# Chapter 11: Boilers and Boiler Calculations¶

## Example 1, page no. 481¶

In [3]:
from __future__ import division

#Variable Declaration:
H = 30 #Height of chimney(in m):
Ta = 27+273 #Ambient air temperature(in K):
m = 20 #Mass per kg of fuel required for complete combustion(in kg):
hw = 12 #Height in the water column(in mm):

#Calculations:
Tg = (Ta*353*H)/(353*H-hw*Ta)*(m)/(m+1)#Temperature of burnt gases(in K):

#Results:
print "Temperature of the burnt gases: ",round(Tg,2),"K"

Temperature of the burnt gases:  432.86 K


## Example 2, page no. 482¶

In [5]:
from __future__ import division

#Variable Declaration:
m = 18 #Mass per kg of fuel required for complete combustion(in kg):
hw = 20 #Height in the water column(in mm):
Ta = 27+273 #Ambient air temperature(in K):
Tg = 300+273 #Temperature of burnt gases(in K):

#Calculations:
H = hw/(353*(1/Ta-(m+1)/(m*Tg)))#Height of chimney(in m):

#Results:
print "Height of chimney: ",round(H,2),"m"

Height of chimney:  37.99 m


## Example 3, page no. 482¶

In [7]:
from __future__ import division

#Variable Declaration:
H = 20 #Height of chimney(in m):
Tg = 380+273 #Temperature of burnt gases(in K):
Ta = 27+273 #Ambient air temperature(in K):

#Calculations:
m = 2*Ta/(Tg-2*Ta)   #Air supplied(in kg air per fuel):

#Results:
print "Air supplied:",round(m,2),"kg/kg of fuel"

Air supplied: 11.32 kg/kg of fuel


## Example 4, page no. 482¶

In [9]:
from __future__ import division

#Variable Declaration:
H = 60   #Height of chimney(in m):
Ta = 17+273 #Ambient air temperature(in K):
Tg = 300+273 #Temperature of burnt gases(in K):
Tga = 150+273 #Temperature of the artificial burnt gases(in K):
m = 19  #Mass per kg of fuel required for complete combustion(in kg):
Cpg = 1.0032 #Specific heat of hot gases(in kJ/kg.K):
c = 32604 #Calorific value of burnt fuel(in kJ/kg):

#Calculations:
hw = 353*H*(1/Ta-(m+1)/(m*Tg)) #Draught (in mm of water column):
n = 9.81*H*(m/(m+1)*Tg/Ta-1)/(Cpg*(Tg-Tga)*10**3)*100 #Chimney efficiency:
Q = (m+1)*Cpg*(Tg-Tga) #Extra heat carried away by flue gases(in kJ):

#Results:
print "Draught: ",round(hw,2)," mm of water"
print "Chimney efficiency",round(n,4),"%"
print "Extra heat carried away by flue gases per kg of fuel burnt",round(Q,1)," kJ"

Draught:  34.13  mm of water
Chimney efficiency 0.3431 %
Extra heat carried away by flue gases per kg of fuel burnt 3009.6  kJ


## Example 5, page no. 483¶

In [12]:
from __future__ import division

#Variable Declaration:
H = 80   #Height of chimney(in m):
Ta = 27+273 #Ambient air temperature(in K):
m = 20 #Mass per kg of fuel required for complete combustion(in kg):
Tga = 110+273 #Temperature of the artificial burnt gases(in K):
Cpg = 1.0032 #Specific heat of hot gases(in kJ/kg.K):

#Calculations:
Tg = Ta*2*(m+1)/m #Temperature of burnt gases(in K):
hw = 353*H*(1/Ta-(m+1)/(m*Tg)) #Draught in water column(in mm):
n = 9.81*H*(m/(m+1)*Tg/Ta-1)/(Cpg*(Tg-Tga)*10**3)*100 #Chimney efficiency:

#Results:
print "Hot gas temperature in chimney: ",round(Tg),"K"
print "Natural draught: ",round(hw,2),"mm of water"
print "Chimney efficiency: ",round(n,4),"%"

Hot gas temperature in chimney:  630.0 K
Natural draught:  47.07 mm of water
Chimney efficiency:  0.3167 %


