path: root/backup/Fluid_Mechanics-Fundamentals_&_Applications_version_backup/Chapter14.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 14: Turbomachinery"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-1, Page No:767"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "#Variable Deceleration\n",
      "V_dot_cfm=range(0,1500,250) #Volumetric Flow rate in cubic feet per second\n",
      "V_dot_mps=transpose(V_dot_cfm)/2118.83 #Volumetric flow rate in m^/s\n",
      "rho_air=1.184 #Density of air in kg/m^3\n",
      "rho_water=998 #Density of water in kg/m^3\n",
      "Patm=101.3 #Atmospheric Pressure in kPa\n",
      "v=1.562*10**-5 #Kinematic Viscosity in m^2/s\n",
      "D=0.23 #Diameter in m\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "f=0.0209 #Friction coefficient from table\n",
      "L=13.4 #Length in m\n",
      "V=6.81 #Velocity of flow in m/s\n",
      "alpha=1.05 #Constant\n",
      "C=(1/0.0254) #Conversion factor\n",
      "\n",
      "#Minor Loss Coefficients\n",
      "ml_1=1.3\n",
      "ml_2=0.21\n",
      "ml_3=1.8\n",
      "\n",
      "#Calculations\n",
      "Re=(4*V_dot_mps)/(v*pi*D)  #Reynolds Number\n",
      "\n",
      "#Friction coefficient values from Moddy Chart\n",
      "f1=[0,0.023,0.022,0.0185,0.0175,0.0162]\n",
      "f=transpose(f1)\n",
      "\n",
      "#Cross Sectional Area\n",
      "A=(pi*D**2)/4 #Area of the pipe cross section in m^2\n",
      "\n",
      "V1=transpose(V_dot_mps)/A #Velocity array in m/s\n",
      "V=transpose(V1) #Velocity in m/s\n",
      "\n",
      "#Minor Losses\n",
      "Kl=ml_1+(5*ml_2)+ml_3 #Minor losses \n",
      "\n",
      "H_required=(alpha+(f*(L/D))+Kl)*(V**2/(2*g)) #Required net head in m of air\n",
      "\n",
      "H_required_inches=H_required*(rho_air/rho_water)*C #Head Required in inches of water\n",
      "\n",
      "H_av=[0.9,0.95,0.9,0.77,0.4,0] #Table values taken fro plotting\n",
      "\n",
      "#Result\n",
      "print \"The Plot shows the variation of the head required and the head available as a function\"\n",
      "print \"Of V_dot. The intersection point tells the operating point.\"\n",
      "\n",
      "plt.plot(V_dot_cfm,H_required_inches,V_dot_cfm,H_av)\n",
      "plt.ylabel('H,inches H2O')\n",
      "plt.xlabel('V_dot,cfm')\n",
      "plt.show()\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Plot shows the variation of the head required and the head available as a function\n",
        "Of V_dot. The intersection point tells the operating point.\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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Du3BGhzO4sdeNdGqqRn8yy8nJIScnJ+6vm8jO7BqEzuw+wHfAR+zYmd0MWObu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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bc1ac10>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-2, Page No:770"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "rho=998 #Density in kg/m^3\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "V_dot=0.0233 #Volumetric flow rate in m^3/s\n",
      "H_small=7.3 #Head in m\n",
      "H_big=21.9 #Head in m\n",
      "n_pump_small=0.7 #Efficiency of the pump in fraction small\n",
      "n_pump_big=0.765 #Efficiency of pump in fraction big\n",
      "#Calculations\n",
      "bhp_small=(rho*g*V_dot*H)/n_pump_small #Required bhp in kW\n",
      "\n",
      "#Similarly for 241.3mm impeller we get 6.53kW\n",
      "bhp_big=(rho*g*V_dot*H_big)/n_pump_big\n",
      "\n",
      "#Result\n",
      "print \"The required bhp is\",round(bhp_small,2),\"W\"\n",
      "print \"The required bhp is\",round(bhp_big,2),\"W\"\n",
      "print \"Clearly the small one is better as it uses less power\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The required bhp is 2378.92 W\n",
        "The required bhp is 6530.38 W\n",
        "Clearly the small one is better as it uses less power\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-4, Page No:780"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "n_dot=900 #Speed in rpm\n",
      "V_closed=0.45 #Volume of motor oil in cm^3\n",
      "n=0.5 #Number of rotations\n",
      "\n",
      "#Calculations\n",
      "V_dot=n_dot*(2*V_closed/n) #Volumetric Fow rate in cm^3/min\n",
      "\n",
      "#Result\n",
      "print \"The volumetric Flow rate is\",round(V_dot),\"cm^3/min\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The volumetric Flow rate is 1620.0 cm^3/min\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-5, Page No:784"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "n_dot=1750 #Speed in rpm\n",
      "w=183.3 #Angular Speed in rad/s\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "alpha1=0 #Angle in degrees\n",
      "alpha2=40 #Angle in degrees\n",
      "b1=0.052 #Inlet blade width in m\n",
      "b2=0.023 #Outlet blade width in m\n",
