# Chapter 6 : Properties of Steam¶

## Example 6.1 Page No : 14¶

In [1]:
import math

# Variables :
m = 2.; 			#Kg
p = 8.;	    		#bar
H = 5535.;			#KJ

# Calculations and Results
h = H/m;			#KJ/Kg
hg = 2767.5;		#KJ/Kg
print "Specific Enthalpy in KJ/Kg : %.1f"%h
print "Given Enthalpy in KJ/Kg : %.1f"%hg
print ("Given enthalpy  =  specific enthalpy. System is dry saturated.");

m = 1;			#Kg
p = 2550*10**3/10**5;			#bar
v = 0.2742;			#m**3/Kg
print "Specific volume in m**3/Kg : %.4f"%v
vg = 0.078352;			#m**3
print "Given specific volume in m**3/Kg : %.4f"%vg

Ts = 225+273;			#K
print ("Since v>vg. System is super heated.");
Tsup = v/vg*Ts;			#K
print "Temperature of super heated steam in degree C :%.1f"%(Tsup-273)

m = 1;			#Kg
p = 60;			#bar
h = 2470.73;			#KJ/Kg
print "Enthalpy in KJ/Kg : %.1f"%h

hg = 2475;			#KJ/Kg
print "Given enthalpy in KJ/Kg : %.1f"%hg
print ("Since h>hg. System is in vapour state.");
#let x be the dryness fraction
#h = hf+x*hg
hf = 1213.69;			#KJ/Kg
hfg = 1517.3;			#KJ/Kg
x = (h-hf)/hfg;
print "Dryness fraction : %.1f"%x
#Steam table is used to get some data.

Specific Enthalpy in KJ/Kg : 2767.5
Given Enthalpy in KJ/Kg : 2767.5
Given enthalpy  =  specific enthalpy. System is dry saturated.
Specific volume in m**3/Kg : 0.2742
Given specific volume in m**3/Kg : 0.0784
Since v>vg. System is super heated.
Temperature of super heated steam in degree C :1469.8
Enthalpy in KJ/Kg : 2470.7
Given enthalpy in KJ/Kg : 2475.0
Since h>hg. System is in vapour state.
Dryness fraction : 0.8


## Example 6.2 Page No : 16¶

In [2]:

# Variables :
p = 5;			#bar
x = 0.98;
ts = 151.84;			#degree C
hf = 652.8;			#KJ/Kg
hfg = 2098;			#KJ/Kg
vg = 0.373;			#m**3/Kg

# Calculations and Results
print "Temperature of steam in degree C : %.2f"%ts
h = hf+x*hfg;			#KJ/Kg
print "Enthalpy of steam in KJ/Kg : %.2f"%h
v = x*vg;			#m**3/Kg
print "Specific volume in m**3/Kg ; %.4f"%v
#Steam table is used to get some data.

Temperature of steam in degree C : 151.84
Enthalpy of steam in KJ/Kg : 2708.84
Specific volume in m**3/Kg ; 0.3655


## Example 6.3 Page No : 16¶

In [3]:

# Variables :
m = 1;			#Kg
p = 12;			#bar
x = 0.95;
ts = 187.96;			#degree C
vg = 0.1632;			#m**3/Kg
hf = 814.7;			#KJ/Kg
hfg = 1970.7;			#KJ/Kg

# Calculations and Results
print "Temperature of steam in degree C : ",ts

v = x*vg;			#m**3/Kg
print "Specific volume in m**3/Kg ; ",v
h = hf+x*hfg;			#KJ/Kg
print "Enthalpy of steam in KJ/Kg : %.1f"%h
u = h-p*10**5*v/1000;			#KJ/Kg
print "Internal energy in KJ/Kg : %.1f"%u
#Steam table is used to get some data.

Temperature of steam in degree C :  187.96
Specific volume in m**3/Kg ;  0.15504
Enthalpy of steam in KJ/Kg : 2686.9
Internal energy in KJ/Kg : 2500.8


## Example 6.4 Page No : 16¶

In [4]:

# Variables :
m = 1.;		        	#Kg
p = 8.;			        #bar
Tsup = 280.;			#degree C
h1 = 2950.4;			#KJ/Kg(at 250 degree C)
h2 = 3057.3;			#KJ/Kg(at 300 degree C)
Tsup1 = 250.;			#degree C
Tsup2 = 300.;			#degree C

# Calculations and Results
hsup = h1+(h2-h1)/(Tsup2-Tsup1)*(Tsup-Tsup1);			#KJ/Kg
print "Specific enthalpy in KJ/Kg : %.1f"%hsup

v1 = 0.293;			#m**3/Kg(at 250 degree C)
v2 = 0.324;			#m**3/Kg(at 300 degree C)
vsup = v1+(v2-v1)/(Tsup2-Tsup1)*(Tsup-Tsup1);			#m**3/Kg
print "Specific volume in m**3/Kg : ",vsup

S1 = 7.04;			#KJ/KgK(at 250 degree C)
S2 = 7.235;			#KJ/KgK(at 300 degree C)
Ssup = S1+(S2-S1)/(Tsup2-Tsup1)*(Tsup-Tsup1)
print "Specific enthalpy in KJ/KgK : ",Ssup

#Steam table is used to get some data.

