Chapter 15: Steam Condenser

Example 1, page no. 695

In [3]:
from __future__ import division
 

#Variable Declaration: 
h = 71 #Height of mercury column in condenser(in mm of Hg):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
mw = 800 #Rate at which cooling water is circulated(in kg/min):
ms = 25 #Condensate available at(in kg/min):
R = 0.287 #Gas constant(in kJ/kg.K):
Cpw = 4.18 #Specific heat of water(in kJ/kg.K):
#From steam tables:
ps = 5.62                   #kPa
hf = 146.68                 #kJ/kg
hfg = 2418.6                #kJ/kg

#Calculations:
pt = (76-h)*10**(-2)*d*10**6*9.81*10**(-3)#Absolute pressure in the condenser(in kPa):
pa = pt-ps #Partial pressure of air(in kPa):
ma = pa/((273+35)*R) #Mass of air per m**3 of condenser volume:
hs = mw/ms*Cpw*(25-15)+Cpw*30#Enthalpy of steam(in kJ/kg):
x = (hs-hf)/hfg#Dryness fraction of the steam entering:
n = h*d*10**4*g/(76*d*10**4*g-ps*10**3)*100#Vacuum efficiency:

#Results: 
print "Mass of air of condenser volume: ",round(ma,3),"kg/m**3"
print "Dryness fraction of steam entering: ",round(x,4)
print "Vacuum efficiency: ",round(n,2),"%"

Mass of air of condenser volume:  0.012 kg/m**3
Dryness fraction of steam entering:  0.5442
Vacuum efficiency:  98.9 %

Example 2, page no. 695

In [5]:
from __future__ import division
  

#Variable Declaration: 
h = 70 #Height of mercury column in condenser(in mm of Hg):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
r = 2500 #Leakage of air in condenser:
R = 0.287 #Gas constant(in kJ/kg.K):
#From steam tables:
ps = 4.246                  #kPa 
vg = 32.89                  #m**3/kg

#Calculations:
pt = (76-h)*10**(-2)*d*10**6*9.81*10**(-3)#Absolute pressure in the condenser(in kPa):
pa = pt-ps #Partial pressure of air(in kPa):
m = 1/r #Mass of air accoumpanying per kg of steam due to leakage(in kg):
v = m*R*(273+30)/pa #Volume of air per kg of steam(in m**3/kg):
m1 = v/vg #Mass of water vapour accompanying air:

#Results: 
print "Capacity of air pump: ",round(v*10**3,2)," x 10^-3 m**3 per kg steam"
print "Mass of water vapour accompanying air: ",round(m1*10**4,2)," x 10^-4 kg/kg of steam"

Capacity of air pump:  9.26  x 10^-3 m**3 per kg steam
Mass of water vapour accompanying air:  2.82  x 10^-4 kg/kg of steam

Example 3, page no. 696

In [7]:
from __future__ import division

#Variable Declaration: 
h = 67 #Height in mercury column in condenser(in cm):
pt = 10.67 #Absolute pressure in the condenser(in kPa):
ps = 7.384 #Partial pressure of steam(in kPa):
ms = 50 #Mass flow rate of steam(in kg/min):
mw = 1000 #Mass flow rate of water(in kg/min):
Cpw = 4.18 #Specific heat of water(in kJ/kg.K):
R = 0.287 #Gas constant(in kJ/kg.K):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
#From steam tables:
hf = 167.57                 #kJ/kg 
hfg = 2406.7                #kJ/kg
vg = 19.52                  #m**3/kg

#Calculations:
cv = 76-(75-h) #Corrected vacuum(in cm):
pa = pt-ps #Partial pressure of air(in kPa):
n = h*d*10**4*g/(75*d*10**4*g-ps*10**3)*100	#VAcuum efficiency:
u = 40-35 #Undercooling of condensate(in C):
n1 = (25-10)/(46.9-10)*100 #Condenser efficiency:
h = mw/ms*Cpw*(25-10)+Cpw*40 #Enthalpy of steam(in kJ/kg):
x = (h-hf)/hfg      #Dryness fraction:
m = pa/(R*(273+40)) #Mass of air per m**3 of condenser volume(in kg/m**3):
m1 = pa*vg/(R*(273+40)) #Mass of air in 1kg of uncondensate steam(in kg):