      "V_dot=0.13 #Volumetric Flow rate in m^3/s\n",
      "rho_water=1000 #Density of water in kg/m^3\n",
      "rho_air=1.2 #Density of air in kg/m^3\n",
      "r1=0.04 #Inlet radius in m\n",
      "r2=0.08 #Outlet radius in m\n",
      "\n",
      "#Calcualtions\n",
      "V1_n=V_dot/(2*pi*r1*b1) #Normal Component of Velocity in m/s\n",
      "V1=V1_n #Since Vt is zero Velocity in m/s\n",
      "V2_n=V_dot/(2*pi*r2*b2) #Normal Component of velocity in m/s\n",
      "V2_t=V2_n*tan((alpha2*pi)/180) #Tangential Component of velocity in m/s\n",
      "\n",
      "#Applying the Bernoullis principle \n",
      "H=(w/g)*(r2*V2_t) #Net head in m\n",
      "Hwater_column=H*(rho_air/rho_water)*1000 #Equivalent water column in mm of water\n",
      "\n",
      "bhp=rho_air*g*V_dot*H #bhp required in W\n",
      "\n",
      "#Result\n",
      "print \"The net Head produced is\",round(Hwater_column),\"mm of water\"\n",
      "print \"The brake horsepower required is\",round(bhp,1),\"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The net Head produced is 17.0 mm of water\n",
        "The brake horsepower required is 21.6 W\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-6, Page No:786"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "r1=0.1 #Inlet Radius in m\n",
      "r2=0.18 #Outlet radius in m\n",
      "b1=0.05 #Inlet width in m\n",
      "b2=0.03 #Outlet width in m\n",
      "V_dot=0.25 #Volumetric Flow rate delivered in m^3/s\n",
      "n=1720 #Speed of the impeller in rpm\n",
      "rho=1226 #Density of the fluid in kg/m^3\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "H=14.5 #Head in m\n",
      "\n",
      "#Calculations\n",
      "#Required horse power\n",
      "W_water_horsepower=rho*g*V_dot*H #Required Horse Power in W\n",
      "W_dot_water_hp=W_water_horsepower/745.7 #Required Horse Power in hp\n",
      "\n",
      "w=n*(2*pi/60) #Angular Speed in rad/s\n",
      "\n",
      "beta1=(arctan((V_dot)/(2*pi*b1*w*r1**2)))*(180/pi) #Blade inlet angle in degrees\n",
      "\n",
      "#Using elemetary analysis\n",
      "V2_n=V_dot/(2*pi*r2*b2) #Normal Component of Velocity in m/s\n",
      "\n",
      "V2_t=(g*H)/(w*r2) #Tangential Component of velocity in m/s\n",
      "\n",
      "#Simplfying Calculation\n",
      "a=w*r2-V2_t\n",
      "\n",
      "beta2=arctan(V2_n/a)*(180/pi) #Angle in degrees\n",
      "\n",
      "#Result\n",
      "print \"The angel beta1 is\",round(beta1,2),\"degrees\"\n",
      "print \"The angle beta2 is\",round(beta2,2),\"degrees\"\n",
      "print \"The horsepower required is\",round(W_dot_water_hp,1),\"hp\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The angel beta1 is 23.84 degrees\n",
        "The angle beta2 is 14.73 degrees\n",
        "The horsepower required is 58.5 hp\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-7, Page No:792"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "D_propeller=0.34 #Overall Diameter of the propeller in m\n",
      "alpha=14 #Angle of attack in degrees\n",
      "n=1700 #Speed of the propeller in rpm\n",
      "D_hub=0.055 #Diameter of the hub assembly in m\n",
      "V=13.4 #Velocity of the plane in m/s\n",
      "\n",
      "#Calculations\n",
      "C=60/(2*pi) #Conversion factor\n",
      "phi1=(arctan((V*C)/(n*D_hub*0.5)))*(180/pi) #Angle in degrees\n",
      "theta1=alpha+phi1 #Pitch Angle at arbitrary radius  in degrees\n",
      "phi2=(arctan((V*C)/(n*D_propeller*0.5)))*(180/pi) #Angle in degrees\n",
      "theta2=alpha+phi2 #Pitch angle at the tip in degrees\n",
      "\n",
      "#Result\n",
      "print \"The pitch angle at any radius is\",round(theta1,1),\"degrees\"\n",
      "print \"The pitch angle at the tip is\",round(theta2,1),\"degrees\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The pitch angle at any radius is 83.9 degrees\n",
        "The pitch angle at the tip is 37.9 degrees\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-8,Page No:797"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "V_in=47.1 #Velocity at the inlet in m/s\n",
      "beta_st=60 #trailing edge at Angle in degrees\n",
      "n=1750 #Speed of the impeller in rpm\n",
      "r=0.4 #Radius in m\n",
      "\n",
      "#Calculations\n",
      "V_st=V_in/cos((beta_st*pi)/180) #Velocity leaving the trail in m/s\n",
      "\n",
      "u_theta=((n*2*pi)/60)*r #Tangential Velocity of rotor blades in m/s\n",
      "\n",
      "beta_r1=(arctan((u_theta+V_in*tan((beta_st*pi)/180))/V_in))*(180/pi) #Angle of leading edge in degrees\n",
      "\n",
      "beta_rt=(arctan(u_theta/V_in))*(180/pi) #Angle in degrees\n",
      "\n",
      "#Result\n",
      "print \"The leading edge and trailing edge angles are\",round(beta_r1,2),\"degrees and\",round(beta_rt,2),\"degrees\"\n",