Specific enthalpy in KJ/Kg : 3014.5
Specific volume in m**3/Kg :  0.3116
Specific enthalpy in KJ/KgK :  7.157


## Example 6.5 Page No : 17¶

In [5]:

# Variables :
p1 = 0.1;			#bar
p2 = 0.1;			#bar
x1 = 0.95;
t3 = 20.;			#degree C
t2 = 35.;			#degree C
t4 = 45.;			#degree C
hf1 = 191.8;			#KJ/Kg
hfg1 = 2397.9;			#KJ/Kg

# Calculations
h1 = hf1+x1*hfg1;			#KJ/kg
h2 = 188.4;			#KJ/Kg(at 45 degree C)
h3 = 83.9;			#KJ/Kg(at 20 degree C)
h4 = 146.6;			#KJ/Kg(at 35 degree C)
#m1*(h1-h2) = mw*(h4-h3)
mwBYm1 = (h1-h2)/(h4-h3);			#Kg of water/Kg of steam

# Results
print "Ratio of mass flow rate of cooling water to condensing steam(Kg of water/Kg of steam): %.3f"%mwBYm1
#Steam table is used to get some data.

Ratio of mass flow rate of cooling water to condensing steam(Kg of water/Kg of steam): 36.386


## Example 6.6 Page No : 18¶

In [1]:

# Variables :
V = 3.;			#m**3
t = 200.;			#degree C
Pat = 1.;			#bar
Pgauge = 7.;			#bar
P = Pgauge+Pat;			#bar
ts = 170.41;			#degree C
tsup = t;			#degree C
vsup = 0.261;			#m**3/Kg
hsup = 2838.6;			#KJ/Kg

# Calculations and Results
m = V/vsup;			#Kg
H = m*hsup;			#KJ
print "Total Enthalpy in KJ : %.2f"%H
#H = U+p*V
U = H-P*10**5*V/1000;			#KJ
print "Total internal energy of system in KJ : %.2f"%U
print "Mass of steam in Kg : %.3f"%m
#Steam table is used to get some data.

Total Enthalpy in KJ : 32627.59
Total internal energy of system in KJ : 30227.59
Mass of steam in Kg : 11.494


## Example 6.7 Page No : 18¶

In [7]:

# Variables :
mw = 1.;			#Kg
m_steam = 39.;			#mass of dry steam in Kg

# Calculations
ms = mw+m_steam;			#Kg
x = m_steam/ms;			#dryness fraction

# Results
print "Dryness fraction ; ",x

Dryness fraction ;  0.975


## Example 6.8 Page No : 18¶

In [8]:

# Variables :
m = 10.;			#Kg
p = 10.;			#bar
x = 0.9;
t1 = 20.;			#degree C
hf = 762.6;			#KJ/Kg
hfg = 2013.6;			#KJ/Kg

# Calculations and Results
H = m*(hf+x*hfg);			#KJ;
print "Enthalpy of wet steam in KJ : ",H

hf1 = 83.9;			#KJ/Kg(at 20 degree C)
Hf1 = m*hf1;			#KJ

#Steam table is used to get some data.

Enthalpy of wet steam in KJ :  25748.4
Heat added in KJ :  24909.4


## Example 6.9 Page No : 19¶

In [7]:

# Variables :
t = 50.;			#degree C
p1 = 13.;			#bar
Cpw = 4.187;			#KJ/KgK
Cp = 0.0535;			#KJ/KgK
x1 = 0.97;
hf = Cpw*(t-0);			#KJ/Kg
hf1 = 814.7;			#KJ/Kg(at p1 = 13 bar)
hfg1 = 1970.7;			#KJ/Kg(at p1 = 13 bar)
hg1 = 2785.4;			#KJ/Kg(at p1 = 13 bar)

# Calculations and Results
Q = hf1+x1*hfg1-hf;			#KJ/Kg
print "Heat required to produce steam in KJ/Kg : %.2f"%Q
Q1 = hg1-hf;			#KJ/Kg
print "Heat required to produce dry saturated steam in KJ/Kg : ",Q1
tsup1SUBts1 = 40;			#degree C
Q2 = hg1+Cp*(tsup1SUBts1)-hf;			#KJ/Kg
print "Heat required to produce super heated steam in KJ/Kg : ",Q2
#Steam table is used to get some data.
#Ans is wrong in the book for last part.

Heat required to produce steam in KJ/Kg : 2516.93
Heat required to produce dry saturated steam in KJ/Kg :  2576.05
Heat required to produce super heated steam in KJ/Kg :  2578.19


## Example 6.10 Page No : 19¶

In [8]:

# Variables :
p = 8;			#bar
x = 0.8;
vf = 0.001115;			#m**3/kg
vg = 0.24;			#m**3/kg
hf = 720.9;			#kJ/kg(at p = 8 bar)
hfg = 2046.5;			#kJ/kg(at p = 8 bar)
m = 1;			#kg

# Calculations and Results
We = 100*p*(x*vg-vf);			#kJ/kg
print "External workdone during evaporation in kJ/kg : %.2f"%We

Q = x*hfg-We;			#KJ
print "External latent heat of steam in kJ: %.2f"%Q

#Steam table is used to get some data.
#Ans is wrong in the book for last part.