## Example 6, page no. 484¶

In [14]:
from __future__ import division

from math import sqrt,pi

#Variable Declaration:
R = 2.5*10**3 #Rate at which coal is burnt(in kg/hr):
m = 20   #Mass per kg of fuel required for complete combustion(in kg):
Tg = 327+273 #Temperature of burnt gases(in K):
Ta = 27+273 #Ambient air temperature(in K):
h = 7+6+3+2 #Pressure head(in mm):
na = 0.90 #Ratio of actual natural draught to theoretical draught:
g = 9.81 #Acceleration due to gravity(in m/s**2):

#Calculations:
hw = h/na #Actual natural draught(in mm of water):
H = hw/(353*(1/Ta-(m+1)/(m*Tg))) #Height of chimney(in m):
dg = 353/Tg*(m+1)/m #Density of hot gases(in kg/m**3):
hg = H*((m+1)/m*Tg/Ta-1) #Height of hot gases column(in m):
Mg = R*hw/3600 #Mass flow rate of hot gases(in kg/s):
C = sqrt(2*g*hg) #Velocity of got gases(in m/s):
D = sqrt((4*Mg)/(pi*C*dg)) #Diameter of chimney(in m):

#Results:
print "Height of chimney:",round(H,2),"m"
print "Diameter of chimney:",round(D,2),"m"

Height of chimney: 35.78 m
Diameter of chimney: 1.01 m


## Example 7, page no. 485¶

In [16]:
from __future__ import division

#Variable Declaration:
hw = 50    #Draught in water column(in mm):
T = 300+273 #Temperature of burnt gases(in K):
m = 19   #Mass per kg of fuel required for complete combustion(in kg):
T1 = 27+273 #Ambient air temperature(in K):
T0 = 273 #Zero temperature(in K):
n = 0.90 #Mechanical efficiency:
d = 1.293 #Density of hot gases(in kg/m**3):

#Calculations:
M = 2000/3600 #Rate at which coal is burnt(in kg/s):
P = hw*9.81 #Pressure applied by the draught water(in N/m**2):
PFD = P*m*M*T1/(d*T0*n*1000) #Power required in FD fan(kW):
P1D = P*m*M*T/(d*T0*n*1000) #Power required in 1D fan(kW):

#Results:
print "Power for FD fan:",round(PFD,2),"kW"
print "Power for 1D fan:",round(P1D,2),"kW"

Power for FD fan: 4.89 kW
Power for 1D fan: 9.34 kW


## Example 8, page no. 486¶

In [18]:
from __future__ import division

#Variable Declaration:
Cpg = 1.0032 #Specific heat of hot gases(in kJ/kg.K):
Tg = 177+273 #Temperature of burnt gases(in K):
Ta = 27+273 #Ambient air temperature(in K):
Tn = 327+273 #Natural draught temperature(in K):
mn = 25     #Mass per kg of fuel required for natural draught(in kg):
ma = 20  #Mass per kg of fuel required for artificial draught(in kg):
r = Tg/Ta #Ratio of brake power for induced draught to forced draught:

#Calculations:
Qgad = (ma+1)*Cpg*(Tg-Ta) #Heat carried by hot flue gases in artificial draught(in per kg of fuel burnt):
Qgnd = (mn+1)*Cpg*(Tn-Ta) #Heat carried by hot flue gases in natural draught(in per kg of fuel burnt):
rh = Qgad/Qgnd #Ratio of heat carried away:

#Results:
print "Ratio of power required: ",round(r,1)
print "Ratio of heat carried away: ",round(rh,3)

Ratio of power required:  1.5
Ratio of heat carried away:  0.404


## Example 9, page no. 486¶

In [22]:
from __future__ import division

#Variable Declaration:
T = 27+273 #Feed water supply temperature(in K):
P = 10    #Mean steam generation pressure(in bar):
x = 0.95 #Dryness fravtion of steam generated:
Q = 2500 #Feed water supplied(in kg/hr):
Q1 = 275 #Coal burnt(in kg/hr):
d = 300   #Difference in mass of water after trial:
hf = 762.81 #kJ/kg #From steam tables:
hg = 2778.1 #kJ/kg
hfg = 2015.29 #kJ/kg

