Chapter 8 : Humidity and Humidity chart

Example 8.1 pageno : 206

In [1]:
# variables 
T = 280.                #K
P = 105.                #kPa
Pas = 13.25             #kPa ( Vpaour pressure of acetone )
Pa = Pas                # ( As gas is saturated, partial pressure = vapour pressure )

# Calculation 
Mfr = Pa / P            #(Mole fraction) 
Mpr = Mfr * 100 
print "(a)The mole percent of acetone in the mixture = %.2f %%"%Mpr
Ma = 58.048             #(molecular weight of acetone)
Mn = 28.                #(molecular weight of nitrogen)
N = 1.                  #mole
Na = Mfr * N 
Nn = N - Na 
ma = Na * Ma  
mn = Nn * Mn 
mtotal = ma + mn 
maper = ma *100 / mtotal 
mnper = mn *100/ mtotal 

# Result
print "(b)Weight percent of acetone = %.2f %%"%maper
print "Weight percent of nitrogen = %.2f %%"%mnper
Vstp = 22.4             #m**3/kmol
Pstp = 101.3            #kPa
Tstp = 273.15           #K
V = Vstp * Pstp * T / ( Tstp * P ) 
C = ma/V 
print "(c)Concentration of vapour = %.4f kg/m**3"%C

(a)The mole percent of acetone in the mixture = 12.62 %
(b)Weight percent of acetone = 23.04 %
Weight percent of nitrogen = 76.96 %
(c)Concentration of vapour = 0.3307 kg/m**3

Example 8.2 pageno : 207

In [2]:
import math 

# Variables 
P = 101.3               #kPa
Per1 = 10.              #%

# Calculation 
Pa = P * Per1 / 100     # ( a - benzene )
Ps = Pa                 #( saturation )
#lnPs = 13.8858 - 2788.51/(T - 52.36)
T = 2788.51 / ( 13.8858 - math.log(Ps)) + 52.36 

# Result
print "Temperature at which saturation occurs = %.1f K"%T

Temperature at which saturation occurs = 293.4 K

Example 8.3 pageno : 207

In [3]:
# variables 
Pdryair = 101.3                             #kPa
Pacetone = 16.82                            #kPa

# Calculation 
Nratio = Pacetone / (Pdryair - Pacetone) 
mratio = Nratio * 58.048 / 29               # ( Macetone = 58.048, Mair = 29 )
macetone = 5.                               #kg ( given )
mdryair = macetone / mratio 

# Result
print "Minimum air required = %.2f kg"%mdryair

Minimum air required = 12.55 kg

Example 8.4 pageno : 209

In [5]:
import math 

# Variables 
Pa = 15.                    #kPa ( partial pressure of acetone)
Ptotal = 101.3              #kPa

# Calculation and Result 
Mfr = Pa / Ptotal 
print "(a)Mole fraction of acetone = %.4f "%Mfr
Macetone = 58.048 
Mnitrogen = 28. 
mafr = Mfr * Macetone / ( Mfr * Macetone + (1-Mfr)* Mnitrogen ) 
print "(b)Weight fraction of acetone = %.4f"%mafr
Y = Mfr / ( 1 - Mfr ) 
print "(c)Molal humidity = %.4f"%Y,"moles of acetone/moles of nitrogen"
Y1 = Y * Macetone / Mnitrogen   
print "(d)Absolute humidity = %.4f"%Y1,"kg acetone/kg nitrogen"
Pas = 26.36                 #kPa ( vapour pressure)
Ys = Pas / ( Ptotal - Pas)  #saturation humidity
print "(e)Saturation humidity = %.4f"%Ys,"moles of acetone/moles of nitrogen"
Y1s = Ys * Macetone / Mnitrogen 
print "(f)Absolute saturation humidity = %.4f"%Y1s,"kg acetone/kg nitrogen"
V = 100.                    #m**3
Vstp =22.4143               #m**3/kmol
Pstp = 101.3                #kPa
Tstp = 273.15               #K
T = 295.                    #K
N = V * Ptotal * Tstp / (Vstp * Pstp * T ) 
Nacetone = N * Mfr 
macetone = Nacetone * Macetone 
print "(g)Mass of acetone in 100m**3 of the total gas = %.1f"%macetone,"kg"