#Results:
print "Corrected vacuum: ",round(cv,2),"cm of Hg"
print "Vacuum efficiency: ",round(n,2),"%"
print "Undercooling: ",round(u,2),"°C"
print "Dryness fraction of steam entering: ",round(x,4)
print "Mass of air/m**3 of condenser volume: ",round(m,4),"kg/m**3"
print "Mass of air in per kg of uncondensate steam: ",round(m1,3),"kg"

Corrected vacuum:  68.0 cm of Hg
Vacuum efficiency:  96.45 %
Undercooling:  5.0 °C
Dryness fraction of steam entering:  0.5209
Mass of air/m**3 of condenser volume:  0.0366 kg/m**3
Mass of air in per kg of uncondensate steam:  0.714 kg

Example 4, page no. 697

In [9]:
from __future__ import division
  
from math import pi

#Variable Declaration: 
h = 69 #Height in mercury column in condenser(in cm):
T1 = 30 #Inlet temperature(in °C):
L = 60 #Leakage(in kg/hr):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
R = 0.287 #Gas constant(in kJ/kg.K):
n = 240 #Rpm of engine:
r = 1.5 #L/D ratio:
#From steam tables:
ps = 4.246                  #kPa 
vg = 32.89                  #m**3/kg
pt = (76-h)*d*10**4*g     #Absolute pressure at inlet to air pump(in kPa):
pa = 5.09  #Partial pressure of air(in kPa):
V = L*R*(273+T1)/pa #Volume of 60 kg air(in m**3/hr):
D = ((V*4)/(pi*r*n*60))**(1/3)*100 #Bore diameter(in cm):
l = D*r #Stroke length(in cm):
m = V/vg #Mass of water vapour extracted with air(in kg/hr):

#Results: 
print "Capacity of air pump: ",round(V,1),"m**3/hr"
print "Bore: ",round(D,2),"cm"
print "Stroke: ",round(l,2),"cm"
print "Mass of water vapour extracted with air: ",round(m,2),"kg/hr"

Capacity of air pump:  1025.1 m**3/hr
Bore:  39.24 cm
Stroke:  58.86 cm
Mass of water vapour extracted with air:  31.17 kg/hr

Example 5, page no. 698

In [11]:
from __future__ import division
 

#Variable Declaration: 
h = 70 #Height in mercury column in condenser(in cm):
T = 30+273 #Inlet temperature(in K):
m = 5*10**(-4) #Leakage(in kg/kg of steam):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
R = 0.287 #Gas constant(in kJ/kg.K):
Cpw = 4.18 #Specific heat of water(in kJ/kg.K):
dT = 15 #Increase in temperature of cooling water(in K):
x = 0.90 #Dryness fraction:
#From steam tables:
hf = 125.79                 #kJ/kg
hfg = 2430.5                #kJ/kg
vg = 32.89                  #m**3/kg
ps = 4.246                  #kPa

#Calculations:
pt = (77-h)*d*10**4*g    #Absolute pressure in condenser(in kPa):
pa = 5.094 #Partial pressure of air(in kPa):
V = m*10**3*R*T/pa    #Volume of air extracted per minute(in m**3/min):
ms = V/vg      #Mass of steam extracted in maixture(in kg/min):
mt = m*10**3+ms    #Mass handled by air extraction pump(in kg/min):
h = hf+x*hfg #Enthalpy of steam entering(in kJ/kg):
mw = 1000*(h-Cpw*T)/(Cpw*dT) #Water circulation rate(in kg/min):