#Calculations:
h = hf+x*hfg #Enthalpy of steam generated(in kJ/kg):
mw = Q+d #Mass of water evaporator per hour(in kg/hr):
Ae = mw/Q1 #Actual evaporation(in per kg of coal):
Ee = Ae*h/2257 #Equivalent evaporation(in kg per kg of coal):

#Results:
print "Actual evaporation: ",round(Ae,2)," kg per kg of coal"
print "Equivalent evaporation: ",round(Ee,2),"kg per kg of coal"

Actual evaporation:  10.18  kg per kg of coal
Equivalent evaporation:  12.08 kg per kg of coal


## Example 10, page no. 487¶

In [24]:
from __future__ import division

#Variable Declaration:
p = 10  #Average pressure of the steam(in bar):
Ww = 15  #Weight of water consumed(in ton):
Wc = 1.5 #Weight of coal produced(in ton):
n = 1-0.03-0.04 #Percentage coal that caan be burnt:
nm = 0.03 #Composition of moisture in coal:
Tf = 35  #Temperature of feed water(in C):
hg = 2778.1     #From steam tables(kJ/kg)

#Calculations:
h = hg-4.18*Tf #Enthalpy of steam generated(in kJ/kg):
m = Ww/Wc #Steam generated per kg of coal(in kg):
nb = m*h/(30.1*10**3)*100 #Boiler efficiency:
Ee = m*h/(2257*(1-nm)) #Equivalent evaporation per kg of dry coal(in kg:
Eea = Ee*(1-nm)/n #Equivalent evaporation per kg of combustible present in coal(in kg):

#Results:
print "Boiler efficiency: ",round(nb,2),"%"
print "Equivalent evaporation per kg of dry coal: ",round(Ee,2),"kg"
print "Equivalent evaporation per kg of combustible present in coal: ",round(Eea,2),"kg"

Boiler efficiency:  87.44 %
Equivalent evaporation per kg of dry coal:  12.02 kg
Equivalent evaporation per kg of combustible present in coal:  12.54 kg


## Example 11, page no. 488¶

In [26]:
from __future__ import division

#Variable Declaration:
t = 24 #Time of trial(in hrs):
p = 16 #Pressure at which steam is generated(in bar):
c = 10000 #Coal consumed(in kg):
r = 2500 #Rate of steam generation(in kg/hr):
Tf = 27    #Feed water temperature(in C):
hsa = 3000 #Total heating surface area(in m**2):
ga = 4   #Total grate area(in m**2):
C = 28000 #Calorific value of coal(in kJ/kg):
hg = 2794   #From steam tables(kJ/kg)
L = 2257 #Latent heat at 100 C:

#Calculations:
m = c/t  #Coal  burnt per hour(in kg/hr):
mg = m/ga #Coal burnt per m**2 of grate per hour:
r1 = r/m #Rate of steam generated per kg of coal(in kg steam/kg coal):
Q = r1*(hg-4.18*Tf)  #Heat added to steam per kg of coal(in kJ):
Ee = Q/L #Equivalent evaporation from and at 100 C per kg of coal(in kg):
Eepm = Ee*m/hsa #Equivalent evaporation from and at 100 C per m**2 of total surface per hour(in kg):
n = Ee*L/C*100 #Boiler efficiency:

#Results:
print "Mass of coal burnt per m**2 of grate per hour: ",round(mg,2),"kg"
print "Equivalent evaporation from and at 100 C per kg of coal: ",round(Ee,2),"kg"
print "Equivalent evaporation from and at 100 C per m**2 of total surface per hour: ",round(Eepm,2),"kg"
print "Boiler efficiency: ",round(n,2),"%"

Mass of coal burnt per m**2 of grate per hour:  104.17 kg
Equivalent evaporation from and at 100 C per kg of coal:  7.13 kg
Equivalent evaporation from and at 100 C per m**2 of total surface per hour:  0.99 kg
Boiler efficiency:  57.45 %