(a)Mole fraction of acetone = 0.1481 
(b)Weight fraction of acetone = 0.2649
(c)Molal humidity = 0.1738 moles of acetone/moles of nitrogen
(d)Absolute humidity = 0.3603 kg acetone/kg nitrogen
(e)Saturation humidity = 0.3517 moles of acetone/moles of nitrogen
(f)Absolute saturation humidity = 0.7292 kg acetone/kg nitrogen
(g)Mass of acetone in 100m**3 of the total gas = 35.5 kg

Example 8.5 pageno : 211

In [7]:
# variables 
Pa = 15.                    #kPa ( Partial pressure )
Pas = 26.36                 #kPa ( Vapour pressure )

# Calculation 
RS = Pa * 100 / Pas  
Y = 0.1738 
Ys = 0.3517 
PS = Y * 100 / Ys 

# Result
print "Relative humidity = %.1f"%RS,"%"
print "Percent humidity = %.2f"%PS,"%"

Relative humidity = 56.9 %
Percent humidity = 49.42 %

Example 8.6 page no : 211

In [11]:
import math 

# Variables 
mwater = 0.0109                     #kg
V = 1.                              #m**3
T = 300.                            #K
P = 101.3                           #kPa
Vstp =22.4143                       #m**3/kmol
Pstp = 101.3                        #kPa
Tstp = 273.15                       #K

# Calculation 
N = V * P * Tstp / (Vstp * Pstp * T ) 
Nwater = mwater / 18.016 
Nfr = Nwater / N 
Pwater = Nfr * P 

# Result
print "(a)Partial pressure of water vapour = %.2f"%Pwater,"kPa"
Ps = math.exp(16.26205 - 3799.887/(T - 46.854)) 
RS = Pwater * 100 / Ps 
print "(b)Relative saturation = %.2f"%RS,"%"
Y1 = Pwater *18 / ((P - Pwater)*29) 
print "(c)Absolute humidity = %.2e"%Y1,"kg water / kg dry air"
Y1s = Ps *18 / ((P - Ps)*29) 
PS1 = Y1 * 100 / Y1s 
print "(d)Percent saturation = %.2f"%PS1,"%"
PS = 10.                            #%
Y1S = Y1 * 100/PS   
#Y1S = Pas/(P - Pas ) * 18 /29
Pas1 = 29 * P * Y1S / (18 + 29*Y1s) 
T1 = 3799.887 / (16.26205-math.log(Pas1)) + 46.854 
print "(e)Temperature at which 10%% saturation occurs = %.1f"%T1,"K"

(a)Partial pressure of water vapour = 1.51 kPa
(b)Relative saturation = 43.17 %
(c)Absolute humidity = 9.38e-03 kg water / kg dry air
(d)Percent saturation = 42.31 %
(e)Temperature at which 10% saturation occurs = 326.9 K

Example 8.7 page no : 213

In [13]:
# variables 
T = 300.                        #K
P = 100.                        #kPa
S = 25000.                      #kJ/m**3
T1= 295.                        #K
P1 = 105.                       #kPa
RS = 50.                        #%
Ps = 3.5                        #kPa
Ps1 = 2.6                       #kPa
Vstp = 22.4143                  #m**3/kmol
Pstp = 101.3                    #kPa
Tstp = 273.15                   #K
V = 1.                          #m**3

# Calculation 
N = V * P * Tstp/(Vstp * Pstp * T) 
Nfuel = N * (P - Ps)/P 
Smol = S / Nfuel                #kJ/kmol
N1 = V * P1 * Tstp/(Vstp * Pstp * T1) 
Pwater = Ps1 * RS /100 
Nfuel1 = N1 * (P1 - Pwater )/P1 
S1 = Smol * Nfuel1 

# Result
print "Heating value of gas at 295K and 105kPa = %.f"%S1,"kJ/m**3"

# note : answer may vary because of rounding error.

Heating value of gas at 295K and 105kPa = 27321 kJ/m**3

Example 8.8 pageno : 215

In [16]:
import math 
# Variables 
T = 300.                            #K
T1 = 335.                           #K
P = 150.                            #kPa

