Chapter 9: GAS POWER SYSTEMS

Example 9.01, page: 228

In [1]:
from __future__ import division
import math

# Initialization  of  Variable
r = 8 #compression ratio
T1 = 540 #degR
V1 = 0.02 #ft3
T3 = 3600 #degR
P1 = 1 #atm
R = 1545/28.97 #ft*lbf/lb-degR

#calculations:
#from Table T-9E
u1 = 92.04 #Btu/lb
vr1 = 144.32
#from isentropic process 1-2
vr2 = vr1/r
#from Table T-9E
T2 = 1212 #degR
u2 = 211.3 #Btu/lb
#Pressure
P2 = P1*T2*r/T1
P3 = P2*T3/T2
#from Table T-9E
u3 = 721.44 #Btu/lb
vr3 = 0.6449
#from isentropic process 3-4
vr4 = vr3*r
#from Table T-9E
T4 = 1878 #degR
u4 = 342.2 #Btu/lb
#pressure
P4 = P1*T4/T1
#Thermal Eff
n = 1 - (u4 - u1)/(u3 - u2)
#net work per cycle
m = P1*14.696*144*V1/(R*T1)
Wcycle = m*((u3-u4)-(u2-u1))
#mean effective pressure
mep = Wcycle/(V1*(1 - 1/r))*778/(144*14.696)

#Results
print  "a)pressure and temperature at 2 are", round(P2,2),"atm and", T2,"degR"
print  "  pressure and temperature at 3 are", round(P3,2),"atm and", T3,"degR"
print  "  pressure and temperature at 4 are", round(P4,2),"atm and", T4,"degR"
print  "b)thermal  efficiency  is", round(n*100,0),"%"
print  "c)mean  effective  pressure is",round(mep,2),"atm"

a)pressure and temperature at 2 are 17.96 atm and 1212 degR
  pressure and temperature at 3 are 53.33 atm and 3600 degR
  pressure and temperature at 4 are 3.48 atm and 1878 degR
b)thermal  efficiency  is 51.0 %
c)mean  effective  pressure is 8.03 atm

Example 9.02, page: 232

In [2]:
from __future__ import division
import math

# Initialization  of  Variable
r = 18 #compression ratio
T1 = 300 #K
rc = 2 #cut-off ratio
P1 = 0.1 #MPa
R = 8314/28.97 #J/kg-K

#calculations:
#from Table T-9
u1 = 214.07 #kJ/kg
vr1 = 621.2
#from isentropic process 1-2
vr2 = vr1/r
#from Table T-9
T2 = 898.3 #K
h2 = 930.98 #kJ/kg
#Pressure
P2 = P1*T2*r/T1
P3 = P2
#temp
T3 = rc*T2
#from Table T-9
h3 = 1999.1 #kJ/kg
vr3 = 0.6449
#from isentropic process 3-4
vr4 = vr3*r/rc
#from Table T-9
T4 = 887.7 #degR
u4 = 664.3 #kJ/kg
#pressure
P4 = P1*T4/T1
#Thermal Eff
n = 1 - (u4 - u1)/(h3 - h2)
#net work per cycle per unit mass
Wmcycle = (h3-h2)-(u4-u1)
#specific vol at 1
v1 = R*T1/(P1*1000000)
#mean effective pressure
mep = Wmcycle/(v1*(1 - 1/r)*1000)

#Results
print  "a)pressure and temperature at 2 are", round(P2,2),"MPa and", T2,"degR"
print  "  pressure and temperature at 3 are", round(P3,2),"MPa and", T3,"degR"
print  "  pressure and temperature at 4 are", round(P4,2),"MPa and", T4,"degR"
print  "b)thermal  efficiency  is", round(n*100,1),"%"
print  "c)mean  effective  pressure is",round(mep,2),"MPa"

a)pressure and temperature at 2 are 5.39 MPa and 898.3 degR
  pressure and temperature at 3 are 5.39 MPa and 1796.6 degR
  pressure and temperature at 4 are 0.3 MPa and 887.7 degR
b)thermal  efficiency  is 57.8 %
c)mean  effective  pressure is 0.76 MPa

Example 9.03, page: 238

In [3]:
from __future__ import division
import math

# Initialization  of  Variable
r = 10 #compression ratio
T1 = 300 #K
AV1 = 5 #m3/s
P1 = 100 #kPa
R = 8314/28.97 #J/kg-K

#calculations:
#from Table T-9
h1 = 300.19 #kJ/kg
Pr1 = 1.386
#reduced pressure at 2
Pr2 = r*Pr1
#from Table T-9
h2 = 579.9 #kJ/kg
T3 = 1400 #K
h3 = 1515.4 #kJ/kg
Pr3 = 450.5
#reduced pressure at 4
Pr4 = Pr3/r
#from Table T-9
h4 = 808.5 #kJ/kg