      "print \"We select number like 13 15 and 17  rotor blades\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The leading edge and trailing edge angles are 73.09 degrees and 57.28 degrees\n",
        "We select number like 13 15 and 17  rotor blades\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-9, Page No:802"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "n=1170 #Speed of the pump in rpm\n",
      "H=23.5 #Required head in ft\n",
      "V_dot=320 #Gasoline pumped gallon/minute\n",
      "Ratio=3.658*10**-4 #Nsp/Nsp_US ratio\n",
      "\n",
      "#Calcualtions\n",
      "Nsp_US=(n*V_dot**0.5)/(H**0.75) #Pump specific speed in US units\n",
      "Nsp=Nsp_US*(Ratio) #Normalizes pump specific speed\n",
      "\n",
      "#Result\n",
      "print \"The Nsp_US value is\",round(Nsp_US,2),\"and Nsp value is\",round(Nsp,3),\"which tells\"\n",
      "print \"A centrifugal Pump is the best suitable one\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Nsp_US value is 1960.92 and Nsp value is 0.717 which tells\n",
        "A centrifugal Pump is the best suitable one\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-10, Page No:804"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "wa=1 #Setting as unit speed\n",
      "\n",
      "#Calculations\n",
      "wb=2*wa #Speed \n",
      "bhp_ratio=(wb/wa)**3 #Ratio od required shaft power \n",
      "\n",
      "#Result\n",
      "print \"The ratio of required shaft power is\",round(bhp_ratio)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The ratio of required shaft power is 8.0\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-11, Page No:805"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "#Variable Decleration\n",
      "D_A=0.06 #Diameter of pump A in m\n",
      "n_A=1725 #Operating Speed in rpm\n",
      "w_A=180.6 #Operating Angular Speed in rad/s\n",
      "V_B_dot=2.4*10**-3 #Volumetric Flow rate in m^3/s\n",
      "V_A_dot=5*10**-4 #Volumetric Flow rate in m^3/s\n",
      "H_A=1.5 #Head in m\n",
      "rho_water=998 #Density of water in kg/m^3\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "n_pump_A=0.81 #Efficiency of pump A in fraction\n",
      "H_B=4.5 #Head in m\n",
      "rho_B=1226 #Density of fluid in kg/m^3\n",
      "\n",
      "#Calculations\n",
      "#Part(a)\n",
      "bhp_A=(rho_water*g*V_A_dot*H_A)/n_pump_A #Required Power in W\n",
      "\n",
      "C_Q=V_A_dot/(w_A*D_A**3) #Capacity Coefficient \n",
      "\n",
      "C_H=(g*H_A)/(w_A**2*D_A**2) #Head Coefficient\n",
      "\n",
      "C_P=bhp_A/(rho_water*w_A**3*D_A**5) #Power Coefficient\n",
      "#Plotting\n",
      "V_dot1=range(100,800,100) #Volumetric flow rate in cm^3/s\n",
      "H1=[180,185,175,170,150,95,54] #Head in cm\n",
      "n_pump1=[32,54,70,79,81,66,38] #Efficiency of the pump in percentage\n",
      "#BHP calculations\n",
      "V_dot=transpose(V_dot1)\n",
      "H=transpose(H1)\n",
      "n_pump=transpose(n_pump1)\n",
      "bhp_A1=rho_water*g*V_dot\n",
      "bhp_A2=bhp_A1*H\n",
      "bhp_A=bhp_A2/n_pump\n",
      "\n",
      "\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "ax.plot(V_dot1,bhp_A)\n",
      "plt.xlabel('V_dot,cm^3/s')\n",
      "plt.ylabel('H,cm and n in %')\n",
      "ax2 = ax.twinx()\n",
      "ax2.plot(V_dot1,H1,V_dot1,n_pump1)\n",
      "plt.ylabel('bhp,W')\n",
      "ax.grid()\n",
      "plt.show()\n",
      "\n",
      "\n",
      "#Curve Fitted Data Yields\n",
      "CQ_star=0.0112\n",
      "CH_star=0.133\n",
      "CP_star=0.00184\n",
      "npump_star=0.812\n",
      "\n",
      "#Part(b)\n",
      "Db=((V_B_dot**2*CH_star)/(CQ_star**2*g*H_B))**0.25 #Design Diameter of pump B in m\n",
      "\n",
      "w_B=V_B_dot/(CQ_star*Db**3) #Angular speed at B in rad/s\n",
      "\n",
      "bhp_B=CP_star*rho_B*w_B**3*Db**5 #Required brake horse power in W\n",
      "\n",
      "\n",
      "#Result\n",
      "print \"The required diameter of Pump is\",round(Db,3),\"m\"\n",
      "print \"The required rotational speed is\",round(w_B),\"rad/s\"\n",
      "print \"The required Brake Horse Power is\",round(bhp_B),\"W\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p8h82dZK7eMndZzfzWixBqJocfJ9/DnPmQIUK0ZYo/zJvHtxyi9k4Xa1atKXx\nF14yUq7u8RaRNiKyXkR+EpEnMrheVkRmiMgKEVktIl1D7Zsf8LtfPNb0U4W+fU04dCCQdwMVa/qF\nk0jolpY66YYbIp86yc+fXUaIyIcislNEVgXVvSQi60RkpYhMFJGSQdf6O2PzehFxdUu7a0ZKROKA\nN4E2QC2gk4jUTNesJ7BcVesBicArIlIwxL4WS9hITYWePY1xmjsXzjor2hJZALp3N8aqSxdIyfIs\ncEse+Qgz3gYzC6itqhcBG4H+AM7x8bdixuY2wFsi4potcXMm1QDYpKpbVDUZGA+0S9dmB1DCeV8C\n+FNVj4fY1/f4+WRQiB39UlJMBvOVK42Lr3Tp8Nw3VvRzg0jq9sYbcPCgifyLFH7+7DJCVecD+9LV\nzVbVVKf4A1DJed8OGKeqyaq6BdiEGbNdIZSME2kHICZwcu6+j7PpVhHYGlTeBlyers17wDcish04\nA7glB30tljxz/DjcdRfs2GFSHhUvHm2JLOlJS53UoAHUrWvSUlkizj3AOOd9BWBR0LVtmDH7FETk\nMWAB8D9nApJjsp1Jich/gJeAxsClzuuyEO4dSkTDk8AKVa0A1ANGiMgZIfTLF/jdLx5t/Y4dM4li\n9+41mSTCbaCirZ+bRFq3tNRJDz8My5a5/zw/f3Y5RUSeAo6p6idZNMtsvK8