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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter7-Axial compressor Aerodynamics"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg397"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate specific work at pitch line and rotor torque per unit mass flow rate\n",
      "w=5600. ##rpm\n",
      "rm=0.5 ##m\n",
      "Ct2=145. ##m/s\n",
      "Um=w*2*math.pi*rm/60. ##Rotor tangential speed at pitchline in m/s\n",
      "Ct1=0.\n",
      "dU=Ct2-Ct1\n",
      "wc=Um*dU/1000. ## in kJ/kg\n",
      "tpm=rm*(dU)\n",
      "print'%s %.6f %s'%(\"Specific work at pitchline in\",wc, \"kJ/kg\")\n",
      "print'%s %.1f %s'%(\"Rotor torque per unit mass flow rate in \",tpm,\"m^2/s\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Specific work at pitchline in 42.516221 kJ/kg\n",
        "Rotor torque per unit mass flow rate in  72.5 m^2/s\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex2-pg407"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate rotor anugular speed and rotor exit swirl and rotor specific work at pitch line and rotor mass flow rate and stotor mass flow rate and flow efficient\n",
      "rm=0.5\n",
      "Um=212. ##m/s\n",
      "Czm=155. ##m/s\n",
      "Ct1m=28. ##m/s\n",
      "Rm=0.6\n",
      "alfar=1. ##alfar=alfa3/alfa1.\n",
      "w=Um*60./(rm*2*math.pi)\n",
      "print'%s %.f %s'%(\"Rotor angular speed w in\",w,\" rpm\")\n",
      "Ct2m=2.*Um*(1.-Rm)-Ct1m\n",
      "print'%s %.f %s'%(\"Rotor exit swirl in\",Ct2m,\" m/s\")\n",
      "wcm=Um*(Ct2m-Ct1m)/1000.\n",
      "print'%s %.f %s'%(\"Rotor specific work at pitchline Wcm in\",wcm,\" kJ/kg \")\n",
      "Wt2m=Ct2m-Um\n",
      "print'%s %.f %s'%(\"Rotor relative velocity vector at rotor exit in\",Wt2m,\" m/s\")\n",
      "print(\"Hence vector is 155k-70.4e\")\n",
      "##Since alfa3=alfa1, rotor and stator torques are equal and opposite each other.\n",
      "trm=rm*(Ct2m-Ct1m)\n",
      "tsm=-1*trm\n",
      "print'%s %.f %s'%(\"Rotor torque per unit mass flow rate in\",trm,\" m^2/s\")\n",
      "print'%s %.f %s'%(\"stotor torque per unit mass flow rate in\",tsm,\" m^2/s\")  \n",
      "pshm=(Ct2m-Ct1m)/Um\n",
      "phm=Czm/Um\n",
      "print'%s %.f %s'%(\"Stage loading parameter at pitchline\",pshm,\"\")\n",
      "print'%s %.f %s'%(\"Flow coefficient\",phm,\"\")\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rotor angular speed w in 4049  rpm\n",
        "Rotor exit swirl in 142  m/s\n",
        "Rotor specific work at pitchline Wcm in 24  kJ/kg \n",
        "Rotor relative velocity vector at rotor exit in -70  m/s\n",
        "Hence vector is 155k-70.4e\n",
        "Rotor torque per unit mass flow rate in 57  m^2/s\n",
        "stotor torque per unit mass flow rate in -57  m^2/s\n",
        "Stage loading parameter at pitchline 1 \n",
        "Flow coefficient 1 \n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3-pg409"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#determine circulation and D-factor\n",
      "Um1=200. ## in m/s\n",
      "Um2=Um1\n",
      "Cz1=150. ##in m/s\n",
      "Cz2=Cz1\n",
      "b2=-35. ##in degree \n",
      "Cm=7. ##in cm\n",
      "Sm=7. ##in cm\n",
      "W1m=((Um1**2.)+Cz1**2.)**(1/2.) \n",
      "Wt2m=Cz2*math.tan(-35/57.3)\n",
      "W2m=((Cz1)**2.+(Wt2m)**2.)**(1/2.)\n",
      "print\"%s %.1f %s\"%(\"W1m in \",W1m,\"m/s:\")\n",
      "print\"%s %.4f %s\"%(\"W2m in \",W2m,\"m/s \")\n",
      "sigma=Cm/Sm\n",
      "Wt1m=-1.*Um1\n",
      "Dm=1.-(W2m/W1m)+(abs(Wt2m-Wt1m))/(2.*sigma*W1m)\n",
      "print\"%s %.4f %s\"%(\"D-factor Dm\",Dm,\" \")\n",
      "Tm=Sm/100.*abs(Wt1m-Wt2m)\n",
      "print\"%s %.7f %s\"%(\"Circulation Tm in \",Tm,\"m^2/s\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "W1m in  250.0 m/s:\n",
        "W2m in  183.1104 m/s \n",
        "D-factor Dm 0.4575  \n",
        "Circulation Tm in  6.6485249 m^2/s\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex4-pg421"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate static pressure rise co-efficent \n",