# Calculation 
#lnPs = 13.8858 - 2788.51 / ( T - 52.36)
Ps = math.exp(13.8858 - 2788.51 / ( T - 52.36)) 
Ps1 = math.exp(13.8858 - 2788.51 / ( T1 - 52.36)) 
Pa = Ps                             #(Vapour pressure at dew point is equal to the partial pressure of the vapour)
Y = Pa / (P - Pa) 
Ys = Ps1 / (P - Ps1) 
PS = Y * 100 / Ys 

# Result 
print "(a)Percent saturation = %.2f"%PS,"%"
Ma = 78.048 
Mb = 28 
Q = Y * Ma / Mb  
print "(b)Quantity of benzene per kilgram of nitrogen = %.4f"%Q,"kg benzene/kg nitrogen"
V = 1.                              #m**3 ( basis )
Vstp = 22.4143                      #m**3/kmol
Pstp = 101.3                        #kPa
Tstp = 273.15                       #K
N = V * P * Tstp/(Vstp * Pstp * T1) 
y = Y / ( 1 + Y ) 
Nbenzene = N * y 
C = Nbenzene * Ma 
print "(c)Kilogram of benzene per m**3 of nitrogen = %.4f"%C,"kg/m**3"
P1 = 100.                           #kPa
Pbenzene = y * P1 
T1 = 2788.51 / ( 13.8858 - math.log (Pbenzene)) + 52.36 
print "(d)Dew point = %.2f"%T1,"K"
Per1 = 60                           #%
Y2 = Y * (1- Per1/100.) 
#Y2 = Pa / (P - Pa)
P = Pa / Y2 + Pa 
print "(e)Pressure required = %.1f"%P,"kPa"

(a)Percent saturation = 17.17 %
(b)Quantity of benzene per kilgram of nitrogen = 0.2827 kg benzene/kg nitrogen
(c)Kilogram of benzene per m**3 of nitrogen = 0.3871 kg/m**3
(d)Dew point = 291.39 K
(e)Pressure required = 354.3 kPa

Example 8.9 pageno : 216

In [18]:
# variables 
T = 300.                    #K
T1 = 285.                   #K
Pwater = 3.56               #kPa
Pwater1 = 1.4               #kPa
V = 1.                      #m**3 ( Basis )
Vstp = 22.4143              #m**3/kmol

# Calculation 
N = V / Vstp 
Pstp = 101.3                #kPa
Y = Pwater / (Pstp - Pwater) 
Y1 = Pwater1 / (Pstp - Pwater1) 
Nremoved = Y - Y1 
Ndryair = N * 1 / (1 + Y) 
mremoved = Ndryair * Nremoved * 18.016 

# Result
print "(a)amount of water removed = %.4f"%mremoved,"kg"
Nremaining = Ndryair * Y1  
V1 = (Ndryair + Nremaining) * Vstp  
print "(b)Volume of gas at stp after drying = %.4f"%V1,"m**3"

(a)amount of water removed = 0.0174 kg
(b)Volume of gas at stp after drying = 0.9784 m**3

Example 8.11 page no : 220

In [20]:
# variables 
Td = 328.                       #K ( dry bulb )
P = 101.3                       #kPa
PS = 10.                        #%
#refering to the psychometric chart, corresponding to 328 K and 10% saturation
Y1 = 0.012                      #kg water / kg dry air
print "(a)Absolute humidity = ",Y1,"kg water / kg dry air"
#Y1 = Pa * 18 / ( P - Pa ) * 29

# Calculation 
Pa = Y1 * P * 29 /( 18 + Y1 * 29 ) 

# Result
print "(b)Partial Pressure of water vapour = %.3f"%Pa,"kPa"
#using psychometric chart, saturation humidity at 328 K is given as
Y1s = 0.115                     #kg water / kg dry air
print "(c)The absolute humidity at 328K = ",Y1s,"kg water / kg dry air"
#at saturation partial pressure = vapour pressure
Pas = Y1s * P * 29 /( 18 + Y1s * 29 )  
print "(d)Vapour Pressure of water vapour = %.1f"%Pas,"kPa"
RS = Pa * 100 / Pas 
print "(e)Percent relative saturation = %.2f"%RS,"%"
#using psychometric chart, moving horizontally keeping humidity constant to 100% saturation, we get dew point as,
T = 290.                        #K
print "(f)Dew point = ",T,"K"