#Thermal Eff
n = 1 - (h4 - h1)/(h3 - h2)
#back work ratio
bwr = (h2 - h1)/(h3-h4)
#net wpower developed
mdot = AV1*P1*1000/(R*T1)
Wmcycledot = mdot*((h3-h4)-(h2-h1))

#Results
print  "a)thermal  efficiency  is", round(n*100,1),"%"
print  "b)back work ratio is", round(bwr*100,1),"%"
print  "c)mean  effective  pressure is",round(Wmcycledot,0),"kW"

a)thermal  efficiency  is 45.7 %
b)back work ratio is 39.6 %
c)mean  effective  pressure is 2481.0 kW

Example 9.04, page: 242

In [4]:
from __future__ import division
import math

# Initialization  of  Variable
r = 10 #compression ratio
T1 = 300 #K
AV1 = 5 #m3/s
P1 = 100 #kPa
R = 8314/28.97 #J/kg-K
nt = 0.8
nc = nt

#calculations:
#from Table T-9
h1 = 300.19 #kJ/kg
Pr1 = 1.386
#reduced pressure at 2
Pr2 = r*Pr1
#from Table T-9
h2 = 579.9 #kJ/kg
T3 = 1400 #K
h3 = 1515.4 #kJ/kg
Pr3 = 450.5
#reduced pressure at 4
Pr4 = Pr3/r
#from Table T-9
h4 = 808.5 #kJ/kg
#turbine work per unit mass
Wtmdot = nt*(h3-h4)
#Compressor work per unit mass
Wcmdot = (h2 - h1)/nc
#new enthalpy at 2
h2 = h1 + Wcmdot
#heat transfer to the working fluid per unit of mass flow
Qinmdot = h3 - h2
#Thermal Eff
n = (Wtmdot - Wcmdot)/Qinmdot
#back work ratio
bwr = Wcmdot/Wtmdot
#net wpower developed
mdot = AV1*P1*1000/(R*T1)
Wmcycledot = mdot*(Wtmdot - Wcmdot)

#Results
print  "a)thermal  efficiency  is", round(n*100,1),"%"
print  "b)back work ratio is", round(bwr*100,1),"%"
print  "c)mean  effective  pressure is",round(Wmcycledot,0),"kW"

a)thermal  efficiency  is 24.9 %
b)back work ratio is 61.8 %
c)mean  effective  pressure is 1254.0 kW

Example 9.05, page: 245

In [5]:
from __future__ import division
import math

# Initialization  of  Variable
nreg = 0.8

#calculations:
#from Example 9.3
h1 = 300.19 #kJ/kg
h2 = 579.9 #kJ/kg
h3 = 1515.4 #kJ/kg
h4 = 808.5 #kJ/kg

#specific enthalpy hx
hx = nreg*(h4 - h2) + h2

#Thermal Eff
n = ((h3 - h4) - (h2 - h1))/(h3 - hx)

#Results
print  "a)thermal  efficiency  is", round(n*100,1),"%"

a)thermal  efficiency  is 56.8 %

Example 9.06, page: 247

In [6]:
from __future__ import division
import math

# Initialization  of  Variable
Pa = 11.8 #lbf/in2
Ta = 430 #degR
Va = 620 #mi/hr
V1 = 0
P2P1 = 8 #P2/P1
T3 = 2150 #degR
P5 = 11.8 #lbf/in2

#Calculations:
#from Table T-9E
ha = 102.7 #Btu/lb
h1 = ha + (Va**2)/(2*32.2*778)
#
Pr1 = 1.051
Pra = 0.6268
P1 = Pr1*Pa/Pra
#
P2 = P2P1*P1
#
Pr2 = Pr1*P2P1
h2 = 216.2 #Btu/lb
h3 = 546.54 #Btu/lb
P3=P2
h4 = h3 + h1 - h2
#
Pr4 = 113.8
Pr3 = 233.5
P4 = P3*Pr4/Pr3
#
P5 = Pr4*P5/P4
#
h5 = 265.8 #Btu/lb
V5 = (2*(h4 - h5)*32.2*778)**0.5

#Results
print  "Pressure  at 1 is", round(P1,2),"lbf/in2"
print  "Pressure  at 2 is", round(P2,1),"lbf/in2"
print  "Pressure  at 4 is", round(P4,1),"lbf/in2"
print  "velocity  at nozzle exit is", round(V5,0),"ft/s"
#answer wrong in book

Pressure  at 1 is 19.79 lbf/in2
Pressure  at 2 is 158.3 lbf/in2
Pressure  at 4 is 77.1 lbf/in2
velocity  at nozzle exit is 2960.0 ft/s