#Results: 
print "Mass handled by air pump: ",round(mt,4),"kg/min"
print "Water circulation rate: ",round(mw,2),"kg/min"

Mass handled by air pump:  0.7595 kg/min
Water circulation rate:  16693.78 kg/min

Example 6, page no. 699

In [13]:
from __future__ import division
 
#Variable Declaration: 
h = 70 #Height in mercury column in condenser(in cm):
T = 30+273 #Inlet temperature(in K):
x = 0.85 #Dryness fraction:
m = 300 #Rate at which steam enters(in kg/min):
v = 50 #Velocity of water flow:
ph = 5 #Pressure head(in m):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
R = 0.287 #Gas constant(in kJ/kg.K):
Cpw = 4.18 #Specific heat of water(in kJ/kg.K):
#From steam tables:
ps = 4.246                  #kPa 
mw = 7415                   #kg/min
A = 24.79 #Cooling surface area required(in m**2):

#Calculations:
pt = (76-h)*d*10**4*g #Absolute pressure in condenser(in kPa):
pa = pt-ps #Partial pressure of air(in kPa):
V = mw/1000 #Volume flow of water(in m**3/min):
a = V/v #Flow surface area required(in m**2):
vh = 1/2*(v/60)**2/g #Velocity head present(in m):
th = ph+vh #Total head required(in m):

#Results:
print "Flow surface area required: ",round(a,4),"m**2"  
print "Cooling surface area required: ",round(A,2),"m**2"
print "Head required: ",round(th,4),"m"

Flow surface area required:  0.1483 m**2
Cooling surface area required:  24.79 m**2
Head required:  5.0354 m

Example 7, page no. 700

In [15]:
from __future__ import division
   
#Variable Declaration: 
m1 = 350 #Mass of steam entering(in kg/min):
v = 0.02 #Volume of water required(in m**3 per kg steam):
r = 0.05/100 #Amount of air mass going into condenser:
r1 = 5/100 #Volume of air dissolved in the water injected:
h = 68 #Height in mercury column in condenser(in cm):
T = 20+273 #Inlet temperature(in K):
p = 101.3 #Atmospheric pressure(in kPa):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
R = 0.287 #Gas constant(in kJ/kg.K):
Cpw = 4.18 #Specific heat of water(in kJ/kg.K):
n = 0.90 #Volumetric efficiency:
#From steam tables:
ps = 4.246 #kPa 
vf = 0.001004 #m**3/kg

#Calculations:
pt = (76-h)*d*10**4*g*10**(-3)#Absolute pressure in condenser(in kPa):
pa = pt-ps #Partial pressure of air(in kPa):
V1 = m1*v #Volume of cooling water required per minute(in m**3/min):
m2 = m1*r #Mass of air going into condenser(in kg/min):
V = V1*r1 #Volume of air entering per minute with cooling water(in m**3/min):
m = p*V/(R*T) #Mass of air with cooling water(in kg):
mt = m+m2 #Total mass of air inside condenser(in kg):
V2 = mt*R*(273+30)/pa #Volume of air corresponding:
V3 = m1*vf #Volume of steam condensed(in m**3/min):
Vt = V3+V2+V1 #Total volume(in m**3/min):
C = Vt/n #Actual capacity of air pump(in m**3/min):

#Results: 
print "Capacity of air pump: ",round(C,2),"m**3/min"

Capacity of air pump:  17.14 m**3/min

Example 8, page no. 701

In [17]:
from __future__ import division

#Variable Declaration: 
H = 65 #Height in mercury column in condenser(in cm):
ms = 20 #Rate at which steam enters(in kg/min):
m = 12 #Mass of cooling water per kg of steam:
H1 = 66 #Height in mercury column in air pump(in cm):
p = 101.3 #Atmospheric pressure(in kPa):
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
R = 0.287 #Gas constant(in kJ/kg.K):
Cpw = 4.18 #Specific heat of water(in kJ/kg.K):
#From steam tables:
ps = 7.384                  #kPa
ps1 = 5.628                 #kPa
hf = 167.57                 #kJ/kg
hfg = 2406.7                #kJ/kg

