Ch-4 : Vapour Power Cycles

Ex - 4.1 : Pg - 177

In [1]:
#initialisation of variables
t1=523.3 #temparature under p1=40 bar in k
t2=314.5 #temparature under p2=0.80 bar in k
s4=2.797 #entropy under p1=40 bar 
s1=6.070 #entropy under p1=40 bar
sf3=0.593 #entropy under p2=0.08 bar
sfg3=7.634 #entropy under p2=0.08 bar
h4=1087 #kj/kg
h1=2801 #kj/kg
hf3=174 #kj/kg under p2=0.08bar
hfg3=2402 #kj/kg under p2=0.08bar
#CALCULATIONS
eff=(t1-t2)/t1
x3=(s4-sf3)/sfg3
x2=(s1-sf3)/sfg3
h3=hf3+(x3*hfg3)
h2=hf3+(x2*hfg3)
wt=h1-h2
cw=h4-h3
wr=(wt-cw)/wt
#RESULTS
print '(a)efficiency of carnot cycle is %0.3f'%(eff)
print '\n(b)quality is %0.4f'%(x3)
print '\n(c)gross work of expansion is %0.1f'%(wt)
print '\n(d)work ratio is %0.3f'%(wr)

(a)efficiency of carnot cycle is 0.399

(b)quality is 0.2887

(c)gross work of expansion is 903.7

(d)work ratio is 0.757

Ex - 4.2 : Pg - 179

In [2]:
#initialisation of variables
v=0.1008*10**-2
p1=40 #pressure in bar
p2=0.08 #pressure in bar
wt=903.8 #kj/kg
wp=4.02 #kj/kg
h1=2801 #kj/kg
h3=174 #kj/kg
#CALCULATIONS
pw=v*(p1-p2)
wn=wt-wp
qs=h1-(h3+wp)
reff=wn/qs
wr=wn/wt
#RESULTS
print '\nrankine efficiency and work ratio is %0.3f and %0.3f'%(reff,wr)

rankine efficiency and work ratio is 0.343 and 0.996

Ex - 4.3 : Pg - 180

In [3]:
#initialisation of  variables
h3=174 #kj/kg
h4=178.02 #kj/kg
ieff=0.50 #isentropic efficiency of compression
wt=903.8 #kj/kg
feff=0.75 #furnace efficiency
ieeff=0.85#isentropic expansion efficiency
wp=4.02 #kj/kg
h1=2801 #kj/kg
#CALCULATIONS
hx=((h4-h3)/0.5)+174
wr=wp/ieff
atu=ieeff*wt
hs=h1-hx
nwo=atu-wr
eff=nwo/hs
oeff=eff*feff
wrt=nwo/atu
ssc=3600/nwo
hr=3600/oeff
#RESULTS
print 'steam and heat rates are %0.2fkg/kwh and %0.1fkj/kwh'%(ssc,hr)

steam and heat rates are 4.74kg/kwh and 16536.7kj/kwh

Ex - 4.4 : Pg - 183

In [4]:
#initialisation of variables
h1=3221.6 #kj/kg
s1=7.399 #kj/kgk
sf2=0.521 #kj/kgk
sfg2=7.808 #kj/kgk
hf2=152 #kj/kg
hfg2=2415 #kj/kg
t1=653 #temp in k
t2=309.2 #temp in k
v=0.1006*10**-2
p1=10 #pressure in bar
p2=0.06 #pressure in bar
h3=152 #kj/kg
x=110
y=639.7
z=610
a=2015
#CALCULATIONS
x2=(s1-sf2)/sfg2
h2=hf2+(x2*hfg2)
wo=h1-h2
hs=h1-h3
theff=wo/hs
sr1=3600/wo
ceff=(t1-t2)/t1
wp=v*(p1-p2)
h4=h3+wp
reff=(x+y)/(z+a)
sr2=3600/(x+y)
hr=3600/reff
print 'steam rate and carnot efficiency are %0.2fkg/kwh and %00.3f'%(sr1,ceff)
print '\nsteam rate and heat rate are %0.2fkg/kwh and %0.f kJ/kWh'%(sr2,hr)

