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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "CHAPTER12:LINEARIZED SUPERSONIC FLOW"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E01 : Pg 395"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "import math \n",
      "from math import pi,sqrt\n",
      "alpha = 5*pi/180;                    # angle of attack\n",
      "M_inf = 3;                            # freestream mach number\n",
      "\n",
      "# from eq.(12.23)\n",
      "c_l = 4*alpha/sqrt(M_inf**2 - 1);\n",
      "\n",
      "# from eq.(12.24)\n",
      "c_d = 4*alpha**2/sqrt(M_inf**2 - 1);\n",
      "\n",
      "print\"The cl and cd according to the linearized theory are:cl =\", round(c_l,2)\n",
      "print\"The cl and cd according to the linearized theory are:cd =\",round(c_d,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The cl and cd according to the linearized theory are:cl = 0.12\n",
        "The cl and cd according to the linearized theory are:cd = 0.01\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E02 : Pg 395"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "import math \n",
      "from math import sqrt,pi\n",
      "M_inf = 2.;                       # freestream mach number\n",
      "rho_inf = 0.3648;                # freestream density at 11 km altitude\n",
      "T_inf = 216.78;                  # freestream temperature at 11 km altitude\n",
      "gam = 1.4;                       # ratio of specific heats\n",
      "R = 287.;                         # specific gas constant\n",
      "m = 9400.;                        # mass of the aircraft\n",
      "g = 9.8;                         # acceleratio due to gravity\n",
      "W = m*g;                         # weight of the aircraft\n",
      "S = 18.21;                       # wing planform area\n",
      "# thus\n",
      "a_inf = sqrt(gam*R*T_inf);\n",
      "V_inf = M_inf*a_inf;\n",
      "q_inf = 1./2.*rho_inf*V_inf**2.;\n",
      "\n",
      "# thus the aircraft lift coefficient is given as\n",
      "C_l = W/q_inf/S;\n",
      "\n",
      "alpha = 180./pi*C_l/4.*sqrt(M_inf**2. - 1.);\n",
      "\n",
      "print\"The angle of attack of the wing is:\",alpha,\"degrees\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The angle of attack of the wing is: 1.97493716351 degrees\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E03 : Pg 400"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "# All the quantities are expressed in SI units\n",
      "import math \n",
      "from math import sqrt,pi\n",
      "# (a)\n",
      "M_inf = 2.;                       # freestream mach number\n",
      "rho_inf = 0.3648;                # freestream density at 11 km altitude\n",
      "T_inf = 216.78;                  # freestream temperature at 11 km altitude\n",
      "gam = 1.4;                       # ratio of specific heats\n",
      "R = 287.;                         # specific gas constant\n",
      "m = 9400.;                        # mass of the aircraft\n",
      "g = 9.8;                         # acceleratio due to gravity\n",
      "W = m*g;                         # weight of the aircraft\n",
      "S = 18.21;                       # wing planform area\n",
      "c = 2.2;                         # chord length of the airfoil\n",
      "alpha = 0.035;                   # angle of attack as calculated in ex. 12.2\n",
      "T0 = 288.16;                     # ambient temperature at sea level\n",
      "mue0 = 1.7894e-5;                # reference viscosity at sea level\n",
      "\n",
      "# thus\n",
      "a_inf = sqrt(gam*R*T_inf);\n",
      "V_inf = M_inf*a_inf;\n",
      "\n",
      "# according to eq.(15.3), the viscosity at the given temperature is\n",
      "mue_inf = mue0*(T_inf/T0)**1.5*(T0+110.)/(T_inf+110.);\n",
      "\n",
      "# thus the Reynolds number can be given by\n",
      "Re = rho_inf*V_inf*c/mue_inf;\n",
      "\n",
      "# from fig.(19.1), for these values of Re and M, the skin friction coefficient is\n",
      "Cf = 2.15*10**-3;\n",
      "\n",
      "# thus, considering both sides of the flat plate\n",
      "net_Cf = 2.*Cf;\n",
      "\n",
      "# (b)\n",
      "c_d = 4.*alpha**2./sqrt(M_inf**2. - 1.);\n",
      "\n",
      "print\"(a) Net Cf = \",net_Cf*1e3\n",
      "print\"(b) cd =\",c_d*1e3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Net Cf =  4.3\n",
        "(b) cd = 2.82901631903\n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}