Chapter 13: Compressible Flow around a Body

Example 13.1, Page 444

from __future__ import division
import math


 #Initializing  the  variables
rho0  =  1.8;
R  =  287;
T  =  75+273;                                                          #  Temperature  in  kelvin  
gma  =  1.4;  
Ma  =  0.7;

 #Calculations
P0  =  rho0*R*T;
c  =  (gma*R*T)**0.5;
V0  =  Ma*c;
Pt  =  (P0**((gma-1)/gma)  +  rho0*((gma-1)/gma)*(V0**2/(2*P0**(1/gma))))**(gma/(gma-1));
rhoT  =    rho0*(Pt/P0)**(1/gma);
Tt  =    Pt/(R*rhoT)-273;

print "Staganation Pressure (kN/m2 ) :",round(Pt/1000,1)
print "Temperature (Degree Celcius)  :",round(Tt,1)
print "Density of airstream (kg/m3)  :",round(rhoT,3)

Staganation Pressure (kN/m2 ) : 249.4
Temperature (Degree Celcius)  : 109.1
Density of airstream (kg/m3)  : 2.274

Example 13.2, Page 454

from __future__ import division
import math


 #Initializing  the  variables
R  =  287;
T  =  28+273;
gma  =  1.4;
P  =  1.02*10**5;
rhoHg  =  13.6*10**3;
g  =  9.81;

 #Calculations
 #Case(a)
U0  =  50;
c  =  (gma*R*T)**0.5;
Ma  =  U0/c;
rho  =  P/(R*T);
DelP  =  0.5*rho*U0**2;                                        #Pt-P
ha  =  DelP/(rhoHg*g);

 #Case(b)
U0  =  250;
Ma  =  U0/c;
Pt  =  P*(1+(gma-1)*Ma**2/2)**(gma/(gma-1));    
DelP  =  Pt-P
hb  =  DelP/(rhoHg*g);

 #Case  (c)
U0  =  420;
Ma1  =U0/c;
P2  =  P*((2*gma/(gma+1))*Ma1**2  -  ((gma-1)/(gma+1)));
N  =  Ma1**2  +2/(gma-1);                                      #  Numerator
D  =  2*gma*Ma1**2/(gma-1)-1;
Ma2  =  (N/D)**0.5;
Pt2  =  P2*(1+(gma-1)*Ma2**2/2)**(gma/(gma-1));
hc  =  (Pt2-P2)/(rhoHg*g)  ;    

print "Difference in height of mercury column in case (a) in mm :",round(ha*1000,2)
print "Difference in height of mercury column in case (b) in mm :",round(hb*1000,1)
print "Difference in height of mercury column in case (c) in mm :",round(hc*1000,0)

Difference in height of mercury column in case (a) in mm : 11.06
Difference in height of mercury column in case (b) in mm : 314.2
Difference in height of mercury column in case (c) in mm : 684.0