EvA7sFpFvRWSwiFwn\nIiH7K0KZSV0C1MpFGN3vQOWgcmWMxQ3mCuB5AFX9WUQ2AzWcdtn1BaBr164kJCQAEB8fT7169f6Z\nqqf9oXm1vGLFipiSx0/6HTkCzZoFiIuDr79OpEgRf+nnx/LevQF69izLTTddyOLFsH59bMkXy+VA\nIMCoUaMA/hkvQ8EJZrsGaB5UnX5sr+TUnYKq9nbuUwQzwWmEmZW9JyJ/qWq2sQahpEX6DHhEVbdn\nd7N0/QoCGzDKbQcWA51UdV1Qm1eB/ao6UETKAcuAusCB7Po6/W0IuiXHHDoEN94IZcqYfTiFCkVb\nIktOePZZmD3bpk7KCxmFoItIAvClqtZxym2AV4CmqronqF0t4BPMOlRFYA5QLavBWETiMQbqCucV\nD/wYyn7bUIxUAOOKW8yJBLOqqjdke3ORtpipXhzwgaoOEZEHnBuMFJGymKiSKhjX45C0KWVGfTO4\nvzVSlhxx4ABcdx1UrWoOLIyLi7ZElpySmgodO0J8PLz/PogndvvEFumNlIiMA5oCZYGdwDOYaL7C\nQFoy8YWQ32idAAAgAElEQVSq2sNp/yRmRnQcM4mZmclz3sNEAR7E2JCFwCJV3ZdR+wzvEYKRSsyg\nWlV1XqgPcQu/G6lAIPDP1N2PRFq/ffugbVuoXx9GjHD/JFg/f37R1i0pyaRO6tbNndRJ0dbPbSK1\nmVdEZgJlgNUYA7UQWJWTgTvbNSlVDeRWQIslVtizB1q2hMREePVV++3b6xQvfuJcr1q1bOqkWEVV\nWzt7qGpj3H3/AuqIyJ+YGdXT2d3DpkWy+J4//jCDWLt2MGiQNVB+wqZOyh3RSIskIpUx61GNgeuA\nMqpaMute1khZfM7WrdC8Odx5pzlyw+I/3nkHhg2DRYugRIns21si6u57BGOYGmHWr77H7Jv6Hlit\nqtnmEXHZK2/JC2khpH7Fbf02bzYpdR54IDoGys+fXyzp5kbqpFjSz+MkABOAhqpaVVVvV9W3VXVl\nKAYKsj5PalVm1zCBE3VzJqvFEjk2bjQuvieegIceirY0Frd54w1o1cqkTho8ONrSWNJQ1cfyeo+s\nzpNKcN72cH6OAQTo4jw86pnJrbvPkhFr1pgB67nn4J57oi2NJVLs3m1SJw0eDJ06RVua2CbaR3WI\nyHrn7Zuq+maWbUMIQV/hZCkPrluuqvXzJmbesUbKkp7ly+Gaa+CVV6Bz52hLY4k0K1eaGfSMGXDJ\nJdGWJnaJtpFyZCgLXK6qU7NqF8qalIhIk6BCY8yMyuIyfveLh1u/H36ANm3gzTdjw0D5+fOLVd0u\nusgEUtx0k4nqzC2xqp+XEZGzRaSdiFwvIuVVdU92BgpCM1L3YM4L+VVEfgXecuoslphh/ny4/npz\n5HuHDtGWxhJNOnQwbt727eHo0ezbW9xHRO7FHPfRHrgZ+EFEuoXUN1R3WdqpjKq6P5dyhh3r7rOA\nOQOqc2f45BO7qdNisKmTsibS7j4R2Qg0UtU/nXIZTJql6tn1zTbjhIicBnTAOU9KzKetqvrvvAht\nsYSDqVPh7rvhv/+FK6+MtjSWWKFAARg92qROGj7cndRJlhyxB0gKKic5ddkSirtvCnADkOzcOAk4\nlEMBLbnA737xvOo3caJx63z5ZWwaKD9/fl7QLS110pAhZradE7ygn8f4GVgkIs+KyLOYQxN/EpHe\nIvKvrDqGcp5URVVtHQYhLZaw8ckn0Lu3ieKqH/U4U0uskpAA48fb1EkxwM/OK219ZorzPtujRkMJ\nQX8XE8v+Yx6FDDt2TSp/8uGHZtPmrFlQu3a0pbF4AZs66WRiIQQ9VEIxUuuAasBmTj5PKuoZJ6yR\nyn+MGAFDhxr3TfVsl1wtlhM8+CBs2waTJ9tzxKIQOFED6IMT2+BUq6penV3fUNak2gLnA62A651X\ntgceWvKO3/3iOdXvlVfMa948bxgoP39+XtTtjTfMoZcDBmTf1ov6xTifAf8D/g94POiVLdkaKVXd\noqpbgL+B1KBXtohIGxFZLyI/icgpaZREpI+ILHdeq0TkuHPMMCKyRUR+dK4tDuV5Fv8yaBCMHGkM\n1LnnRlsaixcpXBg+/xzGjTMvywlE5EMR2Rmcs1VESovIbBHZKCKz0sZm51p/Z1xfLyKtQnhEspNY\n9gdVXeq8loUkWwjuvhsw59xXAHYB5wDrVDXL1QARiQM2AC2A34ElQCdVXZdJ++uAR1W1hVPeDFyi\nqnszau+0se4+n6NqMphPmWJcfOXLR1sii9exqZMyPD7+Skzk9seqWsepexHYo6ovOpOMUqraT0Rq\nAZ8AlwEVgTlAdVU9ZfIiIqUxGYp6AbuBiZxYNiKr8T2NUNx9gzBngWxU1XOB5pidw9nRANjkzMSS\ngfFAuyzadwbSf7/xxMKexR1U4V//gmnTIBCwBsoSHsKVOslPqOp8YF+66huA0c770cCNzvt2wDhV\nTXa8bJsw431G/A9YCtyFWZP6HlgW9MqWUIxUsqruAQqISJyqzgUuDaFfRWBrUHmbU3cKIlIUaA38\nN6hagTkislRE7gvheb7D737xrPRLTYUePeD77+Gbb6Bs2cjJFS78/Pl5XbfsUid5Xb8wUU5Vdzrv\ndwLlnPcVMON5GpmO7aqa4ExuagEjgJXAcmC4U5ctoRipfSJyBjAfGCsiwzh553Bm5MQPdz3wnar+\nFVTX2Mm03hZ4yJmOWvIBKSnQrRusXg2zZ0OpUtGWyOJHnn4azj7bRP3ZVYOscdZVsvotZfcb/Bio\nCbwBvIkxUB+H8uxQNvO2A44Aj2HOkioBDAyh3+9A5aByZU62vsHcRjpXn6rucH7uFpFJmOnk/PQd\nu3btSkJCAgDx8fHUq1ePxMRE4MS3Ia+W0+piRZ5I6Hf8OLz/fiJ79sCTTwb43/9iR177+Z0oJyYm\nxpQ8uSl/+22Ae++No1+/Kxk2DC66yF/6BZcDgQCjRo0C+Ge8DIGdTrbyP0TkbExMApw6tldy6rKi\ntqoGz5y+EZG1oQgRcoLZnCIiBTGBE82B7cBiMgiccBLX/gJUUtXDTl1RIE5VD4pIMWAWMFBVZ6Xr\nawMnfMTRo3DbbXDsmMnFd9pp0ZbIkh/YsgUaNYKPP4aWLaMtTWTIaJ+Uc9Dtl+kCJ/5U1aEi0g+I\nTxc40YATgRPVshqMReQ/wAhVXeiUGwIPqeod2ckairsvV6jqcaAnMBNYC3yqqutE5AEReSCo6Y3A\nzDQD5VAOmC8iKzBBGl+lN1D5gbRvQn4lWL/Dh+HGG01i0EmT/GGg/Pz5+Um3tNRJt98OmzaZOj/p\nFwoiMg4T1FBDRLaKyN3AC0BLJ4P51U4ZVV0LTMCM69OBHpkZKGdr0SrgEmCBc+TTFudZocQ2hOTu\nyzWqOh2jRHDdyHTl0ZyIIEmr2wycdBqwxb8kJcENN5j1gdGjoaCrf5UWy6k0bQrPPmv+DhctirY0\nkUdVO2VyKcPDb1R1MDA4hFtfn9VjQ+jvnrsvElh3n/fZvx+uvRZq1IB337XpaizRJb+kTvJS7r5s\n3X3OUb/LRWSfiBx0XgciIZzF3+zda9YALroI3nvP34OCxRukpU7q29dG/MUKoaxJvY7ZiFVGVc9w\nXjaPcATws1981y647LIAV10Fb75p1qL8hp8/P7/qVriwCdqZOvUA3bub7RCW6BLK0LANWJNRyguL\nJaekppqzoC69FK64Al56yR7tbYktypaFV19dyS+/mCPojxyJtkT5m1By9zUE/g3MBY451aqqr7os\nW7bYNSlvsWCBSXOUmgqvvQZNmkRbIoslc44ehbvuMqmTpkyBkiWjLVH48NWaFPAcJsPEaZhTFIsD\nZ7gplMVfbN4Mt95q9kD16gU//GANlCX2KVLEzPrr1DHRfzbPX3QIxUidrartVfUZVR2Y9nJdMovn\n/f7798MTTxjX3oUXwoYNZi9K2vqT1/XLDj/r52fd4IR+BQqYE307dIDGjeHnn6MrV34kFCM1TURa\nuy6JxTccP26yTNeoAbt3w6pV5qC5okWjLZnFknNEzN9v375w5ZWwfHm0JcpfhLImlQQUxaxHJTvV\nGgsRfnZNKvaYORN694Yzz4RXX4X69aMtkcUSPiZOhO7d4dNPoVmzaEuTe7y0JmU381rCwtq1xjht\n2gQvv2x27tuoPYsfmTvXrLG+/bZxA3oRLxmpUDbz3pTu2OB4Ebkxqz6W8OAFv//u3ebcp6ZNoXVr\nWLMG2rULzUB5Qb+84Gf9/KwbZK1fs2bGY9CrF4wcmWkzS5gIZU3q2eBznpz3z7omkcUTHD1q9jjV\nrAmFCsH69fDoo2YzpMXid+rXh/nzzf/Ac8/Z7BRuEsqa1I+qWjdd3aq0dO7RxLr7Io+q2ZHft68J\nzX3xRRMgYbHkR/74A9q2NZF/w4Z5J3OKl9x9oRipj4B9mKN/BXgIKKWqXV2XLhuskYosS5aYzbgH\nD8Irr0Dz5tGWyGKJPvv3m2NmypUzWfyLFIm2RNnjJSMVit3vhYnq+xQYjzml9yE3hbIYYsXvv3Ur\n3HGHWWu6+25Ytiw8BipW9HMLP+vnZ90gZ/qVLAnTp0NyMlx3nfkSZwkf2RopVU1S1SdU9VLn1V9V\nD0VCOEt0SUqCp5+GevXgnHPMZtx77rHZyi2W9Jx2GkyYAFWrwtVXm4AiS3jIcQi6iAwG9gPvq+qf\n2bRtg8miHue0H5rueh+gi1MsCNQEyqrqX9n1dfpbd58LpKSYo7T/