(a)Absolute humidity =  0.012 kg water / kg dry air
(b)Partial Pressure of water vapour = 1.921 kPa
(c)The absolute humidity at 328K =  0.115 kg water / kg dry air
(d)Vapour Pressure of water vapour = 15.8 kPa
(e)Percent relative saturation = 12.13 %
(f)Dew point =  290.0 K

Example 8.12 pageno : 222

In [22]:
# variables 
Ca = 1.884                      #kJ/kgK
Cb = 1.005                      #kJ/kgK
Y1 = 0.012 

# Calculation 
#Cs = Cb + Y1 * Ca
Cs = Cb + Y1 * Ca 

# Result
print "Humid heat of the sample = %.4f"%Cs,"kJ/kgK"
P = 101.3                       #kPa
V = 100.                        #m**3
R = 8.314 
T = 328.                        #K
T1 = 373.                       #K
N = P * V / ( R * T ) 
Pa = 1.921                      #kPa
Ndryair = N * (P - Pa)/P 
mdryair = Ndryair * 29 
Ht = mdryair * Cs * (T1 - T) 
print "Heat to be supplied = %.f"%Ht,"kJ"

Humid heat of the sample = 1.0276 kJ/kgK
Heat to be supplied = 4887 kJ

Example 8.14 pageno : 224

In [23]:
# variables 
P = 101.3                           #kPa
MW = 58. 
T1 = 280.8                          #K
Ps = 5.                             #kPa
pr = 2.                             #kJ/kgK ( Psychometric ratio )
Hvap = 360.                         #kJ/kg
Tw = T1 

# Calculation 
Yw1 = Ps * MW / (( P - Ps) * 29) 
# Tw = Tg - Hvap * ( Yw1 - Y1) / (hG / kY), where hG/kY is the psychmetric ratio pr
Y1 = 0 
Tg = Tw + Hvap * ( Yw1 - Y1) / pr 

# Result
print "The air temperature = %.2f"%Tg,"K"

The air temperature = 299.49 K

Example 8.15 pageno : 225

In [24]:
# variables 
Td = 353.2                      #K
Tw = 308.                       #K
Hvap = 2418.5                   #kJ/kg
pr = 0.950                      #kJ/kg
Ps = 5.62                       #kPa
P = 101.3                       #kPa

# Calculation 
Yw1 = (Ps * 18)/ (( P - Ps) * 29) 
Y1 = Yw1 - pr * ( Td - Tw ) / Hvap 

# Result
print "Humidity = %.4f"%Y1,"kg water/kg dry air"
#humidity can also be directly obtained from psychometric chart, which we get to be 0.018 kg water/kg dry air

Humidity = 0.0187 kg water/kg dry air

Example 8.16 page no : 227

In [1]:
%matplotlib inline

import math
from matplotlib.pyplot import *

# Variables
TK = [283,293,303,313]
PaS = []
Ys = []

# Calculations - part A
for i in range(len(TK)):
    Ps = 13.8858 - (2788.51 / (TK[i] - 52.36))
    PaS.append(round(math.e**Ps,2))
    Ys.append(PaS[i]/(101.3 - PaS[i]) * 78.048/29)
    
# Results
plot(TK,Ys)
plot(TK,Ys,"go")
xlabel("Temperature, K")
ylabel("Y', kg benzene/ kg dry air")

Populating the interactive namespace from numpy and matplotlib
Out[1]:
<matplotlib.text.Text at 0x3797790>