#Calculations:
pt = (76-H)*d*10**4*g*10**(-3)      #Absolute pressure in condenser(in kPa):
pa = pt-ps       #Partial pressure of air(in kPa):
mw = m*ms       #Cooling water required(in kg/min):
h = ((ms+mw)*Cpw*40-mw*Cpw*20)/ms #Enthalpy of steam entering:
x = (h-hf)/hfg      #Dryness fraction of steam entering:
pt1 = (76-H1)*d*10**4*g*10**(-3) #Absolute partial pressure at suction in air pump(in kPa): 
pa1 = pt1-ps1 #Partial pressure of air(in kPa):
V = 2       #Volume of mixture(in m**3):
m1 = pa1*V/(R*(273+35)) #Mass of air entering(in kg/min):
H2 = (p-pt)/(g*d*10**3) #Head(in m):

#Results: 
print "Dryness fraction of steam entering: ",round(x,3)
print "Mass of air entering: ",round(m1,4),"kg/min"
print "Head: ",round(H2,4),"m"

Dryness fraction of steam entering:  0.417
Mass of air entering:  0.1744 kg/min
Head:  0.6496 m

Example 9, page no. 702

In [19]:
from __future__ import division

#Variable Declaration: 
m = 3  #Leakage(in kg/min):
g = 9.81  #Acceleration due to gravity(in m/s**2):
R = 0.287  #Gas constant(in kJ/kg.K):
#From steam tables:
ps = 5.628                      #kPa
ps1 = 5.075                     #kPa
ps2 = 5.352                     #kPa
pt = ps #Absolute pressure in condenser(in kPa):

#Calculations:
pa1 = pt-ps1  #Partial pressure of air(in kPa):
V1 = m*R*(273+33)/pa1 #Volume of air handled by air pump(in m**3/hr):
pa2 = pt-ps2 #Partial pressure of air(in kPa):
V2 = m*R*(273+34)/pa2  #Volume of mixture handled(in m**3/hr):

#Results: 
print "Volume of air handled: ",round(V1,2),"m**3/hr"
print "Volume of mixture handled: ",round(V2,2),"m**3/hr"

Volume of air handled:  476.43 m**3/hr
Volume of mixture handled:  957.71 m**3/hr

Example 10, page no. 703

In [21]:
from __future__ import division

#Variable Declaration: 
H1 = 72 #Height in mercury column at inlet in condenser(in cm):
H2 = 73 #Height in mercury column at outlet in condenser(in cm):
x = 0.92 #Dryness fraction:
d = 0.0135951 #Density of mercury(in kg/cm**3):
g = 9.81 #Acceleration due to gravity(in m/s**2):
R = 0.287 #Gas constant(in kJ/kg.K):
Cpw = 4.18 #Specific heat of water(in kJ/kg.K):
#From steam tables:
hf = 141.97                 #kJ/kg
hfg = 2421.33               #kJ/kg
Tsat1 = 33.87               #°C
Tsat2 = 28.96               #°C

#Calculations:
p1 = (76-H1)*d*10**4*g*10**(-3) #Inlet pressure in condenser(in kPa):
p2 = (76-H2)*d*10**4*g*10**(-3) #Outlet pressure in the condenser(in kPa):
u = Tsat1-Tsat2 #Undercooling(in C):
h = hf+x*hfg #Enthalpy of steam entering(in kJ/kg):
m = (h-Cpw*Tsat2)/(Cpw*13.87) #Cooling water requirement(in kg/kg steam):

#Results: 
print "Undercooling: ",round(u,2),"°C"
print "Cooling water requirement: ",round(m,2),"kg/kg steam"

Undercooling:  4.91 °C
Cooling water requirement:  38.78 kg/kg steam