 = 0.5

#calculations:
#from psychometric chart
va1 = 0.79 #m3/kg(dry air)
va2 = 0.855 #m3/kg(dry air)
w2 = 0.0094
#mass flow rate of dry air at 1 and 2
ma1dot = AV1/va1
ma2dot = AV2/va2
#w3
w3 = (w1*ma1dot + w2*ma2dot)/(ma1dot + ma2dot)
#from fig T-4
#ha1 = (ha + w*hv)1
#ha2 = (ha + whv)2
#ha3 = (ha + w*hv)3
ha1 = 10 #kJ/kg(dry air)
ha2 = 47.8 #kJ/kg(dry air)
ha3 = (ma1dot*ha1 + ma2dot*ha2)/(ma1dot + ma2dot)
#from Fig T-4
T3 = 19 #degC

#Results
print  "a) humidity ratio is", round(w3,4),"kg(vapor)/kg(dry air)"
print  "b) temperature  by  inspection is", T3,"degC"

a) humidity ratio is 0.0074 kg(vapor)/kg(dry air)
b) temperature  by  inspection is 19 degC

Example 10.07, page: 250

In [7]:
from __future__ import division
import math

# Initialization  of  Variable
T1 = 38 #degC
m1dot = 4.5E7 #kg/h
T2 = 30 #degC
m2dot = 4.5E7 #kg/h
T3 = 25 #degC
phi3 = 0.35
T4 = 35 #degC
phi4 = 0.9
T5 = 20 #degC

#calculations:
#from Table T-2 nd T-9
w3 = 0.00688 #kg(vapor)/kg(dry air)
w4 = 0.0327 #kg(vapor)/kg(dry air)
hf1 = 159.21 #kJ/kg
hf2 = 125.79 #kJ/kg
ha4 = 308.2 #kJ/kg
ha3 = 298.2 #kJ/kg
hg4 = 2565.3 #kJ/kg
hg3 = 2547.2 #kJ/kg
hf5 = 83.96 #kJ/kg
#mass flow rate of dry air
madot = m1dot*(hf1 - hf2)/((ha4 - ha3) + w4*hg4 - w3*hg3 - (w4 - w3)*hf5)
#mass flow rate of water
m5dot = madot*(w4 - w3)

#Results
print  "mass  flow  rate of dry air and water are",round(madot,0),"kg/h and", round(m5dot,0),"kg/h"

mass  flow  rate of dry air and water are 20270181.0 kg/h and 523376.0 kg/h