External workdone during evaporation in kJ/kg : 152.71
External latent heat of steam in kJ: 1484.49


## Example 6.11 Page No : 20¶

In [9]:

# Variables :
p1 = 20.;			#bar
Tsup1 = 350.;			#degree C
m1 = 1.;			#Kg
p2 = 20.;			#bar
m2 = 1.;			#Kg
p3 = p1;			#bar
Tsup3 = 250.;			#degree C
m3 = m1+m2;			#Kg
Cp = 2.25;			#KJ/Kg
hg1 = 2797.2;			#KJ/Kg(at p = 20 bar)
hg2 = hg1;			#KJ/Kg(at p = 20 bar)
hg3 = hg1;			#KJ/Kg(at p = 20 bar)
ts1 = 212.37;			#degree C
ts2 = ts1;			#degree C
ts3 = ts1;			#degree C

# Calculations and Results
#m1*h1+m2*h2 = m3*h3
h2 = (m3*(hg3+Cp*(Tsup3-ts3))-m1*(hg1+Cp*(Tsup1-ts1)))/m2;			#KJ/Kg
print "Enthalpy of boiler2 in KJ/Kg :  %.2f"%h2
print "hg2(KJ/Kg)  : ",hg2
print ("steam is wet because h2<hg2")
#h2 = hf2+x2*hfg2			# as steam is wet because h2<hg2
hf2 = 908.6;			#KJ/Kg
hfg2 = 1888.6;			#KJ/Kg
x2 = (h2-hf2)/hfg2;			#
print "Dryness : %.5f"%x2
#Steam table is used to get some data.
#Ans is wrong in the book.

Enthalpy of boiler2 in KJ/Kg :  2656.87
hg2(KJ/Kg)  :  2797.2
steam is wet because h2<hg2
Dryness : 0.92569


## Example 6.12 Page No : 20¶

In [12]:

# Variables :
m = 2.;			#Kg
p = 8.;			#bar
x = 0.8;
hf = 720.9;			#KJ/Kg(at p = 8 bar)
hfg = 2046.5;			#KJ/Kg(at p = 8 bar)

# Calculations and Results
h = hf+x*hfg;			    #KJ/Kg
H = m*h;			        #KJ
print "Total enthalpy of steam in KJ : ",H

Vg = 0.227;			        #m**3/Kg
V = m*x*Vg;			        #m**3
print "Volume in m**3 : ",V

We = p*10**5*V/1000;			#KJ
print "External work of evaporation in KJ : ",We

U = H-We;			        #KJ
print "Total internal energy in KJ : ",U

Sf = 2.061;		    	    #KJ/K
Sfg = 4.578;		    	#KJ/K
S = m*(Sf+x*Sfg);			#KJ/K
print "Total entropy in KJ/K : ",S
#Steam table is used to get some data.

Total enthalpy of steam in KJ :  4716.2
Volume in m**3 :  0.3632
External work of evaporation in KJ :  290.56
Total internal energy in KJ :  4425.64
Total entropy in KJ/K :  11.4468


## Example 6.13 Page No : 21¶

In [10]:

# Variables :
p1 = 600.;			#KPa
p1 = p1/100.;			#bar
T1 = 200.;			#degree C
Vsup1 = 0.352;			#m**3/Kg(at 6 bar)
V1 = Vsup1;			#m**3/Kg
V2 = V1;			#m**3(system is at consmath.tant volume)
Vg2 = V2;			#m**3/Kg(For dry saturated)
Tsup1 = 153.3;			#degree C
Tsup2 = 154.8;			#degree C
vg1 = 0.34844;			#m**3/Kg
vg2 = 0.36106;			#m**3/Kg

# Calculations and Results
ts2 = Tsup1+(Tsup2-Tsup1)/(vg2-vg1)*(V1-vg1);			#degree C
print "Temperature at which steam begins to condense in degree C : %.2f"%ts2

pg1 = 5.2;			#bar
pg2 = 5.4;			#bar
p2 = pg1+(pg2-pg1)/(Tsup2-Tsup1)*(ts2-Tsup1);			#bar
print "Pressure in bar is : %.3f"%p2
#Some data is taken from steam table.

Temperature at which steam begins to condense in degree C : 153.72
Pressure in bar is : 5.256


## Example 6.14 Page No : 23¶

In [11]:

# Variables :
m = 2.;			#Kg
p1 = 15.;			#bar
p2 = 15.;			#bar
Tsup1 = 250.;			#degree C
T1 = Tsup1;			#degree C
V1 = 0.152;			#m**3/Kg(at 15 bar)
hf2 = 844.7;			#KJ/Kg(at p = 15 bar)
hg2 = 2789.9;			#KJ/Kg(at p = 15 bar)
hfg2 = 1945.2;			#KJ/Kg(at p = 15 bar)
h1 = 2923.;			#KJ/Kg
Vg2 = 0.1317;			#m**3/Kg(at 15 bar)
x2 = 0.6;			#dry

# Calculations and Results
h2 = hf2+x2*hfg2;			#KJ/Kg
V2 = x2*Vg2;			#m**3/Kg
w = (p2*V2-p1*V1)*10**5/10**3;			#KJ/Kg
W = m*w;			#KJ
print "Total work done in KJ : ",W

H2subH1 = m*(h2-h1);			#KJ/Kg
print "Change in enthalpy in KJ/Kg : %.1f"%H2subH1

Q = H2subH1;			#KJ
print "Heat transfered in KJ : %.1f"%Q
#Steam table is used to get some data.