7/9MJNPgwVClSrSlslhiH1Xz\nxe7TT2HWLHPqbyySyfHx/YHbgVRgFXA3UAzjRTsH2ALcEhxIFxFZc2GkbgLOAy7K6nx6EYkDNmBO\ndvwdWAJ0UtV1mbS/DnhUVVuE2tcaqfAzd65Zdypa1GzGvfzyaEtksXiP4cNh6FDjBqwT9RCzU0lv\npEQkAfgGqKmqR0XkU2AaUBvYo6ovisgTmHiEfpGUNcexKKo6SVVfzspAOTQANqnqFlVNxqxntcui\nfWdgXC77+pJI+v03bjSLv/fcA08+Cd99576BsusasY+qcuT4Efb8vYdf//qVtbvXsvj3xYz8ciQp\nqf49bCmvn12vXmZTe4sW5n/JAxzAxB4UFZGCmCxD24EbgNFOm9FAxPfIFszsgogMDyoqJrLvn7Kq\nPpzNvSsCW4PK24AMhz0RKQq0BnrktK8lb+zda/Z5jBljwsrHjzf+dYu3SElN4VDyIQ4dO0TSsaRT\n3icdS+LQsUMnvf+nXTbXCxYoSPHCxSlWqBjFChejeOHi7P5rNwM3DqRDzQ50rN2RxpUbE1fALlYG\nc9ttUKYMtG8P779vsrDEKqq6V0ReAX4DDgMzVXW2iJRT1Z1Os51AuUjLlqmRApZxwjgNBJ7mhKEK\nxceWEz/c9cB3Qb7OkPt27dqVBMfxGx8fT7169UhMTAROfBvyajmtzo37JyfDY48F+M9/oFOnRNau\nhbVrAyxa5A/9YqGcXr+5c+eSrMlc3PBiDh07xNwFczmccpgL6lxA0rEklqxcwuGUw1Q6txKHkg+x\ndtNaDqccptRZpUg6lsRvO37jSOoRChYtyKHkQ/x54E8OpxzmGMc4lnKMIgWKcHrc6ZQqVopihYuR\ncjiF0+NOp1K5ShQvXJz9u/dzWtxp1KxakzOLnUny7mRKxpXk0rqXUrxwcTau3shpcaeReEUixQoV\nY/ni5ZwedzrNmzXPUL8x08Ywb/c8ek3vxe5Du2lYoiFNz2xKzxt6ElcgLuq//7yUExMTw3K/QoVg\n6tREbrgBFixYT9u2f0RFn0AgwKhRowD+GS+DEZHzgEeBBEzMwWcicntwG1VVEYn4+kpIa1IislxV\nc5Qq1Dks8VlVbeOU+wOpmQRATAI+VdXxOelr16Ryjip8+SU8/jice67Z71S7drSl8j4pqSls/HMj\ny3YsY+n2pfy480f2Hdl3ygylUIFCFCtcjGKFzIwk/fvihU6tO+l6uhlN2vvTC56ORDFZ4sY/N/LZ\nms+YsHYCuw/ttjOsdGzYAG3amOS0fftGP69lBmtStwItVfVep3wH0BC4Gmimqn+IyNnAXFW9IKKy\numikCmKCH5pjfJuLyTj4oSTwC1BJVQ/nsK+vjVTwt/BwsGKFSQL7xx/GOLVpE7Zb54pw6xcp0huk\nZTuWseKPFZxV7CwuOfsSLq1wKfXK1+PXtb/S9IqmJxmZggWycl54h6w+Oz8YLDf+Nn//3fzPtWxp\n1qsKRDE7RQZG6iJgLHAZZi/sKMy4ew7wp6oOFZF+QHykAydc+49R1eMi0hOYiQkj/0BV14nIA871\ntNSMN2L8n4ez6+uWrH5nxw5zHs5XX8Ezz8B990FBf4yVrhOKQbq++vVcfPbFlDq91El9A1sDVC9T\nPUqSR4/qZarz1FVP8dRVT/1jsNJcgl40WOGiYkX49lu4/npzLP2HH5q8l7GAqq4UkY+BpZgQ9P8B\n72JOYZ8gIt1wQtAjLVumMynnHKm0i6djFtPSsOdJeYDDh82M6bXXoFs3eOopszvekjGhGKRLzr4k\nQ4NkyR4/zLDCwd9/m6M+jh+Hzz+HYsUiL4OX0iLZ86R8SGoqjBsH/fubMPKhQ81OeMsJrEGKLvnd\nYB0/bjwa69bB1KkmCjCSWCMVIfxupHLjF1+wwGzGTU01M6gmTdyRLRxEak0qO4OUZpTCbZC8uuYW\nCuHULRYNViQ+O1Xo188EMs2cCZUru/q4k/CSkbIrEz5h82Z44glYtMikMerc2TvHBoSTUAzSs02f\ntTOkGCK/rmGJGC9HuXLmqI8ZM6BWrWhLFXvYmZTH2b/fGKUPPjCHDqalNMoPhGKQLqlgXHalTy8d\nbXEtOSQWZ1huMWaM2RYyaRI0auT+87w0k7JGyqMcP252sT/7LFxzDQwaBBUqRFsq97AGKX8TbLB2\nHdrFzTVv9p3Bmj4d7rzTJHdu29bdZ1kjFSH8bqQy84vPnGn2O515pkkCWz9HO9hih8z084tBsmtS\n7hAJgxUt/RYuhJtuMvuobr89+/a5xUtGyq5JeYi1a41x+vlneOklkwss2jvX80ooBumZps/EvEGy\nRI7M1rD8MMNq1Ai++cZs+t21y7jv8zt2JuUBdu82m3A//9zsdXrwQShcONpS5Z4fd/7I+NXjmf/b\nfE/OkCyxiZ9cglu3QqtW5ovoCy+E/8uol2ZS1kjFMEePwrBh8OKL0KWLOUyttEfH7t/2/8Ynqz5h\n7Kqx7D+yn04XdqLleS2tQbK4gh8M1p9/wrXXmoi/d98Nb5YYa6QihJ+NVCAAnToFaNAgkZdeguoe\nzK6z9/BePlvzGWNXjWXN7jXcXPNmutTtQpMqTSggBXy9ZgN2TSpWyI3BihX9Dh2Cm2826ZPGjw9f\n5K6XjFQ+3EkT+yxYALfcYkLKp0zxloE6nHyYCWsm0G58O85941y+3vw1vRv1Zvu/tjPy+pFcdc5V\nFBD7Z2eJHGlrWCu7r2Re13mUL16eXtN7Uem1SvSa1otvf/02Zg9wLFYMvvgCSpQw7r99+6ItUeSx\nM6kYY8UKaN3a7Jto1Sra0oRGSmoK32z+hrGrxjJlwxQurXApXep0oX3N9pQoEvUUjxZLhnjJJZia\nCn36wOzZZtNvxYp5u5+XZlLWSMUQGzdCYiIMHw4dOkRbmqxRVZbtWMbYH8cyfs14Kp5RkS51unDb\nhbdx9hlnR1s8iyVHpDdYXS/qylNXPUXxwsWjLdo/qJr16XfeMYaqRo3c38tLRgpV9ezLiO8Pfv1V\ntUoV1Q8/PFE3d+7cqMmTGZv+3KQDAwO1xvAaWvWNqjrgmwG6bve6XN0rFvULJ37Wz8+6bdizQVu9\n3UqrvFZFJ6+bHG1xTuGDD1TLl1ddsiT393DGzqiP4aG87D6pGGDXLnMQ2mOPwd13R1uaU9l1aBef\nrv6UsavG8su+X7il9i181O4jGlZqGNXTYC0WN6hepjr9L+hP6jmpPDj1QUatHMWwNsOoXDKCGWCz\n4J57oGxZk2nmk0+gRYtoS+Qu1t0XZf76C5o1g3btTIqjWCHpWBKT109m7KqxLNy6kGurX0uXOl1o\nWbUlheJi5KQ2i8Vljhw/wtDvhjJ88XD+76r/o2eDnjFzuvL8+Sbyb9gwcz5VTvCSu89VIyUibYDX\nMafrvq+qQzNokwi8BhQC9qhqolO/BTgApADJqtogg76eNlKHDpkgiUsvNcdqRHtSkpySzKyfZzF2\n1Vim/jSVxpUb06VOF9pd0C6mfPMWS6TZsGcDD059kL+O/MXI60ZyWcXLoi0SAKtWmTx//fpBz56h\n98vISIlIPPA+UBtz4O3dwE/Ap5hj5LcAt6jqX+GRPkTc8iNiDNMmIAFjgFYANdO1iQfWAJWcctmg\na5uB0tk8I1QXbMxx5Ihqq1aqXbuqpqRk3CYSfv/U1FRd8NsC7fFVDz3zxTO14fsNdfgPw3Vn0k7X\nn+3ndQ1Vf+vnZ91UM9YvNTVVP17xsZZ7qZz2nNpT9x/ZH3nBMmDzZtXzz1cdMEA1NTW0PmSwJgWM\nBu5x3hcESgIvAn2duieAF9L3c/vl5oaVBsAmVd2iqsnAeKBdujadgf+q6jbH4uxJd90T09Gccvy4\nySBRvDi89150zn1av2c9A74ZQLXh1bhnyj2UL16ehd0WsrDbQno26MlZxc6KvFAWSwwjItxx0R2s\nfWgtR44fodaIWny+9vO0AT5qJCTAd9/BtGnQvTuk5GLLl4iUBK5U1Q8BVPW4qu4HbsAYL5yfN4ZH\n6hzI5tYvWERuBlqr6n1O+XbgclXtFdQmzc1XGzgDeENVxzjXfgH2Y9x9I1X1vQyeodH+A8kpqnDv\nvSY315dfQpEikXv29oPbGb96PGNXjWXHwR3cduFtdKnThYvPvtgGQFgsOWT+r/PpPrU7CfEJjLhm\nBAnxCVGV5+BBaN/ebPwdOxZOOy3ztundfSJSDxgJrAUuApYBjwLbVLWU00aAvWnlSOHmCmAo1qMQ\ncDHQHCgKLBSRRar6E9BEVbeLyJnAbBFZr6rz09+ga9euJCQkABAfH0+9evX+SWcSCAQAYqY8d26A\nt96C339PZPZsWLjQ/ecnHU9id5ndjF01lh+2/kCTMk0Y2moozRKaMf/b+RzceBCpIDHx+7FlW/ZS\nOWVzCq9f8DpLCi3h0ncvpUP5DnSs1JEWV7eIijzLlgV4/HHhgw+a0rYt9O49n+LFU0hMTCQQCDBq\n1CiAf8bLdBTEjMU9VXWJiLwO9AtuoKoqIpGfFbjlRwQaAjOCyv2BJ9K1eQJ4Nqj8PnBzBvd6Buid\nQX32ztcY4t//Vq1bV3Xv3tDa59bvfyT5iE5aN0lvnnCzlhhSQtuNa6cTVk/Qv4/9nav7uUV+XNfw\nC37WTTXn+m36c5O2HtNa67xVR7//7Xt3hAqR48dVH3pItV491R07Mm5DujUpoDywOajcBJgKrAPK\nO3VnA+s1RBsQrpebqyFLgfNFJEFECgO3Al+kazMFaCIicSJSFLgcWCsiRUXkDAARKQa0Ala5KKvr\nDBtmTtycNQtKuTBZTtVU5m2Zx/1f3k+FVyvw2qLXaFm1JZsf2czk2ybTsXZHTi90evgfbLFYOK/0\neUzvMp0nr3ySDhM60P2r7uw7HJ1Ee3FxJmvNTTdBkybm/LnsUNU/gK0ikpYptAUmqO1L4C6n7i5g\nsgsiZ4nbIehtORGC/oGqDhGRBwBUdaTTpg8m1DEVeE9Vh4lIVWCic5uCwFhVHZLB/dVN+cPF6NEw\nYIDZ13DOOeG99487f2Tsj2MZt3oc8afF06VOFzrV6USVklXC+yCLxRISfx35iye/fpLJ6yfzcquX\n6XRhp6it+b7zDjz3HHz11ckneGcSgn4RxptVGPgZMy7HAROAKkQpBN1u5nWZSZOgRw+YOxcuuCA8\n90x/NlPnOp3pUqcLdcrVCc8DLBZLnlm0bREPfPUA5YqV461r36Ja6WpRkeO//zUHpU6YYHKDgrc2\n89ozE1xkzhx44AGYOjV3BiptYRTM2Uwjl47kqo+uov7I+mzet5kR14xgy6NbeKHFC540UMH6+RE/\n6+dn3SA8+jWs1JCl9y2l1XmtaPh+QwZ9O4ijx4/mXbgc0qEDfPqpOf5n4sTs28casZHfw4csXAid\nOpk/iosvzt09jqYcZcKaCYxdNZbAlgCtz2tN70a9aVOtDUUKRjB23WKx5IpCcYXoc0UfOtbqSM/p\nPak3sh4jrzPnqkWSZs1g5kxz0u+e9LtRYxzr7nOBH380CWNHjTIpS3LKb/t/48UFLzJ21Vh7NpPF\n4hNUlUnrJ/HIjEdoWbUlL7Z8kbJFy0ZUhk2bTCq2X36x7r58y08/GcM0fHjODdQv+37hvi/uo/7I\n+hQrVIw1PdYw+47ZdK3X1Rooi8XjiAjta7ZnbY+1lChSgtpv1Wb0itERzVhRrZo5+dtLWCMVRrZt\nM6fpDhxo/L+hsvHPjXSd3JUG7zWgfPHybOy5kaEth7Jx2Ub3hI0B7LqGd/GzbuCufmcUOYPX27zO\ntM7TGL54OFd/fDXr96x37XnpKV8+Yo8KC9ZIhYndu42Lr2dPk/YoFNbsWkPn/3am8YeNOa/UeWx6\neBPPXf0cZYqWcVdYi8USdS6pcAk/3PsDN11wE00+bMLTc5/myPEj0RYr5rBrUmFg/364+mrj3hs0\nKPv2K/5YwaBvBzH/t/k81vAxelzWw7rzLJZ8zLYD23hkxiOs2rmKt699m+ZVm7v6PC+FoFsjlUf+\n/hvatIG6dc06VFZ79pZuX8pz3z7Hkt+X0OeKPjxwyQMUK1wscsJaLJaY5quNX9FzWk+aVGnCq61f\nde00Ai8ZKevuywPHjpmTMc85x6Q9ysxAfb/1e9qObctNn95Ey6ot+fnhn/lXo39la6Cs39/b+Fk/\nP+sG0dPvuurXsabHGs4ufjYXvnUh7y17j1RNjYossYI1UrkkJQXuvBMKF4aPPsr4TKh5W+bR/OPm\ndJnYhRtr3MimXpvo2aCnzaFnsVgypVjhYrzU6iVm3zGbD5Z/wFUfXcXqXaujLVbUsO6+XKBqMkn8\n/LPJJhF8bouqMueXOTz37XPsSNrBk02e5Pa6t1MorlDE5bRYLN4mVVN5d9m7DJg7gHvr38uApgMo\nWqhonu/rJXefNVI5RBX69oVvvzVpj844I61emfbTNJ779jkOHD3AU1c+xa0X3krBAjaph8ViyRt/\nJP3BYzMf44dtPzDimhG0PT8XWQKC8JKRsu6+HDJkCMyYAdOnGwOVqqlMWjeJS9+7lP5f96d3o96s\nenAVXep2ybOBsn5/b+Nn/fysG8SefuWLl2dch3G8fe3b9Jzek1s+u4XtB7dHW6yIYI1UDnjrLfjw\nQ3MmVMn4FCasmUC9d+oxaP4gBlw1gBXdV9CxdkfiCsRFW1SLxeJDWldrzeoHV3N+6fO56J2LGLF4\nBCmpKdEWy1Wsuy9E/vMf6N8fvgkc54dD43l+/vPEnxbPgKsG0LZa26idF2OxWPIna3atofvU7hxL\nOcbI60ZSr3y9kPt6yd1njVQIfPEF3Nc9mV7vjWHUz4OpWKIiA64aQPNzm1vjZLFYokaqpvLR8o/o\n/yuZncsAAA9PSURBVHV/7qh7BwObDaR44eLZ9vOSkXLV3ScibURkvYj8JCJPZNImUUSWi8hqEQnk\npG8kmDHnKF1ee4e4R88n8OcnfHDDB8zrOo8WVVu4bqBizS8ebqx+3sXPuoF39CsgBeh2cTdW91jN\n7r93U/ut2kxZPyXX9xOROGc8/tIplxaR2SKyUURmiUh82IQPEdeMlIjEAW8CbYBaQCcRqZmuTTww\nArheVS8Ebg61r9scTj5MnwnDuXZGNWq3/4L/dhrHnDvn0DShaSTFsFgslmw5q9hZfHzTx3zU7iP6\nzunLTZ/exNb9W3Nzq0eAtUCai6ofMFtVqwNfO+WI4pq7T0QaAc+oahun3A9AVV8IatMDKK+qT+e0\nr1MfdnffoWOHeGfpOwyd/woH1jXghWv+j0dvuTSsz7BYLBa3OHL8CEO/G8rwxcN56sqn6HV5r1Mi\njTNy94lIJWAU8DzwL1W9XkTWA01VdaeIlAcCqpqLc8Zzj5vuvopAsCnf5tQFcz5QWkTmishSEbkj\nB33DyoGjBxgyfwhVh1VlzoZFyNjpfNR6sjVQFovFU5xW8DSeSXyGBfcs4MuNX9LgvQYs+X1JKF1f\nAx4HgvMwlVPVnc77nUC5MIubLW7uNA1lilMIuBhoDhQFForIohD7AtC1a1cSEhIAiI+Pp169eiQm\nJgIn/MpZlQ8mH+R/hf7Hm0ve5KLiF9Gv/FCGP92VgX3h7LMDBAJZ93ez/Prrr+dYHy+VrX7eLQev\n2cSCPFa/U8s7Vu9gQJUBbCu9jdaDWlNuWznql6pP9arVSY+IXAfsUtXlIpJ4SgNAVVVEopHiR115\nAQ2BGUHl/sAT6do8ATwbVH4fsy6VbV+nXnPLnkN79Kmvn9IyQ8to18lddcOeDbp7t2qtWqovvJDr\n24aVuXPnRlsEV7H6eRc/66bqP/32HNqj3aZ004qvVNTP1nymztgZPJYOxnivNgM7gEPAGGA9ZkkG\n4GxgvebBLuTm5eaaVEFgA2aWtB1YDHRS1XVBbS7ABEi0BooAPwC3Ahuz6+v015zKvzNpJ68sfIUP\nln9Ah5od6NekH1VLVeXAAWjeHFq0MFklLBaLxW/M/3U+3ad2Z+1DazMNQReRpkAfNWtSLwJ/qupQ\nJzYgXlUjGjzh6j4pEWkLvA7EAR+o6hAReQBAVUc6bfoAd2P8oO+p6rDM+mZw/5CN1PaD23lxwYt8\nvPJjOtfpTN/GfalSsgoAhw+bAwtr1jRZJezWJ4vF4leOpRyjSMEi2Rmp3qp6g4iUBiYAVYAtwC2q\n+lfkpM0Hm3l/2/8bQ78byrjV4+haryt9ruhDhTMq/HM9ORnatzd5+MaMgbgYymgUCAT+8S/7Eauf\nd/GzbuB//by0mde3Kbp/2fcLQ+YPYeL6idxb/17W91x/yimXKSlw110ms/no0bFloCwWi8Xiw5nU\nhj0bGPzdYKZunMqDlz7Iow0fpUzRMqf0VYUePWDdOpPR/HR7DqHFYskn2JlUFFizaw3Pz3+e2b/M\n5uEGD7Pp4U3En5Z5Bo+nnoKlS+Hrr62BslgslljF80d1rPhjBTdPuJmrP76auuXq8vPDPzOg6YAs\nDdTQoTB5splBlSgRQWFzSPBeDT9i9fMuftYN/K+fl/D8TOqasdfQ54o+jL5xNMUKF8u2/ciR5jV/\nPpQtGwEBLRaLxZJrPL8m9fexvzm9UGj+unHj4PHHYd48OO88l4WzWCyWGMVLa1KeN1Khyj91KnTr\nBnPmwIUXuiyYxWKxxDBeMlKeX5MKhXnz4O67YcoUbxkov/vFrX7exc+6gf/18xK+N1JLl0LHjjB+\nPFx+ebSlsVgsFktO8LW7b+1auPpqEyjRrl0EBbNYLJYYxrr7YoDNm6F1a3j5ZWugLBaLxav40kjt\n2AEtW0K/fnD77dGWJvf43S9u9fMuftYN/K+fl/Cdkdq7F1q1MoESDz0UbWksFsv/t3fuwXaNZxj/\nPRIZDkrTi2umwaBktEKlKqRIREJrepUwpaW3MTWJmioxjHZMp2Sm07tRRjUM0RIyoSUJMqop4pIj\nEY5L5UxdkqAGiZBG8/SP79uy7NnnIrLP3mt5fzN7zlrvt9Ze73P2nv3Od3vfIHg/VGpOavXqVA9q\nzBiYPj1KbgRBEDSiTHNSlQlSb70Fxx0He+wBl18eASoIgqAnyhSkmjrcJ2mCpC5JT0k6p0H7EZJe\nk7Q4vy4otHVLWpLti3p7zvr1MHlySnN02WXVCVBVHxcPfeWlytqg+vrqkTRM0gJJyyQ9KmlKtg+V\nNF/Sk5LmSeo5KWqTaFqQkjSIVBp+ArAfcKKkfRtcerftkfl1UcFu4IhsH9XTczZsgNNOg3Xr2q9o\n4fuls7Oz1S40ldBXXqqsDaqvrwHrgR/aHgEcAvwg/16fC8y3vTdwZz4fUJrZkxoFPG272/Z64Hqg\n0WLw3vo9ffaJpk6F7m6YNQuGDNk0R9uVV18d0CrNA07oKy9V1gbV11eP7ZW2O/PxGuBxYFfgeGBG\nvmwG8KWB9q2ZQWpX4NnC+XPZVsTAoZIekfQ3SfvVtd0h6UFJ3+3pIQsXwq23QkfHZvM7CILgA4uk\n4cBI4H5gR9urctMqYMeB9qeZpTr6syLjYWCY7