## Example 12, page no. 489¶

In [28]:
from __future__ import division

#Variable Declaration:
p = 30 #Pressure at which steam is generated(in bar):
Ts = 300 #Temperature of steam(in C):
r = 11  #Rate at which feed water enters(in kg/s):
T1 = 100 #Temperature at which feed water enters the economiser(in C):
m = 5000 #Mass of fuel used(in kg):
C = 35000 #Calorific value of fuel(in kJ/kg.K):
T = 27  #Temperature of feed water(in C):
hg = 2993.5 #From steam tables:
L = 2257 #Latent heat at 100 C:

#Calculations:
ms = r*3600/m #Mass of steam genrated per kg of fuel(in kg/kg fuel):
Q = hg-4.18*T #Heat added per kg of fuel(in kJ):
Ee = ms*Q/L #Equivalent evaporation from and at 100 C per kg of coal(in kg):
n = Ee*L/C*100 #Boiler efficiency:
Q1 = ms*4.18*(T1-T)  #Heat utilised in economiser per kg of fuel(in kJ):
P = Q1/C*100 #Percentage of energy utilised in economiser:

#Results:
print "Equivalent evaporation per kg of fuel: ",round(Ee,2),"kg"
print "Boiler efficiency: ",round(n,2),"%"
print "Percentage of energy utilised in economiser: ",round(P,1),"%"

Equivalent evaporation per kg of fuel:  10.11 kg
Boiler efficiency:  65.18 %
Percentage of energy utilised in economiser:  6.9 %


## Example 13, page no. 489¶

In [30]:
from __future__ import division

#Variable Declaration:
m = 8 #Mass of steam genrated per kg of fuel:
Ts = 400 #Temperature of steam(in C):
p = 30   #Pressure of feed water(in bar):
T = 40  #Temperature of feed water(in C):
T1 = 150 #Temperature at which feed water leaves the economiser(in C):
x = 0.98 #Dryness fraction:
C = 29000 #Calorific value(in kJ/kg.K):
h = 3230.9 #Enthalpy of steam generated(in kJ/kg): #From steam tables:
hf = 1008.42                            #kJ/kg
hfg = 1795.78                           #kJ/kg

#Calculations:
Q = h-4.18*T #Heat to be added(in kJ):
n = m*Q/C*100 #Boiler efficiency:
Q1 = 4.18*(T1-T) #Heat added in economiser per kg of steam generated(in kJ/kg):
r1 = Q1/Q*100 #Percentage fraction of heat in economiser:
Q2 = (hf+x*hfg)-4.18*T1 #Heat added in evaporator per kg of steam generated(in kJ/kg):
r2 = Q2/Q*100 #Percentage fraction of heat in economiser:
Q3 = Q-Q1-Q2 #Heat added in super heater per kg of steam generated by difference(in kJ/kg):
r3 = Q3/Q*100 #Percentage fraction of heat in economiser:

#Results:
print "Boiler efficiency: ",round(n,2),"%"
print "Percentage fraction of heat in economiser: ",round(r1,2),"%"
print "Percentage fraction of heat in evaporator: ",round(r2,2),"%"
print "Percentage fraction of heat in superheater: ",round(r3,2),"%"

Boiler efficiency:  84.52 %
Percentage fraction of heat in economiser:  15.01 %
Percentage fraction of heat in evaporator:  69.89 %
Percentage fraction of heat in superheater:  15.1 %


## Example 14, page no. 490¶

In [32]:
from __future__ import division

#Variable Declaration:
T1 = 20 #Temperature at which feed water enters and leaves the economiser(in C):
T2 = 125
r = 3 #Rate at which feed water leaves the economiser(in kg/s):
T3 = 425 #Temperature of flue gases at inlet and outlet of economiser(in C):
T4 = 300
r1 = 18 #Rate at which coal is supplied(in kg/min):
nc = 0.80 #% of C in coal:
Cpg = 1.05 #Specific heat of flue gases(in kJ/kg.K):
Ta = 15 #Atmospheric temperature(in C):
m1 = 23.65 #Mass of dry flue gases at inlet and exit of economiser(in kg):				#From table:
m2 = 24.78

#Calculations:
A = m2-m1 #Air leakage in economiser per kg of coal:
Q1 = m1*Cpg*T3+A*Cpg*Ta #Heat entering economiser with flue gases and leakage(in kJ):
Q2 = m2*Cpg*T4   #Heat entering economiser with flue gases and leakage(in kJ):
Q = Q1-Q2 #Heat lost in economiser per kg of coal(in kJ):
Q3 = (r*60/r1)*4.18*(T2-T1)	#Heat picked up by feed water in economiser per kg of coal(in kJ):