Total work done in KJ :  -218.94
Change in enthalpy in KJ/Kg : -1822.4
Heat transfered in KJ : -1822.4


## Example 6.15 Page No : 24¶

In [12]:
# Variables :
p_gauge = 15.;			#bar
p_at = 750.;			#mm of Hg
p_at = p_at/760.*1.01325;			#bar
p = p_gauge+p_at;			#bar
ms = 200.;			#Kg/hr
Cpw = 4.187;			#KJ/KgK
t1 = 80.;			#degree C
hf1 = Cpw*t1;			#KJ/Kg
hf2 = 858.6;			#KJ/Kg(at p = 16 bar)
hg2 = 2791.8;			#KJ/Kg(at p = 16 bar)
hfg2 = 1933.2;			#KJ/Kg(at p = 16 bar)
ts = 201.37;			#degree C
x2 = 0.8;			#dry

# Calculations and Results
h2 = hf2+x2*hfg2;			#KJ/Kg
q = ms*(h2-hf1);			#KJ/hr
q = q/3600;			#KJ/s
print "Heat transfer in boiler in KJ/s : %.3f"%q

tsup = ts+t1;			#degree C
Cp = 2.2;			#KJ/KgK
hsup3 = hg2+Cp*(tsup-ts);			#KJ/Kg
qsup = ms*(hsup3-h2)/3600;			#KJ/s
print "Heat transfered in superheated steam in KJ/s : %.3f"%qsup

Vg = 0.1237;			#m**3/Kg(at 16 bar)
Ts = 201.37+273;			#K
Tsup = tsup+273;			#K
Vsup = Tsup/Ts*Vg;			#m**3/Kg
density = 1/Vsup;			#Kg/m**3
print "Density of steam in Kg/m**3 : %.3f"%density
#Steam table is used to get some data.

Heat transfer in boiler in KJ/s : 115.011
Heat transfered in superheated steam in KJ/s : 31.258
Density of steam in Kg/m**3 : 6.917


## Example 6.16 Page No : 27¶

In [16]:

# Variables :
m = 1.5;			#Kg
p1 = 5;			#bar
x1 = 0.8;			#dry
x2 = 0.4;			#dry
Vg1 = 0.373;			#m**3/Kg(at 5 bar)
hf1 = 640.1;			#KJ/Kg(at p = 5 bar)
hfg1 = 2107.4;			#KJ/Kg(at p = 5 bar)
Vg2 = x1/x2*Vg1;			#m**3/Kg
p2 = 4.;			#bar(at Vg2 = 0.746)
hf2 = 529.6;			#KJ/Kg(at p = 4 bar)
hfg2 = 2184.9;			#KJ/Kg(at p = 4 bar)

# Calculations
V1 = x1*Vg1;		    	#m**3/Kg
V2 = V1;			        #m**3/Kg
h1 = hf1+x1*hfg1;			#KJ/Kg
h2 = hf2+x2*hfg2;			#KJ/Kg
Q = m*((h2-h1)-100*(p2*V2-p1*V1));			#KJ

# Results
print "Quantity of heat in KJ : ",Q
#Steam table is used to get some data.

Quantity of heat in KJ :  -1338.93


## Example 6.17 Page No : 27¶

In [13]:

# Variables :
p1 = 1;			#bar
x1 = 0.523;			#dry
Vg1 = 1.694;			#m**3/Kg(at 1 bar)
hf1 = 417.5;			#KJ/Kg(at p = 1 bar)
hfg1 = 2258;			#KJ/Kg(at p = 1 bar)

# Calculations
h1 = hf1+x1*hfg1;			#KJ/Kg
V1 = x1*Vg1;			#m**3/Kg
V2 = V1;			#m**3/Kg(Consmath.tant volume process)
Vg2 = V2;			#m**3/Kg
p2 = 2;			#bar;			#at Vg2 from steam table
hg2 = 2706.3;			#KJ/Kg(at 2 bar)
h2 = hg2;			#KJ/Kg
W = 0;			#KJ/Kg of steam
q = W+(h2-h1)-100*(p2*V2-p1*V1);			#KJ/Kg

# Results
print "Heat transfered in KJ/Kg : %.1f"%q

#Steam table is used to get some data.

Heat transfered in KJ/Kg : 1019.3


## Example 6.18 Page No : 28¶

In [14]:

# Variables :
V1 = 0.9;			#m**3
p1 = 8;			#bar
x1 = 0.9;			#dry
p2 = 4;			#bar
Vg1 = 0.24;			#m**3/Kg(at 8 bar)
hf1 = 720.9;			#KJ/Kg(at p = 8 bar)
hfg1 = 2046.5;			#KJ/Kg(at p = 8 bar)
Vg2 = 0.462;			#m**3/Kg(at 4 bar)
hf2 = 604.7;			#KJ/Kg(at p = 4 bar)
hfg2 = 2132.9;			#KJ/Kg(at p = 4 bar)

# Calculations and Results
#h1 = h2 : hf1+x1*hfg1 = hf2+x2*hfg2
x2 = ((hf1+x1*hfg1)-hf2)/hfg2;			#dry
print "Dryness fraction of steam : %.3f"%x2

m1 = V1/x1/Vg1;			#Kg
V2 = V1;			#m**3
m2 = V2/x2/Vg2;			#Kg
m = m1-m2;			#Kg
print "Mass of steam blown off in Kg : %.4f"%m
#Steam table is used to get some data.

Dryness fraction of steam : 0.918
Mass of steam blown off in Kg : 2.0447


## Example 6.19 Page No : 31¶

In [15]:
import math

# Variables :
m = 5.;			#Kg
p1 = 10.;			#bar
x1 = 0.9;			#dry
p2 = 4.;			#bar
ts1 = 179.88;			#degree C(at 10 bar)
print "Final condition of steam,(Temperature in degree C) : ",ts1