bWSJgKzgb1z22jbKyR9DJgvqcv2PfVvMHcubL/9\n5nO6neju7m61C00l9JWXKmuD6uvrCUnbArOAqbZXqzDBb9uSBnylXdNW90k6BPiJ7Qn5fBqwwfYl\nvdyzHDjI9it19guBNbZ/UWcv79LEIAiCFlK/uk/SlsCtwG22f5VtXaS1ASsl7QwssP3JgfSzmT2p\nB4G9ctfxBWAScGLxAkk7Ai/mCD2KFDRfkdQBDMqRfBtgPPDT+geUZQllEARBO6PUZboSeKwWoDJz\ngG8Cl+S/swfat6YFKdtvSzoDmAsMAq60/bik7+f2PwBfA06X9DawFpicb98JuCl3NQcD19qe1yxf\ngyAIPuCMBr4BLJG0ONumARcDf5H0baAbOGGgHSv1Zt4gCIKg2rR17j5Jf5S0StLSgq3HzWWSpuWN\nw12SxrfG6/6xKZvnSqZvK0n3S+qU9Jikn2d7JfTVkDQobzi/JZ9XRl+jDfVV0SdpB0k3Sno8fz8/\nWyFt+2hjgoTFSgkTppRWn+22fQGHk5ZCLi3YpgM/zsfnABfn4/2ATmBLYDjwNLBFqzX0om0n4IB8\nvC3wBLBvVfRlnzvy38HAfcBhVdKX/T4LuBaYU6XvZ/Z5OTC0zlYJfaQ9P6cVvp/bV0Vbnc4tgBXA\nsLLqa7kD/fgnD68LUl2ktfu1H/qufDwNOKdw3e3AIa32/z3onA2Mq6I+oAN4ABhRJX3AbsAdwJHA\nLdlWJX3LgY/U2UqvLwekZxrYS6+tgabxwD1l1tfWw3090NPmsl1IG4ZrNNo83Jb0c/Nc6fRJ2kJS\nJ0nHAtvLqJA+4JfA2cCGgq1K+hptqK+Cvt2BlyRdJelhSVfkVcRV0FbPZGBmPi6lvjIGqXdwCvu9\nrfxo+1Uh9Zvnim1l12d7g+0DSD2OMZKOrGsvrT5JXyBtn1hMD+m7yqwvM9r2SGAiKZfb4cXGEusb\nDBwIXGr7QOAN6nLSlVjbO0gaAnwRuKG+rUz6yhikVknaCSBvLnsx258njbvW2C3b2pa8eW4WcI3t\n2v6DyuirYfs14K/AQVRH36HA8Uob0GcCR0m6hurow/aK/Pcl4GZSPs4q6HsOeM72A/n8RlLQWlkB\nbUUmAg/lzw9K+tmVMUjVNpfBuzeXzQEmSxoiaXdgL6DXEh+tROpz8xyUW99Ha6uHJG0NHA0spiL6\nbJ9ne5jt3UlDKnfZPpmK6JPUIWm7fFzbUL+UCuizvRJ4VlItBds4YBlwCyXXVseJbBzqg7J+dq2e\nFOtj0m8mKVvFf0nJak8FhpImq58E5gE7FK4/j7QypQs4ptX+96HtMNJcRifpx3sxqaxJVfTtT8rN\n2AksAc7O9kroq9P6eTau7quEPtK8TWd+PQpMq5i+T5MW8zwC3ERaTFEJbdnfbYCXge0KtlLqi828\nQRAEQdtSxuG+IAiC4ANCBKkgCIKgbYkgFQRBELQtEaSCIAiCtiWCVBAEQdC2RJAKgiAI2pYIUkEQ\nBEHbEkEqqBSS7qqvhyPpTEmX9uPeP0n6ah/XnJkzaDQFSSdJWifp/Dr7qEJ9oCWSJtW1nyvppGb5\nFQStIoJUUDVmktIUFZkEXNePe/tKugkwlVR6ZLMj6ShSVvV9gXGSTik0LwUOckr4Oh74vaRBhfbx\nwNxm+BUErSSCVFA1ZgHHSRoM75RB2cX2PxpdLOl3uRrpfODj5IzmksbmMg5LJF2Z85pNIZU1WCDp\nzgbvdbCkhUrViO+TtK2kb0manSuhLpd0hqQf5fe+V9KH8737AxcB420/AxwLnCTpaADbb9qulQTZ\nGnjN9v/yvR8Chtj+j6SvS1qafbh7s/xHg6CFRJAKKoXtV0jJMY/NpsnAnxtdK+krwN6knssppMzm\nlrQVcBVwgu1PkUo7nG77N6RckkfYHlv3XkOA64EpTuVJxgFv5uYRwJeBg4GfAa87lYi4Nz8X20tt\nj3bOWG17re0JtucXnjFK0jJSMtSzCo8fR8rJBnABKdAdQCrTEASlJoJUUEWKQ36TeHcm6CKHA9c5\nsQK4K9v3AZbbfjqfzwDG9PHMfYAVth8CsL0m93RMKvj4hu2XgVdJ2bYhDeEN768o24tsjyCVlfh1\n7kEBHAPclo8XAjMkfYcUXIOg1ESQCqrIHGCspJFAh1Nhwp5oVLCwfl5KDWzvhXWF4w2F8w1sQiCx\n3QX8i1RSAVKdp0W57XTgfFJ9oIckDd1En4OgLYggFVQO22uABaQhu94WTPwdmJTL3O8M1CoHPwEM\nl7RnPj8ZqM3vrAZqPRgkXS3pM6QSBzvnYyRtlxc2NKzaW7u9v5okDS/Ms32CFKCekjQC6HIuZyBp\nz9zjuhB4iVTALghKSwwHBFVlJqlO0Ak9XWD75ryi7jHg38A/s32dpFOBG3JgWARclm+7HLhd0vN5\nXmp/4AXb6/Oy8N/mJeprSYUe61cM1h/3t4d2GHCupPXAeuB7tl+XNJGNQ30A0yXtRQqAd9he0s/3\nD4K2JOpJBcEmkueErrA9qc+Lm+fDPOBk26ta5UMQNJMIUkEQBEHbEsN9QeXJe5CurjO/ZftzrfAn\nCIL+Ez2pIAiCoG2J1X1BEARB2xJBKgiCIGhbIkgFQRAEbUsEqSAIgqBtiSAVBEEQtC3/BzGnaNSG\n31xmAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b66eed0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The required diameter of Pump is 0.108 m\n",
        "The required rotational speed is 168.0 rad/s\n",
        "The required Brake Horse Power is 160.0 W\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-12, Page No:819"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "rho=998 #Density of fluid in kg/m^3\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "V_dot=12.8 #Volumetric Flow rate in m^3/s\n",
      "H_gross=325 #Gross Head in m\n",
      "C=10**-6 #COnversion Factor\n",
      "n_turbine=0.952 #Efficiency of turbine in fraction\n",
      "n_generator=0.945 #Efficiency of generator in fraction\n",
      "n_other=1-0.035 #Other efficieny in fraction\n",
      "no=12 #Number of Turbines\n",
      "\n",
      "#Calculations\n",
      "W_dot=rho*g*V_dot*H_gross*C #Ideal Power produced in MW\n",
      "\n",
      "W_electrical_dot=W_dot*n_turbine*n_other*n_generator #Actual Electric Power in mW\n",
      "\n",
      "W_total=no*W_electrical_dot #Total Power produced in MW\n",
      "\n",
      "#Result\n",
      "print \"The electrical power generated is\",round(W_total),\"MW\"\n",
      "#The answer differs due to decimal point accuracy\n",
      "#Answer in the text has been rounded off and multiplied hence the inconsistency"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The electrical power generated is 424.0 MW\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-13, Page No:820"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "r2=2.5 #Inlet Radius in m\n",
      "r1=1.77 #Outlet raius in m\n",
      "b2=0.914 #Runner blade width at inlet in m\n",
      "b1=2.62 #Runner blade width at outlet in m\n",
      "n_dot=120 #Speed in rpm\n",
      "w=12.57 #Rad/s\n",
      "alpha1=10 #Angle in degrees\n",
      "alpha2=33 #turning of flow in degrees\n",
      "V_dot=599 #Volumetric Flow rate in m^3/s\n",
      "H_gross=92.4 #Gross Head in m\n",
      "C=10**-6 #Conversion Factor\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "\n",
      "#Calculations\n",