steam rate and carnot efficiency are 3.82kg/kwh and 0.526

steam rate and heat rate are 4.80kg/kwh and 12605 kJ/kWh

Ex - 4.5 : Pg - 188

In [5]:
#initialisation of variables
h1=3157 #kj/kg
h2=2725 #kj/kg
h3=3299 #kj/kg
h4=2257.9 #kj/kg
h5=1940.3 #kj/kg
h6=152 #kj/kg
x4=0.872
x5=0.7405
v=0.1006*10**-2 #volume
p1=100 #pressure in bar
p2=0.06 #pressure in bar
#CALCULATIONS
wp=v*(p1-p2)*100
h7=h6+wp
wt1=h1-h5
wn1=wt1-wp
qs1=h1-h7
wr1=wn1/wt1
reff=wn1/qs1
#reheat cycle
wt2=(h1-h2)+(h3-h4)
wn2=wt2-wp
wr2=wn2/wt2
qs2=h1-h7+h3-h2
teff=wn2/qs2
pd=wn2/3600
pdi=(pd-0.3352)/0.3352
df=1-pdi
#RESULTS
print 'work ratio and rakine efficiency of rankine cycle is %0.4f and %0.3f'%(wr1,reff)
print 'dryness fraction of steam is 0.872'
print '\nheat supplied is %0.2f'%(qs1)
print '\npower developed is %0.2f'%(pd)
print '\npower developed per kg of steam is %0.4f'%(pdi)

work ratio and rakine efficiency of rankine cycle is 0.9917 and 0.403
dryness fraction of steam is 0.872

heat supplied is 2994.95

power developed is 0.41

power developed per kg of steam is 0.2124

Ex - 4.6 : Pg - 195

In [6]:
#initialisation of variables
h1=2979 #kj/kg
h2=2504.3 #kj/kg
h3=1987.4 #kj/kg
h4=152 #kj/kg
h6=561 #kj/kg
#CALCULATIONS
m=(h6-h4)/(h2-h4)
wo=(h1-h2)+(1-m)*(h2-h3)
qs=h1-h6
teff=wo/qs
ssc=3600/wo
#RESULTS
print 'work output is %0.1f kJ/kg'%(wo)
print '\nheat supplied is %0.f kJ/kg'%(qs)
print '\nthermal efficiency is %0.3f'%(teff)
print '\nspecific steam consumption is %0.2fkg/kwh'%(ssc)

work output is 901.7 kJ/kg

heat supplied is 2418 kJ/kg

thermal efficiency is 0.373

specific steam consumption is 3.99kg/kwh

Ex - 4.7 : Pg - 196

In [7]:
#initialisation of variables
h1=3222.5 #kj/kg
h2=3127.5 #kj/kg
h3=2692.5 #kj/kg
h4=2406.7 #kj/kg
h5=360 #kj/kg
h6=360 #kj/kg
h7=584 #kj/kg
h8=962 #kj/kg
#CALCULATIONS
m1=(h8-h7)/(h2-h7)
m2=((1-m1)*(h7-h5))/(h3-h5)
wo=(h1-h2)+(1-m1)*(h2-h3)+(1-m1-m2)*(h3-h4)
qs=h1-h8
teff=wo/qs
sr=3600/wo
#RESULTS
print 'work output is %0.1f kJ/kg'%(wo)
print '\nheat supplied is %0.1f kJ/kg'%(qs)
print '\nthermal efficiency is %0.4f'%(teff)
print '\nsteam rate is %0.2f kg/kwh'%(sr)

work output is 685.3 kJ/kg

heat supplied is 2260.5 kJ/kg

thermal efficiency is 0.3032

steam rate is 5.25 kg/kwh

Ex - 4.8 : Pg - 197

In [8]:
from __future__ import division
#initialisation of variables
h1=2990 #kj/kg
h2=2710 #kj/kg
h3=2325 #kj/kg
h4=152 #kj/kg
h5=152 #kj/kg
h7=505 #kj/kg
wo=612 #kj/kg
qs=2485 #kj/kg
#CALCULATIONS
m=(h7-h4)/(h2-h4)
mph=m*30000
ip=((h1-h2)+(1-m)*(h2-h3))*(30000/3600)
teff=wo/qs
#when there is no feeding
eff=(h1-h3)/(h1-h4)
sc=(3600/(h1-h3))*ip
#RESULTS
print 'internal powers is %0.f kW'%(ip)
print '\nthermal efficiency when feeding is there is %0.4f'%(teff)
print '\nwhen there is no feed heating,thermal efficiency is %0.4f'%(eff)
print '\nsteam consumption is %0.f kg/h'%(sc)