Vg1 = 0.1943;			#m**3/Kg(at 8 bar)
hf1 = 762.6;			#KJ/Kg(at p = 10 bar)
hfg1 = 2013.6;			#KJ/Kg(at p = 10 bar)
h1 = hf1+x1*hfg1;			#KJ/Kg
V1 = x1*Vg1;			#KJ/kg
u1 = h1-p1*V1*10**5/1000;			#KJ/Kg
U1 = m*u1;			#KJ
Tsup2 = 179.88;			#degree C
t11 = 150;			#degree C
h11 = 2752;			#KJ/Kg(at 4bar,150 degree C)
v11 = 0.471;			#m**3/Kg(at 4bar,150 degree C)
s11 = 6.929;			#KJ/KgK(at 4bar,150 degree C)
t22 = 200;			#degree C
h22 = 2860.4;			#KJ/Kg(at 4bar,200 degree C)
v22 = 0.534;			#m**3/Kg(at 4bar,200 degree C)
s22 = 7.171;			#KJ/KgK(at 4bar,200 degree C)
h2 = h11+(h22-h11)/(t22-t11)*(ts1-t11);			#KJ/Kg
v2 = v11+(v22-v11)/(t22-t11)*(ts1-t11);			#m**3/Kg
s2 = s11+(s22-s11)/(t22-t11)*(ts1-t11);			#m**3
u2 = h2-p2*10**5*v2/1000;			#KJ/Kg
U2 = m*u2;			#KJ
deltaU = U2-U1;			#KJ
print "Change in internal energy in KJ : %.1f"%deltaU

sf1 = 2.138;			#KJ/KgK
sfg1 = 4.445;			#KJ/Kg
s1 = (sf1+x1*sfg1);			#KJ/KgK
deltaS = m*(s2-s1);			#KJ/K
Q = (ts1+273)*(deltaS);			#KJ
print "Heat transfer in KJ : %.1f"%Q

W = Q-deltaU;			#KJ
print "Workdone in KJ : %.1f"%W
#Steam table is used to get some data.
#Answer is not accurate in the book.

Final condition of steam,(Temperature in degree C) :  179.88
Change in internal energy in KJ : 1066.8
Heat transfer in KJ : 2117.5
Workdone in KJ : 1050.7


## Example 6.20 Page No : 33¶

In [17]:
import math

# Variables :
m = 2.;			#Kg
p1 = 15.;			#bar
V1 = 0.3;			#m**3
p2 = 1.5;			#bar
v1 = V1/m;			#m**3/Kg

# Calculations and Results
#p1*v1**(1.3) = p2*v2**(1.3)
v2 = math.exp((math.log(p1)+1.3*math.log(v1)-math.log(p2))/1.3);			#m**3/Kg
Vg2 = 1.1635;			#m**3/Kg(at 1.5 bar)
x2 = v2/Vg2;			#dry
print "Dryness of steam : %.4f"%x2
n = 1.3;
W = m*(p1*v1-p2*v2)*10**5/(n-1);			#J
W = W/1000;			#KJ
print "Workdone in KJ : %.1f"%W
#Steam table is used to get some data.
#Answer is wrong in the book.

Dryness of steam : 0.7578
Workdone in KJ : 618.3


## Example 6.21 Page No : 36¶

In [21]:

# Variables :
m1 = 5.;			#Kg
p1 = 5.;			#bar
Tsup1 = 200.;			#degree C
p2 = 0.1;			#bar
h1 = 2855;			#KJ/Kg(from molliers diagram)
h2 = 2235;			#KJ/Kg(from molliers diagram)

# Calculations
W = m1*(h1-h2);			#KJ

# Results
print "Workdone in KJ : ",W
#Steam table is used to get some data.

Workdone in KJ :  3100.0


## Example 6.22 Page No : 37¶

In [18]:

# Variables :
p1 = 160.;			#bar
Tsup1 = 550.;			#degree C(from steam table)
deltaS = 0.1;			#KJ/KgK
p2 = 0.2;			#bar
t11 = 500.;			#degree C
t22 = 600.;			#degree C
h11 = 3297.1;			#KJ/Kg(at 4bar,500 degree C)
h22 = 3571.;			#KJ/Kg(at 4bar,600 degree C)

# Calculations
h1 = h11+(h22-h11)/(t22-t11)*(Tsup1-t11);			#KJ/Kg
s11 = 6.305;			#KJ/KgK(at 4bar,500 degree C)
s22 = 6.639;			#KJ/KgK(at 4bar,600 degree C)
s1 = s11+(s22-s11)/(t22-t11)*(Tsup1-t11);			#KJ/KgK
s2 = deltaS+s1;			#KJ/KgK
hf2 = 251.4;			#KJ/Kg(at 0.2 bar)
hfg2 = 2358.2;			#KJ/Kg(at 0.2 bar)
sf2 = 0.832;			#KJ/KgK(at 0.2 bar)
sfg2 = 7.077;			#KJ/KgK(at 0.2 bar)
#s2 = sf2+x2*sfg2
x2 = (s2-sf2)/sfg2;			#dryness
h2 = hf2+x2*hfg2;			#KJ
Wsf_a = h1-h2;			#KJ/Kg

# Results
print "Actual Work of expansion in KJ : %.1f"%Wsf_a
#Steam table is used to get some data.

Actual Work of expansion in KJ : 1270.0


## Example 6.23 Page No : 37¶

In [3]:

# Variables :
mdot = 2.;			#Kg/s
p1 = 10.;			#bar
Tsup1 = 200.;			#degree C(from steam table)
p2 = 1.;			#bar
h1 = 2826.8;			#KJ/Kg(at 10bar,200 degree C)
S1 = 6.692;			#KJ/KgK(at 10bar,200 degree C)
ts2 = 99.63;			#degree C(at 1bar)
Vg2 = 1.694;			#m**3/Kg(at 1bar)
hf2 = 417.5;			#KJ/Kg(at 1bar)
hfg2 = 2258.;			#KJ/Kg(at 1bar)
sf2 = 1.303;			#KJ/KgK(at 1bar)
sfg2 = 6.057;			#KJ/KgK(at 1bar)