Example 8.17 pageno : 228

In [25]:
# variables 
Tin = 380.7                             #K
Pin = 101.3                             #kPa
Tdew = 298.                             #K
mremoved = 2.25                         #kg
V = 100.                                #m**3
#using humidity chart, humidity of air at dry bulb temperature of 380.7K and dew point = 298K is,
Y = 0.02                                # kg water /kg dry air
print "(a)Humidity of air entering the drier = ",Y,"kg water /kg dry air"
Tstp = 273.15                           #K
Vstp = 22.4143                          #m**3/kmol

# Calculation 
N = V * Tstp / ( Vstp * Tin ) 
MY = Y * 29 / 18.                       #molal humidity
Ndryair = N / ( 1 + MY ) 
mdryair = Ndryair *29 
mwaterin = mdryair * Y 
mwaterout = mwaterin + mremoved 
Yout = mwaterout / mdryair 
# percent humidity is calculated using the chart, and is
PY = 55.                                #%

# Result
print "(b)exit air humidity = %.3f"%Yout,"kg water /kg dry air"
print "Percent humidity = ",PY,"%"
#from the humidity chart 
Twet = 313.2                            #K
Td = 322.2                              #K
print "(c)exit air wet bulb temperature = ",Twet,"K"
print "(c)exit air dry bulb temperature = ",Td,"K"
MYout = Yout * 29 / 18 
Nout = Ndryair * ( 1 + MYout ) / 1 
V1 = Nout * Vstp * Td / Tstp 
print "(d)Volume of exit air = %.2f"%V1,"m**3"

(a)Humidity of air entering the drier =  0.02 kg water /kg dry air
(b)exit air humidity = 0.045 kg water /kg dry air
Percent humidity =  55.0 %
(c)exit air wet bulb temperature =  313.2 K
(c)exit air dry bulb temperature =  322.2 K
(d)Volume of exit air = 87.94 m**3

Example 8.18 pageno : 231

In [27]:
# variables 
P = 101.3                       #kPa
Td = 303.                       #K
Tw = 288.                       #K
#using psychometric chart,
Y1 = 0.0045                     #kg water/ kg dry air
PY = 18.                        #%
Theated = 356.7                 #K
Cb = 1.005 
Ca = 1.884 

# Calculation 
Cs = Cb + Y1 * Ca 
Q = 1 * Cs * (Theated - Td) 

# Result
print "(a)Humidity of the initial air = %.4f"%Y1,"kg water/ kg dry air"
print "(b)Percent humidity = ",PY,"%"
print "(c)Temperature to which the air is heated = ",Theated,"K"
print "(d)Heat to be suppplied = %.2f"%Q,"kJ"

(a)Humidity of the initial air = 0.0045 kg water/ kg dry air
(b)Percent humidity =  18.0 %
(c)Temperature to which the air is heated =  356.7 K
(d)Heat to be suppplied = 54.42 kJ

Example 8.19 pageno : 232

In [3]:
# variables 
Tw = 313.                           #K
Td = 333.                           #K
#Using th psychometric chart,
Y = 0.04                            #kg water/ kg dry air
PS = 26.5                           #%
VS = 1.18                           #m**3/kg dry air ( volume of saturated air )
VD = 0.94                           #m**3/kg dry air ( volume of dry air )

# Calculation 
VH = VD + PS * (VS - VD )/100 
HS = 470.                           #J / kg dry air ( enthalpy of saturated air )
HD = 60.                            #J / kg dry air ( enthalpy of dry air )
H = HD + PS * ( HS - HD )/100 
Cs = 1.005 + (Y * 1.884)
H = Cs*(333 - 273.15) + Y*2502.3
# Result
print "(a)Absolute Humidity of the air = ",Y,"kg water/ kg dry air"
print "(b)Percent humidity = ",PS,"%"
print "(c)Humid volume = ",VH,"m**3/kg dry air"
print "(d)Enthalpy of wet air = ",H,"kJ/kg dry air"
print "Enthalpy of humid air : %.2f kJ/kg dry air"%H

(a)Absolute Humidity of the air =  0.04 kg water/ kg dry air
(b)Percent humidity =  26.5 %
(c)Humid volume =  1.0036 m**3/kg dry air
(d)Enthalpy of wet air =  164.751546 kJ/kg dry air
Enthalpy of humid air : 164.75 kJ/kg dry air