#Results:
print "Heat released by the flue gases: ",round(Q,2),"kJ per kg of coal"
print "Air leakage: ",round(A,2),"kg per kg of coal"
print "Heat gained by feed water: ",round(Q3),"kJ per kg of coal"
print "___Please check there is a calculation mistake in book in calculating Q3____"

Heat released by the flue gases:  2765.91 kJ per kg of coal
Air leakage:  1.13 kg per kg of coal
Heat gained by feed water:  4389.0 kJ per kg of coal
___Please check there is a calculation mistake in book in calculating Q3____


## Example 15, page no. 492¶

In [34]:
from __future__ import division

#Variable Declaration:
CpKg = 0.84                             #Carbon present per kg:
CpKgDf = 0.0495                         #Carbon present per kgof dry fluegas:
sg = 8                                  #Steam generated (kg per kg of coal):
mh = 0.04*9 #H2O produced during the combustion(kg per kg of coal):
ash = 0.05                              #Ash produced duing cumbustion(kg per kg of coal):
M = 0.015                               #Moisture in coal burnt per kg of coal:
h = 3213.6                              #Enthalpy of heat generated at 40 bar 400°C (KJ/Kg):
C = 4.18                                #Heat capacity of water (KJ/Kg.K):
Ti =  27                                #Feed water temperature at inlet to economiser (°C):
Te = 137                                #Feed water temperature at exit of economiser(°C):
Tfe = 300                               #Flue gas temperature entering air heater(°C):
Tae = 120                               #Temperature of air entering boiler furnace(°C):
Tatm = 15                               #Atmospheric air temperature(°C):
Hs = 32600                              #Heat supplied by the fuel(KJ/Kg coal):
cp = 1.0032                             #Heat capacity of air and dry gas (KJ/Kg.K):
sp = 2.0064                             #Specific pressure of vapour(KJ/Kg.K):

#Calculations:
md = CpKg/CpKgDf #Mass of dry flue gas per kg of coal: #Specific pressure of vapour  =  2.0064 kJ/kg K				#Partial pressure of vapour in flue gas  =  0.075 bar				#For air and dry flue gas, cp  = 1.0032 kJ/kg K				#Calorific value of coal  =  32600 kJ/kg				#Datum temperature  =  15C				#Dry flue gas composition by volume  =  12.5% CO2, 7.5% O2, 80% N2				#Dry coal composition by mass  =  84% C, 4% H2, 7% O2 and remainder ash				#Temperature of air entering boiler furnace  =  120C				#Flue gas temperature leaving air heater and entering chimney  =  150C				#Flue gas temperature entering air heater  = 300C				#Moisture in coal burnt  =  1.5%				#Feed water temperature at exit of economiser  =  137C				#Feed water temperature at inlet to economiser  =  27C				#Steam generated per kg of coal  =  8 kg				#Steam generation: 40 bar, 400C				#Atmospheric air temperature: 15C
ma = md-(1-ash-mh)  #Amount of air supplied for combustion of one kg of dry coal(in kg):
m = M/(1-M)  #Moisture per kg of dry coal(in kg):
mt = round(mh+m,4)#Total moisture per kg of coal(in kg):
sgd = sg/(1-M)  #Steam generated per kg of dry coal(in kg steam):
H = sgd*(h-C*Ti)                       #Heat utilized by steam per kg of coal(KJ):
n = H/Hs*100 #Boiler efficiency:
Hu = ma*cp*(Tae-Tatm)                   #Heat utilized by air(KJ/Kg of coal)
Ha = (md*cp+mt*sp)*(Tfe-Te)             #Heat available in air heater(KJ/Kg of coal):
na = Hu/Ha*100 #Efficiency of heat exchange in air heater:

#Results:
print "Boiler efficiency: ",round(n,2),"%"
print "Efficiency of heat exchange in air heater: ",round(na,2),"%"

