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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter6-Three-dimensional Flows in Axial Turbomachines"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg181"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate the\n",
      "\n",
      "##given data\n",
      "dt = 1.0;##tip diameter in m\n",
      "dh = 0.9;##hub diameter in m\n",
      "alpha1 = 30.;##in deg\n",
      "beta1 = 60.;##in deg\n",
      "alpha2 = 60.;##in deg\n",
      "beta2 = 30.;##in deg\n",
      "N = 6000.;##rotational speed in rev/min\n",
      "rhog = 1.5;##gas density in kg/m^3\n",
      "Rt = 0.5;##degree of reaction at the tip\n",
      "\n",
      "##Calculations\n",
      "omega = 2.*math.pi*N/60.;\n",
      "Ut = omega*0.5*dt;\n",
      "Uh = omega*0.5*dh;\n",
      "cx = Ut/(math.tan(alpha1*math.pi/180.) + math.tan(beta1*math.pi/180.));\n",
      "mdot = math.pi*((0.5*dt)**2 - (0.5*dh)**2)*rhog*cx;\n",
      "Wcdot = mdot*Ut*cx*(math.tan(alpha2*math.pi/180.)- math.tan(alpha1*math.pi/180.));\n",
      "ctheta1t = cx*math.tan(alpha1*math.pi/180.);\n",
      "ctheta1h = ctheta1t*(dt/dh);\n",
      "ctheta2t = cx*math.tan(alpha2*math.pi/180.);\n",
      "ctheta2h = ctheta2t*(dt/dh);\n",
      "alpha1_ = (180./math.pi)*math.atan(ctheta1h/cx);\n",
      "beta1_ = (180./math.pi)*math.atan((Uh/cx) - math.tan(alpha1_*math.pi/180.));\n",
      "alpha2_ = (180./math.pi)*math.atan(ctheta2h/cx);\n",
      "beta2_ = (180./math.pi)*math.atan((Uh/cx) - math.tan(alpha2_*math.pi/180.));\n",
      "k = Rt*(0.5*dt)**2;\n",
      "Rh = 1 - (k/(0.5*dh)**2);\n",
      "\n",
      "##Results\n",
      "print'%s %.2f %s'%('(i)The axial velocity, cx = ',cx,' m/s');\n",
      "print'%s %.2f %s'%('\\n (ii)The mass flow rate =',mdot,' kg/s');\n",
      "print'%s %.2f %s'%('\\n (iii)The power absorbed by the stage = ',Wcdot/10**6,' MW');\n",
      "print'%s %.2f %s %.2f %s %.2f %s %.2f %s'%('\\n (iv)The flow angles at the hub are:\\n alpha1 = ',alpha1_,' deg'and '\\n beta1 =',beta1_,'deg'and '\\n alpha2 = ',alpha2_,'deg' and'\\n beta2 = ',beta2_, 'deg.')\n",
      "print'%s %.2f %s'%('\\n (v)The reaction ratio of the stage at the hub, R =.',Rh,'');\n",
      "\n",
      "\n",
      "##there are small errors in the answers given in textbook\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)The axial velocity, cx =  136.03  m/s\n",
        "\n",
        " (ii)The mass flow rate = 30.45  kg/s\n",
        "\n",
        " (iii)The power absorbed by the stage =  1.50  MW\n",
        "\n",
        " (iv)The flow angles at the hub are:\n",
        " alpha1 =  32.68 \n",
        " beta1 = 55.17 \n",
        " alpha2 =  62.54 \n",
        " beta2 =  8.75 deg.\n",
        "\n",
        " (v)The reaction ratio of the stage at the hub, R =. 0.38 \n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex2-pg185"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate the\n",
      "\n",
      "\n",
      "%matplotlib inline\n",
      "\n",
      "import warnings\n",
      "warnings.filterwarnings('ignore')\n",
      "from math import log\n",
      "import numpy\n",
      "##given data\n",
      "\n",
      "R = 0.5;##degree of reaction\n",
      "Cp = 1005.;##kJ/(kgC)\n",
      "cx1_Ut_rt = 0.4;\n",
      "delT0 = 16.1;##temperature rise\n",
      "Ut = 300.;##in m/s\n",
      "\n",
      "##calculations\n",
      "A1 = cx1_Ut_rt**2 +(0.5-0.18*math.log(1));\n",
      "c1 = 2*(1.-R);\n",
      "c2 = Cp*delT0/(2.*Ut**2 *(1.-R));\n",
      "A2 = 0.56;\n",
      "k = numpy.linspace(0.4,1.0,num=61);\n",
      "i=len(k)\n",
      "\n",
      "cx1_Ut=numpy.zeros(i)\n",
      "cx2_Ut=numpy.zeros(i)\n",
      "R_=numpy.zeros(i)\n",
      "Rn=numpy.zeros(i)\n",
      "import numpy\n",
      "import matplotlib\n",
      "from matplotlib import pyplot\n",
      "\n",
      "for i in range(1,61):\n",
      "    cx1_Ut[i] = math.sqrt(A1 - (c1**2)*(0.5*k[i]**2 - c2*math.log(k[i])));\n",
      "    cx2_Ut[i] = math.sqrt(A2 - (c1**2)*(0.5*k[i]**2 + c2*math.log(k[i])));\n",
      "    R_[i] = 0.778+math.log(k[i]);\n",
      "    Rn[i] = 0.5;\n",
      "\n",
      "\n",
      "##Results\n",
      "pyplot.plot(k,cx1_Ut);\n",
      "pyplot.plot(k,cx2_Ut);\n",
      "pyplot.title(\"Solution of exit axial-velocity profile for a first power stage\")\n",
      " \n",
      "pyplot.plot(k,R_);\n",
      "pyplot.plot(k,Rn);\n",
      "#ylabel(\"Reaction\",\"fontsize\",3) ;##y label \n",
      "#legend([\"True Reaction\";\"Nominal Reaction\"] , opt=1); ##legend box\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[<matplotlib.lines.Line2D at 0x5b06bb0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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XSUpO4s/TfzJ582Qe/uVhmoxrQsibIdz05U08Ov9Rpm6Zyp6ze0hKTspzl9bcptGjR3tc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\n/qVLTVgHQRCENLhscNdaLwQWpvltvNP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       "text": [
        "<matplotlib.figure.Figure at 0x5a893d0>"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}