Chapter 15:Compressible Flow

Example 15.1 Page No376

In [2]:
from __future__ import division

import math

#variable initialization

Mg=44                #molecular weight of carbondioxide

#solution

R=8314/Mg            #gas constant for carbondioxide

print "R=",int(round(R,1)),"N.m/(Kg.K)"

Mg=32                #molecular weight of oxygen

R=8314/Mg            #gas constant for oxygen

print "R=",int(math.ceil(round(R,1))),"N.m/(Kg.K)"
R= 189 N.m/(Kg.K)
R= 260 N.m/(Kg.K)

Example 15.2 Page No376

In [2]:
from __future__ import division

import math

#variable initialization

Mg=28.96            #molecular weight of air

k=1.4               #constant for air 

#solution

R=int(8314/Mg)      #in J/(kg.K)

Cp=(k/(k-1.0))*R

print "Cp=",Cp,"J/(Kg.K)"

Cv=R/(k-1)         #in J/(kg.K)

print "Cv=",Cv,"J/(Kg.K)"

#1 Kcal = 4187 J

print "In heat units"

Cp=Cp/4187

print "Cp=",round(Cp,3),"Kcal/(Kg.K)" 

Cv=Cv/4187

print "Cv=",round(Cv,3),"Kcal/(Kg.K)"
Cp= 1004.5 J/(Kg.K)
Cv= 717.5 J/(Kg.K)
In heat units
Cp= 0.24 Kcal/(Kg.K)
Cv= 0.171 Kcal/(Kg.K)

Example 15.3 Page No376

In [3]:
import math

#variable initialization

T1=15                       #temperature initially in degree

T2=65                       #increased temperature in degree

Cv=670                      #in j/(kg.k)

E=1000                      #enthalpy

Cp=858                      #in j/(kg.k)

#Calculation

T1=273+T1                   #temperature in kelvin

T2=273+T2

m=E/9.81                    #Mass of 1000N of co2

del_u=Cv*(T2-T1)

Tc=m*del_u                  #Total change in internal energy

print "Total change in internal energy=",int(Tc/1000),"kJ"

del_h=Cp*(T2-T1)

Te=m*del_h

print "Total change in enthalpy=",int(Te/1000),"kJ"
Total change in internal energy= 3414 kJ
Total change in enthalpy= 4373 kJ

Example 15.5 Page No377

In [4]:
import math

#variable initialization

R=260                       #in j/(kg.k)

k=1.4                       #given value

T1=27                       #temperature initially in degree

T2=85                       #increased temperature in degree

p1=150                      #Pressure in kPa

p2=450                      #pressure 2 in kPa

m=7                         #kg of oxygen 

#Calculation

Cv=R/(k-1)

T1=T1+273                                         #Temperature in kelvin

T2=T2+273

S=Cv*math.log((((T2/T1)**k)*((p1/p2)**(k-1))))    #Change in entropy per kg

T=m*S

print "Total change in entropy=",round(T,1),"J/K"
Total change in entropy= -873.6 J/K

Example 15.7 Page No378

In [5]:
import math

#variable initialization

k=1.40              #constant for gases

R=260               #gas constant in J/(Kg.K)

T=25                #temperature in degree C

#solution

T=273 +T            #converting into K

C=math.sqrt(k*R*T)  #Speed of sound

print "C=",round(C,1),"m/s"
C= 329.4 m/s

Example 15.8 Page No378

In [6]:
import math

#variable initialization

M=1.5                    #Mach number

p=89.89                  #Pressure in kPa

rho=1.112                #density in kg/m^3

k=1.4                    #constant for gases

#solution

#At 1000 m altitude,

C=math.sqrt((k*(p*1000))/rho)

V=C*M                   #Using Mach number

V=(V*3600)/1000         #Converting V from m/s to Km/h

print "V=",int(math.ceil(round(V,1))),"Km/h"

#At 10,000 m altitude

p=26.42                #Pressure in kPa

rho=0.4125             #density in kg/m^3

C=math.sqrt((k*(p*1000))/rho)

V=C*M

V=(V*3600)/1000       #Converting V from m/s to Km/h

print "V=",int(V),"Km/h"
V= 1817 Km/h
V= 1617 Km/h

Example 15.13 Page No380

In [7]:
import math

#variable initialization

k=1.28                      #given value

R=188                       #in j/(kg.k)

T=30                        #Temperature in degree

V1=150                      #velocity in m/s

P1=500                      #pressure in kPa

#Calculation

T=T+273                     #Converting into kelvin

C=math.sqrt(k*R*T)          #Speed of sound in CO2

M1=V1/C                     #Mach number

T0=T*((1+((k-1)/2)*(M1**2)))

print "T0=",int(T0-273),"degree C"   #In degree celsius

P0=P1*((1+((k-1)/2)*(M1**2)))**(k/(k-1))

print "P0=",round(P0,2),"kPa(abs)"
T0= 43 degree C
P0= 606.65 kPa(abs)

Example 15.15 Page No381

In [8]:
import math

#variable initialization

T0=30                      #temperatuer in degree

p1=50                      #Pressure in kPa

p0=95                      #pressure 2 in kPa

k=1.4                      #given value

R=287                      #in j/(kg.k)

#Calculation

T0=T0+273                        #converting into kelvin

T1=round(T0*(p1/p0)**((k-1)/k),1)#For isentropic flow with subscript zero denoting stagnation values

V1=((2*k*R)/(k-1.0))*(T0-T1)

print "(i)V1=",round((V1**(1/2)),1),"m/s"

rho1=round((p0*1000)/(R*T0),3)   #When compressibility effects are ignored

V1=(2*(p0-p1)*1000)/rho1

print "(ii)V1=",round(math.sqrt(V1),1),"m/s"
 
(i)V1= 319.5 m/s
(ii)V1= 287.1 m/s

Example 15.16 Page No381

In [9]:
import math

#variable initialization

To=35              #temperature in degree C

R=287              #gas constant in (J/Kg.K)

po=250             #pressure in kPa

k=1.4              #constant for gases

V1=200             #velocity in m/s

#solution

To=273+To          #converting into K

Cp=(k*R)/(k-1)

T1=int(To-((V1**2)/(2*Cp)))

#The Mach number M1,at the exit is,

M1=math.sqrt(((To/T1)-1)/0.2)

print "M1=",round(M1,3)
M1= 0.589

Example 15.21 Page No384

In [10]:
import math

#variable initialization

k=1.32                         #given value 

M2=0.40                        #Mach number of downstream

#Calculation

#by using formula M2**2=(2+(k-1)M1**2)/(2*K*M!**2-(k-1))

M1_s=(((M2**2)*2*k)-(k-1))

M1=-((-((M2**2)*(k-1))-2.0)/M1_s)

print "M1=",round(M1**(1/2),3)
M1= 4.476