internal powers is 5099 kW

thermal efficiency when feeding is there is 0.2463

when there is no feed heating,thermal efficiency is 0.2343

steam consumption is 27603 kg/h

Ex - 4.10 : Pg - 202

In [9]:
#initialisation of variables
#for the mercury cycle
ha=360.025 #kj/kg
sa=0.50625 #kj/kgk
sfb=0.0961 #kj/kgk
sfgb=0.5334 #kj/kgk
hfb=38.05 #kj/kg
hfgb=294.02 #kj/kg
#for the steam cycle
h5=2801 #kj/kg
h3=163 #kj/kg
hb=264.2 #kj/kg
h1=2963 #kj/kg
s1=6.364 #kj/kgk
sf2=0.559 #kj/kgk
sfg2=7.715 #kj/kgk
qs=3916.2 #kj/kg
hf2=163 #kj/kg
hfg2=2409 #kj/kg
#CALCULATIONS
xb=(sa-sfb)/sfgb
hb=hfb+(xb*hfgb)
m1=(h5-h3)/(hb-hfb)
x2=(s1-sf2)/sfg2
h2=hf2+(x2*hfg2)
wn=m1*(ha-hb)+(h1-h2)
teff1=wn/qs
hx=ha-(0.8*(ha-hb))
hy=h1-(0.8*(h1-h2))
m2=(h5-h3)/(hx-hfb)
wo=m2*(ha-hx)+(h1-hy)
qs=m2*(ha-hfb)+(h1-h5)
teff2=wo/qs
#RESULTS
print 'thermal efficiency of steam cycle is %0.3f'%(teff1)
print '\nwork output of plant is %0.1f kJ/kg'%(wo)
print '\nheat supplied is %0.1f kJ/kg'%(qs)
print '\nthermal efficiency of the plant is %0.4f'%(teff2)

thermal efficiency of steam cycle is 0.538

work output of plant is 1615.0 kJ/kg

heat supplied is 3625.1 kJ/kg

thermal efficiency of the plant is 0.4455

Ex - 4.11 : Pg - 205

In [10]:
#initialisation of variables
ha=360.025 #kj/kg
hfb=38.05 #kj/kg
hb=264.2 #kj/kg
h1=2963 #kj/kg
h2=1974.6 #kj/kg
h3=163 #kj/kg
h4=1087 #kj/kg
h=1714 #kj/kg
#CALCULATIONS
m=h/(hb-hfb)
wo=7.58*(ha-hb)+(h1-h2)
qs=7.58*(ha-hfb)+(h4-h3)+(h1-h)
teff=(wo/qs)
#RESULTS
print 'thermal efficiency is %0.1f %%'%(teff*100.0)

thermal efficiency is 37.2 %

Ex - 4.12 : Pg - 205

In [11]:
#initialisation of variables
ha=359.11 #under 10 bar pressure in kj/kg
sa=0.5089 #under 10 bar pressure in kj/kgk
sfb=0.0870 #under 0.08 bar pressure in kj/kgk
sfgb=0.57 #under 0.08 bar pressure in kj/kgk
hfb=33.21 #under 0.08 bar pressure in kj/kg
hfgb=294.7 #under 0.08 bar pressure in kj/kg
h=1840.5 #kj/kg
h1=3350 #under 25 bar pressure and 723 k in kj/kg
s1=7.183 #under 25 bar pressure and 723 k in kj/kgk
sf2=0.476 #under 25 bar pressure and 723 k in kj/kgk
sfg2=7.918 #under 25 bar pressure and 723 k in kj/kgk
hf2=138 #under 25 bar pressure and 723 ki n kj/kg
hfg2=2423 #under 25 bar pressure and 723 k in kj/kg
h5=964 #kj/kg
#CALCULATIONS
xb=(sa-sfb)/(sfgb)
hb=hfb+(xb*hfgb)
m=h/(hb-hfb)
x2=(s1-sf2)/sfg2
h2=hf2+(x2*hfg2)
wo=8.47*(ha-hb)+(h1-h2)
qs=8.47*(ha-hfb)+(h5-138)+(h1-2802.5)
teff=(wo/qs)*100
#RESULTS
print 'work output is %0.1f kJ/kg of steam'%(wo) #textbook ans slightly varies
print '\nheat supplied to the plant is %0.1f kJ/kg of steam'%(qs)
print '\nthermal efficiency is %0.1f %%'%(teff)

work output is 2072.4 kJ/kg of steam

heat supplied to the plant is 4133.9 kJ/kg of steam

thermal efficiency is 50.1 %