# Calculations
#S1 = sf2+x2*sfg2
x2 = (S1-sf2)/sfg2;			#dryness
V3 = x2*Vg2;			#m**3/Kg
t2 = ts2;			#degree C
S2 = S1;			#KJ/KgK
Qdot = 0;			#KJ
h2 = hf2+x2*hfg2;			#KJ/Kg
Wsf_dot = Qdot-mdot*((h2-h1));			#KJ/Kg

# Results
print "Final specific volume, v2 = %.4f m**3/kg"%V3
print "Final temperature , t2 = %.2f C"%t2
print "Final specific entropy, S2 = %.3f kJ/kg K"%S2
print "Work output of turbine in KJ/s or W : %.1f"%Wsf_dot

#Steam table is used to get some data.

Final specific volume, v2 = 1.5072 m**3/kg
Final temperature , t2 = 99.63 C
Final specific entropy, S2 = 6.692 kJ/kg K
Work output of turbine in KJ/s or W : 800.6


## Example 6.24 Page No : 39¶

In [2]:

# Variables :
p1 = 7.;			#bar
x1 = 0.8;			#dryness
p2 = 1.;			#bar
hf1 = 697.;			#KJ/Kg(at 7bar)
hfg1 = 2064.9;			#KJ/Kg(at 7bar)
hf2 = 417.5;			#KJ/Kg(at 1bar)
hfg2 = 2258;			#KJ/Kg(at 1bar)

# Calculations and Results
#hf1+x1*hfg1 = hf2+x2*hfg2
x2 = (hf1+x1*hfg1-hf2)/hfg2;			#dryness
print "Final conditio of steam(dryness) : %.4f"%x2

sf2 = 1.303;			#KJ/Kg(at 1bar)
sfg2 = 6.057;			#KJ/Kg(at 1bar)
sf1 = 1.992;			#KJ/Kg(at 7bar)
sfg1 = 4.713;			#KJ/Kg(at 7bar)
deltaS = (sf2+x2*sfg2)-(sf1+x1*sfg1)
print "Change in entropy in KJ/KgK : %.4f"%deltaS
print "Entropy change of surroundings = %.4f KJ/kg K"%(deltaS + 0)
#Steam table is used to get some data.

Final conditio of steam(dryness) : 0.8554
Change in entropy in KJ/KgK : 0.7216
Entropy change of surroundings = 0.7216 KJ/kg K


## Example 6.25 Page No : 40¶

In [25]:
# Variables :
p1 = 10.;			#bar
x1 = 0.9;			#dryness
p2 = 1.;			#bar
hf1 = 762.6;			#KJ/Kg(at 10bar)
hfg1 = 2013.6;			#KJ/Kg(at 10bar)

# Calculations
h1 = hf1+x1*hfg1;			#KJ/Kg
h2 = h1;			#KJ/Kg
hg2 = h2;			#KJ/Kg
p2 = 0.075;			#bar(from steam table)

# Results
print "Pressure at exit in bar : ",p2
#Steam table is used to get some data.

Pressure at exit in bar :  0.075


## Example 6.26 Page No : 40¶

In [22]:
import math

# Variables :
m1dot = 3.;			#Kg/min
p1 = 10.;			#bar
Tsup1 = 250.;			#degree C
m2dot = 5.;			#Kg/min
p2 = 10.;			#bar
x2 = 0.7;			#dryness
p3 = 10.;			#bar
p4 = 5.;			#bar
p5 = 2.;			#bar
m3dot = m1dot+m2dot;			#Kg/min
hsup1 = 2826.8;			#KJ/Kg(at 10bar)
hf2 = 762.6;			#KJ/Kg(at 10bar)
hf3 = 762.6;			#KJ/Kg(at 10bar)
hfg2 = 2013.6;			#KJ/Kg(at 10bar)
hfg3 = 2013.6;			#KJ/Kg(at 10bar)

# Calculations and Results
#m1dot*hsup1+m2dot*(hf2+x2*hfg2) = m3dot*(hf3+x3*hfg3)
x3 = ((m1dot*hsup1+m2dot*(hf2+x2*hfg2))/m3dot-hf3)/hfg3;			#dryness
print "State of steam after mixing(dryness) : %.2f"%x3

x4 = 0.838;			#dryness(from molliers diagram)
print "State of steam after throttling(dryness) : %.3f"%x4

sf3 = 2.138;			#KJ/KgK(From steam table
sfg3 = 4.445;			#KJ/KgK(From steam table
sf4 = 1.860;			#KJ/KgK(From steam table)
sfg4 = 4.959;			#KJ/KgK(From steam table
s4SUBs3 = m3dot/60*((sf4+x4*sfg4)-(sf3+x3*sfg3));			#KJ/Kg
print "Increase in entropy due to throttling in KJ/KgK : %.5f"%s4SUBs3

h4 = 2405;			#KJ/Kg(from Molliers diagram)
h5 = 2265;			#KJ/Kg(from Molliers diagram)
x5 = 0.802;			#dryness
C4 = 0;			#m/s(from S.F.E.E)
#h4+C4**2/2/1000 = h5+C5**2/2/1000
C5 = math.sqrt((h4+C4**2/2/1000-h5)*2*1000);			#m/s
p5 = 2;			#bar(from steam table)
Vg5 = 0.885;			#m**3/Kg(from steam table)
#mdot/60 = A5*C5/x5/Vg5
A5 = m3dot/60/C5*x5*Vg5;			#m**2
print "Exit area of nozzle in cm**2 : %.4f"%(A5*10**4)
#Steam table is used to get some data.