      "#Part(a)\n",
      "#Runner Inlet\n",
      "V2_n=V_dot/(2*pi*r2*b2) #Normal Component of velocity in m/s\n",
      "V2_t=V2_n*tan((alpha2*pi)/180) #Tangential Component in m/s\n",
      "beta2=(arctan(V2_n/(w*r2-V2_t)))*(180/pi) #Runner leading edge angle in degrees\n",
      "\n",
      "#Runner Outlet\n",
      "V1_n=V_dot/(2*pi*r1*b1) #Normal Component of velocity in m/s\n",
      "V1_t=V1_n*tan((alpha1*pi)/180) #Tangential Component in m/s\n",
      "beta1=(arctan(V1_n/(w*r1-V1_t)))*(180/pi) #Runner leading edge angle in degrees\n",
      "\n",
      "#Using Euler Turbomachine Equation\n",
      "W_shaft=rho*w*V_dot*(r2*V2_t-r1*V1_t)*C #Shaft output power in MW\n",
      "\n",
      "H=W_shaft/(rho*g*V_dot*C) #Net Head in m\n",
      "\n",
      "#Part(b)\n",
      "#Similiary repeat calculations for part(b) and part(c)\n",
      "#Result\n",
      "#Results are for only part a\n",
      "print \"The inlet runner blade angle is\",round(beta2,1),\"degrees\"\n",
      "print \"The outlet runner blade angle is\",round(beta1,1),\"degrees\"\n",
      "print \"The output power is\",round(W_shaft),\"MW\"\n",
      "print \"The net head required is\",round(H,1),\"m\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The inlet runner blade angle is 84.1 degrees\n",
        "The outlet runner blade angle is 47.8 degrees\n",
        "The output power is 461.0 MW\n",
        "The net head required is 78.6 m\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-14, Page no:830"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "Cp=0.4 #Power Coefficient \n",
      "n_gearbox=0.85 #Efficiency in fraction\n",
      "rho=1.204 #Density of air in kg/m^3\n",
      "V=10 #Velocity of flow in m/s\n",
      "D=12.5 #Diameter in m\n",
      "\n",
      "#Calculations\n",
      "W_dot_op=(n_gearbox*Cp*pi*rho*V**3*D**2)/8 #Work done in W\n",
      "\n",
      "#Result\n",
      "print \"Electric Power produced is\",round(W_dot_op),\"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Electric Power produced is 25118.0 W\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-15,Page No:832"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "D_A=2.05 #Diameter in m\n",
      "n_A=120 #Speed in rpm\n",
      "w_A=12.57 #Angular Speed in rad/s\n",
      "V_A_dot=350 #Volumetric Flwo rate in m^3/s\n",
      "H_A=7.5 #Head of water in m*10\n",
      "H_B=10.4 #Head of water in m*10\n",
      "bhp_A=242 #Brake Horse Power at A in MW\n",
      "n_turbine_A=0.942 #Efficiency of turbine A\n",
      "rho_A=998 #Density of water in kg/m^3\n",
      "\n",
      "#Calculations\n",
      "a=H_B/H_A\n",
      "rho_B=rho_A #Density in kg/m^3\n",
      "n_B=n_A #Speed at b in rpm\n",
      "D_B=D_A*(a**0.5) #Diameter of the new pump in m\n",
      "V_B_dot=V_A_dot*(n_B/n_A)*((D_B/D_A)**3) #Volumetric Flow rate at B in m^3/s\n",
      "bhp_B=bhp_A*(rho_B/rho_A)*((n_B/n_A)**3)*((D_B/D_A)**5) #Brake Horse Power in MW\n",
      "\n",
      "n_turbine=1-(1-n_turbine_A)*((D_A/D_B)**0.2) #Efficiency correction in fraction\n",
      "\n",
      "#Result\n",
      "print \"The brake horse power is\",round(bhp_B),\"MW\"\n",
      "print \"The diameter of the new turbine is\",round(D_B,2),\"m\"\n",
      "print \"The volumetric Flow rate is\",round(V_B_dot),\"m^3/s\"\n",
      "print \"The corrected efficiency is\",round(n_turbine,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The brake horse power is 548.0 MW\n",
        "The diameter of the new turbine is 2.41 m\n",
        "The volumetric Flow rate is 572.0 m^3/s\n",
        "The corrected efficiency is 0.944\n"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.14-16, Page No:836"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Decleration\n",
      "w_A=12.57 #Angular Speed in rad/s\n",
      "rho_A=998 #Density of fluid in kg/m^3\n",
      "g=9.81 #Acceleration due to gravity in m/s^2\n",
      "H_A=75 #Head in m\n",
      "bhp_A=242*10**6 #Brake Horse Power at A in W\n",
      "H_B=104 #Head in m\n",
      "bhp_B=548 *10**6 #Brake Horse Power at B in W\n",
      "\n",
      "#Calculations\n",
      "#For Turbine A\n",
      "Nst_A=(w_A*bhp_A**0.5)/(rho_A**0.5*g**1.25*H_A**1.25) #Dimensionless specific speed at A\n",
      "\n",
      "#For turbine B\n",
      "w_B=w_A #Angular Speed in rad/s\n",
      "rho_B=rho_A #Density of fluid in kg/m^3\n",
      "Nst_B=(w_B*bhp_B**0.5)/(rho_B**0.5*g**1.25*H_B**1.25) #Dimensionless specific speed at B\n",
      "\n",
      "Nst_US_A=43.46*Nst_B #Turbine specific speed in US units\n",
      "\n",
      "#Result\n",
      "print \"The Turbine Specific Speed in US units is\",round(Nst_US_A,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Turbine Specific Speed in US units is 70.2\n"
       ]
      }
     ],
     "prompt_number": 55
    }
   ],
   "metadata": {}
  }
 ]
}