Chapter 7: Two-Dimentional Idea Flow

Example 7.2, Page 235

In [1]:
from __future__ import division
import math


 #Initializing  the  variables  
x  =  120;                                        #Theta
r  =  1;
v0  =  0.5;
q  =  2;
theta =120;

 #Calculations
Vr = v0*r*math.cos(math.radians(theta))  +q/(2*math.pi)
Vth = -v0*math.sin(math.radians(theta))
V  =  (Vr**2+Vth**2)**0.5;
alpha  =  math.atan(abs(Vth/Vr));
bet  =  x-alpha*180/math.pi;


print "Fluid Velocity(m/s) :",round(V,3)
print "Beta (Degree)       :",round(bet,2)
print "Alpha (Degree)      :",round(alpha*180/math.pi,2)

Fluid Velocity(m/s) : 0.438
Beta (Degree)       : 38.96
Alpha (Degree)      : 81.04

Example 7.3, Page 239

In [1]:
from __future__ import division
import math
from scipy.optimize import fsolve
import sympy
from sympy import RootOf, I, Symbol
 #Initializing  the  variables  
q  =  10;
def  shi(x,y):
    Z  =  (q/2/math.pi)*(math.atan(y/(x-1))-math.atan(y/(x+1))) - 25*y;
    return Z
h  =  0.0000001;
Vinf  =  25;
x=Symbol('x')
 #Calculations
#f = lambda x : x**2 - 2/(5*math.pi) -1
result =  [RootOf(x**2- 2/(5*math.pi) -1,i) for i in (0,1)] 

root1=round(result[0],3)
root2=round(result[1],3)
l  =  abs(abs(root1)+abs(root2));
Ymax  =  0.047;
width  =  2*Ymax;
Vx  =  (shi(1-h,1)-shi(1-h,1-h))/h;           #  At  x=1  the  function  atan  is  not  defined  hence  taking  x  a  little  smaller.
Vy  =  -1*(shi(1-2*h,1)-shi(1-h,1))/h;        #  At  x=1  the  function  atan  is  not  defined  hence  taking  x  a  little  smaller.

V  =  (Vx**2+Vy**2)**0.5;
rho  =  Symbol('rho')
dP  =  rho/2*round((V**2  -  Vinf**2),2);                          #difference  in  pressure

print "Pressure Difference   (N/m2)  :",dP
print "Velocity              (m/s)   :",round(V,2)
print "Length of Rankine Body(m)     :",l
print "Width of Rankine Body (m)     :",width

Pressure Difference   (N/m2)  : 16.93*rho
Velocity              (m/s)   : 25.67
Length of Rankine Body(m)     : 2.124
Width of Rankine Body (m)     : 0.094

Example 7.4, Page 242

In [4]:
from __future__ import division
import math                                              #Example  7.4

 #Initializing  the  variables
a  =  0.02;
r  =  0.05;
V0  =  1;
x  =  135;                                                                #  Theta
def  shi(r,x):
    Z  =  V0*math.sin(math.radians(x))*(r-((a**2)/r));
    return Z
h  =  0.0001;

 #Calculations
Vr  =  57*(shi(r,x+h)-shi(r,x))/(r*h);
Vx  =  -1*(shi(r+h,x)-shi(r,x))/h;

print "Radial Velocity (m/s)             :",round(Vr,3)
print "Normal component of velocity (m/s):",round(Vx,3)

Radial Velocity (m/s)             : -0.591
Normal component of velocity (m/s): -0.82

Example 7.5, Page 246

In [5]:
from __future__ import division
import math


 #Initializing  the  variables
rho  =  1000;
r  =  2;
psi  =  2*math.log(r);

 #Calculations
y  =  psi/math.log(r);                                                  #  y  =  GammaC  /  2*pi
v  =  y/r;
dPbydr  =  rho*v**2/r;
print "Pressuer Gradient (N/m3 ) :",dPbydr

Pressuer Gradient (N/m3 ) : 500.0