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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 7: Two-Dimentional Idea Flow"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.2, Page 235"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables  \n",
      "x  =  120;                                        #Theta\n",
      "r  =  1;\n",
      "v0  =  0.5;\n",
      "q  =  2;\n",
      "theta =120;\n",
      "\n",
      " #Calculations\n",
      "Vr = v0*r*math.cos(math.radians(theta))  +q/(2*math.pi)\n",
      "Vth = -v0*math.sin(math.radians(theta))\n",
      "V  =  (Vr**2+Vth**2)**0.5;\n",
      "alpha  =  math.atan(abs(Vth/Vr));\n",
      "bet  =  x-alpha*180/math.pi;\n",
      "\n",
      "\n",
      "print \"Fluid Velocity(m/s) :\",round(V,3)\n",
      "print \"Beta (Degree)       :\",round(bet,2)\n",
      "print \"Alpha (Degree)      :\",round(alpha*180/math.pi,2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Fluid Velocity(m/s) : 0.438\n",
        "Beta (Degree)       : 38.96\n",
        "Alpha (Degree)      : 81.04\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.3, Page 239"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "from scipy.optimize import fsolve\n",
      "import sympy\n",
      "from sympy import RootOf, I, Symbol\n",
      " #Initializing  the  variables  \n",
      "q  =  10;\n",
      "def  shi(x,y):\n",
      "    Z  =  (q/2/math.pi)*(math.atan(y/(x-1))-math.atan(y/(x+1))) - 25*y;\n",
      "    return Z\n",
      "h  =  0.0000001;\n",
      "Vinf  =  25;\n",
      "x=Symbol('x')\n",
      " #Calculations\n",
      "#f = lambda x : x**2 - 2/(5*math.pi) -1\n",
      "result =  [RootOf(x**2- 2/(5*math.pi) -1,i) for i in (0,1)] \n",
      "\n",
      "root1=round(result[0],3)\n",
      "root2=round(result[1],3)\n",
      "l  =  abs(abs(root1)+abs(root2));\n",
      "Ymax  =  0.047;\n",
      "width  =  2*Ymax;\n",
      "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.\n",
      "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.\n",
      "\n",
      "V  =  (Vx**2+Vy**2)**0.5;\n",
      "rho  =  Symbol('rho')\n",
      "dP  =  rho/2*round((V**2  -  Vinf**2),2);                          #difference  in  pressure\n",
      "\n",
      "print \"Pressure Difference   (N/m2)  :\",dP\n",
      "print \"Velocity              (m/s)   :\",round(V,2)\n",
      "print \"Length of Rankine Body(m)     :\",l\n",
      "print \"Width of Rankine Body (m)     :\",width"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Pressure Difference   (N/m2)  : 16.93*rho\n",
        "Velocity              (m/s)   : 25.67\n",
        "Length of Rankine Body(m)     : 2.124\n",
        "Width of Rankine Body (m)     : 0.094\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.4, Page 242"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math                                              #Example  7.4\n",
      "\n",
      " #Initializing  the  variables\n",
      "a  =  0.02;\n",
      "r  =  0.05;\n",
      "V0  =  1;\n",
      "x  =  135;                                                                #  Theta\n",
      "def  shi(r,x):\n",
      "    Z  =  V0*math.sin(math.radians(x))*(r-((a**2)/r));\n",
      "    return Z\n",
      "h  =  0.0001;\n",
      "\n",
      " #Calculations\n",
      "Vr  =  57*(shi(r,x+h)-shi(r,x))/(r*h);\n",
      "Vx  =  -1*(shi(r+h,x)-shi(r,x))/h;\n",
      "\n",
      "print \"Radial Velocity (m/s)             :\",round(Vr,3)\n",
      "print \"Normal component of velocity (m/s):\",round(Vx,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Radial Velocity (m/s)             : -0.591\n",
        "Normal component of velocity (m/s): -0.82\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.5, Page 246"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "rho  =  1000;\n",
      "r  =  2;\n",
      "psi  =  2*math.log(r);\n",
      "\n",
      " #Calculations\n",
      "y  =  psi/math.log(r);                                                  #  y  =  GammaC  /  2*pi\n",
      "v  =  y/r;\n",
      "dPbydr  =  rho*v**2/r;\n",
      "print \"Pressuer Gradient (N/m3 ) :\",dPbydr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Pressuer Gradient (N/m3 ) : 500.0\n"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}