Boiler efficiency:  77.25 %
Efficiency of heat exchange in air heater:  59.54 %


## Example 17, page no. 496¶

In [36]:
from __future__ import division

#Variable Declaration:
p = 20 #Pressure at which steam is generated(in bar):
Ts = 300 #Temperature at which steam is generated(in C):
T1 = 50 #Temperature of feed water supplied to the boiler(in C):
C = 30000 #Calorific value of fuel(in kJ/kg):
r = 600 #Rate at which coal is used(in kg/hr):
r1 = 5000 #Rate at which steam is generated(in kg/hr):
T = 100 #Temperature of the boiler unit(in C):
L = 2257 #Latent heat(in kJ/kg.K):

#Calculations:
ms = r1/r #Steam generation per unit coal burnt per hour:
hfi = 3023.5 #Final enthalpy of the steam(in kJ/kg):
hfw = 209.33 #Enthalpy of feed water(in kJ/kg):
no = ms*(hfi-hfw)/C*100 #Overall efficiency of boiler:
Ee = ms*(hfi-hfw)/L #Equivalent evaporation of boiler unit(in kg steam per kg of coal):
Eea = Ee*r #Equivalent evaporation of boiler unit at 100 C(in kg/hr):
hfw1 = 313.93 #After fitting economiser the enthalp of feed water(in kJ/kg):
nom = no+5 #Modified overall efficiency of boiler unit:
mc = (hfi-hfw1)*r1*100/(C*nom) #Coal consumption(in kg/hr):
s = r-mc #Saving of coal(in kg/hr):

#Results:
print "Saving of coal: ",round(s,2),"kg/hr"

Saving of coal:  57.03 kg/hr


## Example 18, page no. 497¶

In [38]:
from __future__ import division

#Variable Declaration:
r = 5000 #Rate at which steam is generated(in kg/hr):
p = 20 #Pressure of steam(in bar):
x = 0.98 #Dryness fraction:
T = 60   #Temperature of feed water(in °C):
r1 = 600 #Rate at which coal is supplied(in kg/hr):
r2 = 16 #Rate at which air is supplied(in kg per kg coal):
C = 30000 #Cslorific value of coal(in kJ/kg):
Tr = 20   #Temperature of boiler room(in °C):
nl = 0.86 #Fraction of heat losr with flue gases:
Cpg = 1.005 #Specific heat of flue gases(in kJ/kg.K):
#From steam tables:
hf = 908.79                             #kJ/kg
hfg = 1890.7                            #kJ/kg

#Calculations:
ms = r/r1 #Mass of steam genrated per kg of coal:
hfi = hf+x*hfg #Enthalpy of final steam produced(in kJ/kg):
hfw = 251.13 #Enthalpy of feed water(in kJ/kg):
Q = ms*(hfi-hfw) #Heat used for steam generation(in kJ per kg of coal):
Ql = C-Q #Heat lost per kg of coal:
Qlf = nl*Ql #Heat lost with flue gases(in kJ per kg of coal):
Tgas = Tr+Qlf/((r2+1)*Cpg) #Temperature of flue gases(in °C):

#Results:
print "Temperature of flue gases: ",round(Tgas,2)," °C"

Temperature of flue gases:  476.99  °C


## Example 19, page no. 498¶

In [40]:
from __future__ import division

#Variable Declaration:
Ta = 20+273 #Ambient temperature(in K):
V = 20 #Velocity(in m/s):
hw1 = 30 #Draught lost through grate(in mm of water column):
nm = 0.80 #Mechanical efficiency:
mf = 1000 #Rate at which coal is burnt(in kg/hr):
ma = 16  #Rate at which air is supplied(in kg/hr):
pa = 1.01325 #Ambient pressure(in bar):
d = 1.29 #Density of air(in kg/m**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
T0 = 273 #Zero temperature(in K):

#Calculations:
P1 = d*V**2/2 #Pressure equivalent to velocity head(in N/m**2):
P = P1/g                                #mm of water column
hw = hw1+P #Total draught loss(in mm of water column):
p = hw*g #Pressure required(in N/m**2):
PFD = p*mf*ma*Ta/(d*T0*nm*3600) #F.D. fan power requirement(in W):

#Results:
print "F.D. fan power: ",round(PFD/10**3,2),"KW"

F.D. fan power:  2.55 KW