      "W1=300. ##in m/s\n",
      "wrm=0.03\n",
      "W2min=0.72*W1\n",
      "Cp=1-(W2min/W1)**2-wrm\n",
      "print\"%s %.1f %s\"%(\"Minimum W2 in\",W2min,\" m/s :\")\n",
      "print\"%s %.3f %s\"%(\"Static pressure rise coefficient\",Cp,\"\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Minimum W2 in 216.0  m/s :\n",
        "Static pressure rise coefficient 0.452 \n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex5-pg429"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate total temperature ratio and compressor polytropic efficency\n",
      "ps=1.5\n",
      "es=0.9\n",
      "gm=1.4\n",
      "ts=1.+(1./es)*(ps**((gm-1.)/gm)-1.)\n",
      "ec=(gm-1.)/gm*(math.log(ps))/math.log(ts)\n",
      "print\"%s %.3f %s\"%(\"Total temperature ratio\",ts,\"\")\n",
      "print\"%s %.3f %s\"%(\"Compressor polytropic efficiency\",ec,\"\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Total temperature ratio 1.136 \n",
        "Compressor polytropic efficiency 0.906 \n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex6-pg429"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate mean relative flow angle and rotor section drag co-efficent and rotor circulation and rotor sectional 2d lift co-efficent\n",
      "W1=460. ##in m/s\n",
      "b1=45.##degrees\n",
      "W2=376.\n",
      "b2=30.\n",
      "c=5.25\n",
      "w=0.05\n",
      "s=3.5\n",
      "Wt1=W1*math.sin(45/57.3)\n",
      "Wt2=W2*math.sin(30/57.3)\n",
      "Wtm=(Wt1+Wt2)/2\n",
      "Wz1=W1*math.cos(45/57.3)\n",
      "Wz2=W2*math.cos(30/57.3)\n",
      "Wz=(Wz1+Wz2)/2\n",
      "bm=(math.atan(Wtm/Wz))*180/math.pi\n",
      "sigma=c/s\n",
      "Cd=w/sigma*math.cos(bm/57.3)\n",
      "T=s/100*(abs(Wt1-Wt2))\n",
      "Wm=(Wz**2+Wtm**2)**(1/2.)\n",
      "C1=2.*T/(Wm*(c/100.))-Cd*math.tan(bm/57.3)\n",
      "print\"%s %.4f %s\"%(\"mean relative flow angle :\",bm,\"\")\n",
      "print\"%s %.4f %s\"%(\"The rotor section (2D) drag coefficient :\",Cd,\"\")\n",
      "print\"%s %.4f %s\"%(\"The rotor circulation in m**2/s :\",T,\"\")\n",
      "print\"%s %.4f %s\"%(\"The rotor sectional (2D) lift coefficient :\",C1,\"\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean relative flow angle : 38.2551 \n",
        "The rotor section (2D) drag coefficient : 0.0262 \n",
        "The rotor circulation in m**2/s : 4.8042 \n",
        "The rotor sectional (2D) lift coefficient : 0.4209 \n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex7-pg437"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Example 7.7\"\n",
      "%matplotlib inline\n",
      "import warnings\n",
      "warnings.filterwarnings('ignore')\n",
      "#calculate and draw the garph of degree of reaction for compressor stage with IGV and possible hub radii and possible tip radii\n",
      "import numpy\n",
      "import matplotlib\n",
      "from matplotlib import pyplot\n",
      "Rm=0.5\n",
      "b=0 #b=b/w\n",
      "i=1\n",
      "z0=numpy.linspace(0.,.5,6)\n",
      "z1=numpy.linspace(0.5,1.5,20)\n",
      "for b in z0:\n",
      "\tr=0.5\n",
      "\tvr=z1;\n",
      "\tx=numpy.zeros(20)\n",
      "\tcount=0;\n",
      "\tfor r in z1:\n",
      "\t\tR=(1-b)-((1-b)-Rm)/(r)**2\n",
      "\t\tx[count]=R\n",
      "\t\tcount=count+1;\n",
      "\tpyplot.plot(vr,x)\n",
      "\ti=i+1;\n",
      "\tpyplot.xlabel(\"r/r1 (<---------)Possible hub radii and Possible tip radii(--------->)\")\n",
      "\tpyplot.ylabel(\"R(r)\")\n",
      "\tpyplot.title(\"Degree of reaction for a compressor stage with an IGV\")\n",
      "\tpyplot.legend(\"b/w=0\",\"b/w=0.1\",\"b/w=0.2 so on\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Example 7.7\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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u1tHUGVo06omYGP0n1mg0dUN0dP29y7RoaDQ2Yi40U3yymKK4IjWdLKL4VDEl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\noJxzrsK80ijRDS/cwJm7p3sE6tNP4dFH4TvfqXB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       "text": [
        "<matplotlib.figure.Figure at 0x57bc0f0>"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}