State of steam after mixing(dryness) : 0.82
State of steam after throttling(dryness) : 0.838
Increase in entropy due to throttling in KJ/KgK : 0.02989
Exit area of nozzle in cm**2 : 1.7885


## Example 6.27 Page No : 47¶

In [23]:

# Variables :
ms = 5.;			#Kg
m2 = 140.;			#Kg
p = 10.;			#bar
mc = 20.;			#KJ/K
t1 = 20.;			#degree C
mwdot = 20.;			#Kg
t2 = 40.;			#degree C
Cpw = 4.19;			#KJ/KgK
hfg = 2021.4;			#KJ/Kg(at 10bar)
ts = 179.88;			#degree C

# Calculations
#ms*(x*hfg)+ms*Cpw*(ts-t2) = m2*Cpw*(t2-t1)+mc*(t2-t1)
x = (m2*Cpw*(t2-t1)+mc*(t2-t1)-ms*Cpw*(ts-t2))/ms/hfg;			#dryness

# Results
print "Dryness fraction of steam : %.4f"%x

#Steam table is used to get some data.

Dryness fraction of steam : 0.9104


## Example 6.28 Page No : 47¶

In [24]:

# Variables :
p1 = 15.;			#bar
p2 = 15.;			#bar
p3 = 1.;			#bar
Tsup3 = 150.;			#degree C
mw = 0.2;			#Kg/min
ms = 10.;			#Kg/min

# Calculations and Results
x1 = ms/(ms+mw);			#dryness
print "Dryness factor of steam : %.4f"%x1

hf2 = 844.7;			#KJ/Kg(from steam table,at 15 bar)
hfg2 = 1945.2;			#KJ/Kg(from steam table,at 15 bar)
hsup3 = 2776.3;			#KJ/Kg(from steam table,at 15 bar)
#hsup3 = hf2+x2*hfg2;			#KJ/Kg
x2 = (hsup3-hf2)/hfg2;			#KJ/Kg
x = x1*x2;			#dryness
print "Dryness fraction in the mains : %.4f"%x

#Steam table is used to get some data.

Dryness factor of steam : 0.9804
Dryness fraction in the mains : 0.9735


## Example 6.29 Page No : 48¶

In [25]:

# Variables :
p1 = 1.;			#MPa
p2 = 100.;			#KPa
p1 = p1*10**6./10**5;			#bar
p2 = p2*10**3./10**5;			#bar
hf1 = 762.5;			#KJ/Kg(from steam table)
hfg2 = 2013.6;			#KJ/Kg(from steam table)
hg2 = 2675.5;			#KJ/Kg(from steam table)

# Calculations
#hg2 = hf1+x1*hfg2;			#KJ/Kg
x1 = (hg2-hf1)/hfg2;			#

# Results
print "Dryness fraction in the mains : %.2f"%x1

#Steam table is used to get some data.

Dryness fraction in the mains : 0.95


## Example 6.30 Page No : 49¶

In [26]:

# Variables :
p1 = 900.;			#KN/m**2
p2 = 900.;			#KN/m**2
p3 = 0.1013;			#MN/m**2
p1 = p1/10.**2;			#bar
p3 = p2/10.**2;			#bar
p3 = p3*10.**6/10**5;			#bar
Tsup3 = 115.;			#degree C
ms = 1.8;			#Kg
mw = 0.16;			#Kg

# Calculations
x1 = ms/(ms+mw);			#dryness
hf2 = 742.6;			#KJ/Kg(from steam table)
hfg2 = 2029.5;			#KJ/Kg(from steam table)
hg3 = 2676;			#KJ/Kg(from steam table)
Ts3 = 100;			#degree C
Cp = 2;			#KJ/KgK
#hf2+x2*hfg2 = hg3+Cp*(Tsup3-Ts3);			#KJ/Kg
x2 = (hg3+Cp*(Tsup3-Ts3)-hf2)/hfg2;			#KJ/Kg
x = x1*x2;			#dryness

# Results
print "Dryness fraction of steam in mains : %.4f"%x

#Steam table is used to get some data.

Dryness fraction of steam in mains : 0.8885


## Example 6.31 Page No : 49¶

In [27]:

# Variables :
p1 = 1.5;			#MPa
p1 = p1*10**6/10**5;			#bar
p2 = p1;			#bar
p3 = 0.1;			#MPa
p3 = p3*10**6/10**5;			#bar
Tsup3 = 110;			#degree C
Vw = 0.15;			#litres
Vw = 0.15*10**-3;			#m**3 at 70 degree C
ms = 3.24;			#Kg
Vf = 0.001023;			#m**3/Kg
mw = Vw/Vf;			#Kg
x1 = ms/(ms+mw);			#dryness
hf2 = 844.7;			#KJ/Kg(from steam table)
hfg2 = 1945.2;			#KJ/Kg(from steam table)
hg3 = 2675;			#KJ/Kg(from steam table)
Ts3 = 99.63;			#degree C
Cp = 2;			#KJ/KgK

# Calculations
#hf2+x2*hfg2 = hg3+Cp*(Tsup3-Ts3);			#KJ/Kg
x2 = (hg3+Cp*(Tsup3-Ts3)-hf2)/hfg2;			#KJ/Kg
x = x1*x2;			#dryness

# Results
print "Quality of steam in pipe line(Dryness fraction) : %.4f"%x
#Steam table is used to get some data.

Quality of steam in pipe line(Dryness fraction) : 0.9104


## Example 6.32 Page No : 50¶

In [28]:

# Variables :
p1 = 1.5;			#MPa
p1 = p1*10**6/10**5;			#bar
p_gauge = 7;			#bar
p_at = 1;			#bar
p2 = p_gauge+p_at;			#bar
p3 = 1;			#bar
Tsup3 = 110;			#degree C
mw = 3.5;			#Kg
ms = 48;			#Kg
Cp = 2.1;			#KJ/KgK
x1 = ms/(ms+mw);			#dryness
hf2 = 720.9;			#KJ/Kg(from steam table)
hfg2 = 2059.3;			#KJ/Kg(from steam table)
hg3 = 2675.5;			#KJ/Kg(from steam table)
Ts3 = 99.63;			#degree C

# Calculations
#hf2+x2*hfg2 = hg3+Cp*(Tsup3-Ts3);			#KJ/Kg
x2 = (hg3+Cp*(Tsup3-Ts3)-hf2)/hfg2;			#KJ/Kg
x = x1*x2;			#dryness

# Results
print "Quality of steam in pipe line(Dryness fraction) : %.4f"%x
#Steam table is used to get some data.

Quality of steam in pipe line(Dryness fraction) : 0.8945


## Example 6.33 Page No : 54¶

In [30]:

# Variables :
p1 = 20;			#bar
Tsup3 = 360;			#degree C
pb = 0.08;			#bar
m = 1;			#Kg
hf1 = 173.9;			#KJ/Kg(from steam table)
h1 = hf1;			#KJ/Kg
wp = (p1-pb)/10;			#KJ/Kg
h2 = h1+wp;			#KJ/Kg
h3 = 3160.62;			#KJ/Kg(from steam table)
S3 = 6.994;			#KJ/Kg
Sf4 = 0.593;			#KJ/Kg(from steam table)
Sfg4 = 7.637;			#KJ/Kg(from steam table)
S3 = 6.994;			#KJ/Kg
#S3 = S4 = Sf4+x4*Sfg4
x4 = (S3-Sf4)/Sfg4;			#dryness
hf4 = 173.9;			#KJ/Kg(from steam table)
hfg4 = 2403.2;			#KJ/Kg(from steam table)

# Calculations and Results
h4 = hf4+x4*hfg4;			#KJ/Kg
Ws = h3-h4-wp;			#KJ/Kg
print "Net work done in KJ/Kg : %.3f"%Ws

EtaR = Ws/(h3-h2)*100;			#%
print "Rankine efficiency in  %% : %.2f"%EtaR

#Steam table is used to get some data.

Net work done in KJ/Kg : 970.471
Rankine efficiency in  % : 32.51


## Example 6.34 Page No : 56¶

In [31]:

# Variables :
p1 = 80;			#bar
Tsup3 = 350;			#degree C
pb = 712.5/760*1.01325;			#bar
mdot = 2;			#Kg/s
#mdot = 1;			#Kg
h3 = 2964.;			#KJ/Kg(Molliers diagram)
h4 = 2184.;			#KJ/Kg(Molliers diagram)

# Calculations and Results
WT = h3-h4;			#KJ/Kg
WTdot = mdot*WT;			#KW
print "Total turbine work in KW : ",WTdot

wp = (p1-pb)/10;			#KJ/Kg
hf1 = 411.35;			#KJ/Kg(from steam table)
h1 = hf1;			#KJ/Kg
h2 = h1+wp;			#KJ/Kg
qi = h3-h2;			#KJ/Kg
EtaR = (WT-wp)/qi*100;			#%
print "Rankine efficiency in  %% : %.2f"%EtaR

#Steam table is used to get some data.

Total turbine work in KW :  1560.0
Rankine efficiency in  % : 30.34


## Example 6.35 Page No : 57¶

In [32]:
# Variables :
p1 = 30.	    		#bar
Tsup3 = 350.			#degree C
pb = 0.5;			#bar
h1 = 340.5;			#KJ/Kg(from steam table, at 0.5 bar)
Vw = 0.001;			#m**3/Kg
wp = (p1-pb)*10**5*Vw/1000;			#KJ/Kg
h2 = h1+wp;			#KJ/Kg
h3 = 2854.8;			#KJ/Kg(from steam table, at 30 bar)
S3 = 6.286;			#KJ/KgK
S4 = S3;			#KJ/KgK
Sf4 = 1.091;			#KJ/KgK
Sfg4 = 6.503;			#KJ/KgK

# Calculations and Results
#S4 = Sf4+x4*Sfg4
x4 = (S4-Sf4)/Sfg4;			#dryness
print "Dryness fraction of steam entering in condenser : %.3f"%x4
hf4 = 340.5;			#KJ/Kg(from steam table)
hfg4 = 2305.4;			#KJ/Kg(from steam table)
h4 = hf4+x4*hfg4;			#KJ/Kg
q = h3-h2;			#
print "Heat supplied to stem in boiler in KJ : %.2f"%q

Ws = h3-h4-(h2-h1);			#KJ/Kg
print "Work done in KJ/Kg : %.2f"%Ws

steam_rate = 3600/Ws;			#KJ/KWh
print "Steam rate per in KJ/Kwh :  %.3f"%steam_rate

EtaR = Ws/(h3-h2)*100;			#%
print "Rankine efficiency in  %% : %.2f"%EtaR
#Steam table is used to get some data.

Dryness fraction of steam entering in condenser : 0.799
Heat supplied to stem in boiler in KJ : 2511.35
Work done in KJ/Kg : 669.65
Steam rate per in KJ/Kwh :  5.376
Rankine efficiency in  % : 26.67