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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8: Viscous flow in pipes"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.1 Page no.405"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#given\n",
      "T1=50.0             #degree farenheit\n",
      "D=0.73              #in\n",
      "vol=0.0125        #ft**3\n",
      "T2=140              #degree farenheit\n",
      "\n",
      "vis1=2.73*10**-5                          #lb*s/ft**2 at 50 degree farenheit\n",
      "vis2=0.974*10**-5                        #lb*s/ft**2 at 140 degree farenheit\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "#for 50 degree farenheit\n",
      "#if flow is laminar, maximum Re=2100 Re=d*V*D/vis\n",
      "V1=2100*vis1/(1.94*D/12)\n",
      "t1=vol/(math.pi*((D/12)**2)/4*V1)\n",
      "#if flow is turbulent, minimum Re=4000\n",
      "V2=4000*vis1/(1.94*D/12)\n",
      "t2=vol/(math.pi*((D/12)**2)/4*V2)\n",
      "\n",
      "#for 140 degree farenheit\n",
      "#if flow is laminar, maximum Re=2100 Re=d*V*D/vis\n",
      "V3=2100*vis2/(1.94*D/12)\n",
      "t3=vol/(math.pi*((D/12)**2)/4*V3)\n",
      "#if flow is turbulent, minimum Re=4000\n",
      "V4=4000*vis2/(1.94*D/12)\n",
      "t4=vol/(math.pi*((D/12)**2)/4*V4)\n",
      "\n",
      "#result\n",
      "print(\"For laminar flow\")\n",
      "print \"The time taken to fill the glass at 50 degree F=\",round(t1,2),\"seconds\"\n",
      "print \"The time taken to fill the glass 100 degree F=\",round(t3,2),\"seconds\"\n",
      "print (\"For turbulent flow:\")\n",
      "print \"The time taken to fill the glass at 50 degree F=\",round(t2,2),\"seconds\"\n",
      "print \"The time taken to fill the glass at 140 degree F=\",round(t4,2),\"seconds\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "For laminar flow\n",
        "The time taken to fill the glass at 50 degree F= 8.85 seconds\n",
        "The time taken to fill the glass 100 degree F= 24.81 seconds\n",
        "For turbulent flow:\n",
        "The time taken to fill the glass at 50 degree F= 4.65 seconds\n",
        "The time taken to fill the glass at 140 degree F= 13.03 seconds\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.2 Page no.412"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "vis=0.4                    #Ns/(m**2)\n",
      "d=900                     #kg/(m**3)\n",
      "D=0.02                   #m\n",
      "Q=2.0*(10**-5)      #(m**3)/s\n",
      "x1=0\n",
      "x2=10                   #m\n",
      "p1=200                 #kPa\n",
      "x3=5                     #m\n",
      "\n",
      "#Calculation\n",
      "import math\n",
      "V=Q/(math.pi*(D**2)/4)        #m/s\n",
      "Re=d*V*D/vis\n",
      "print \"a) Reynolds number =\",round(Re,0),\"Hence the flow is laminar.\"\n",
      "\n",
      "pdiff=128*vis*(x2-x1)*Q/(math.pi*(D**4)*1000)\n",
      "#for part b0 p1=p2 Q=math.pi*(pdiff-(sw*l*math.sin(ang)))*(D**4)/(128*vis*l)\n",
      "ang=(math.asin(-128*vis*Q/(math.pi*d*9.81*(D**4))))*180/math.pi\n",
      "#since sin(ang) doesn= not depend on pdiff, the the pressure is constant all along the pipe\n",
      "#hence for c)\n",
      "p3=p1              #kPa\n",
      "\n",
      "#result\n",
      "print \"The pressure drop required if the pipe is horizontal=\",round(pdiff,1),\"kpa\"\n",
      "print \"b) The angle of the hill the pipe must be on if the oil is to flow at the same rate as a) but with (p1=p2) =\",round(ang,2),\"degree\"\n",
      "print \"c) For conditions of part b), the pressure at x3=5 m = \",round(p3,3),\"kpa\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a) Reynolds number = 3.0 Hence the flow is laminar.\n",
        "The pressure drop required if the pipe is horizontal= 20.4 kpa\n",
        "b) The angle of the hill the pipe must be on if the oil is to flow at the same rate as a) but with (p1=p2) = -13.34 degree\n",
        "c) For conditions of part b), the pressure at x3=5 m =  200.0 kpa\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.3 Page no.416"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "from numpy import*\n",
      "T=array([60,80,100,120,140,160])        #degree F\n",
      "d=array([2.07,2.06,2.05,2.04,2.03,2.02])#(slugs/(ft**3))\n",
      "vis=array([0.04,0.019,0.0038,0.00044,0.000092,0.000023])#lb*sec/(ft**2)\n",
      "Q=0.5                            #(ft**3)/sec\n",
      "T1=100.0                           #degree F\n",
      "l=6.0                              #ft\n",
      "D=3.0                              #in\n",
      "\n",
      "#Calculation\n",
      "import math\n",
      "pdiff=128*vis[2]*l*Q/(math.pi*(D/12)**4)\n",
      "print \"The pressure difference is \",round(pdiff,0),\"lb/ft**2\"\n",
      "V=Q/(math.pi*((D/12)**2)/4)     #ft/sec\n",
      "Re=d[2]*V*(D/12)/vis[2]\n",
      "print\"The reynolds number=\",round(Re,0),\"< 2100 hence the flow is laminar\"\n",
      "stress=pdiff*(D/12)/(4*l)      #lb/(ft**2)\n",
      "print \"The wall stress for the given Q and T =\",round(stress,2),\"lb/(ft**2)\"\n",
      "Fp=(math.pi/4)*((D/12)**2)*pdiff          #lb\n",
      "Fv=(2*math.pi)*((D/24))*l*stress        #lb\n",
      "\n",
      "#result\n",
      "print \"The net pressure force =\",round(Fp,2),\"lb\"\n",
      "print \"The net viscous/shear force =\",round(Fv,2),\"lb\"\n",
      "\n",
      "#PLot\n",
      "T=[60,80,100,120,140,160]\n",
      "K=[0.0004125,0.00086842,0.0043421,0.0375,0.173,0.695]\n",
      "xlabel(\"T  F\") \n",
      "ylabel(\"K  ft**5/lbs\") \n",
      "plt.xlim((60,180))\n",
      "plt.ylim((0.0001,1))\n",
      "a=plot(T,K)\n",
      "show(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The pressure difference is  119.0 lb/ft**2\n",
        "The reynolds number= 1374.0 < 2100 hence the flow is laminar\n",
        "The wall stress for the given Q and T = 1.24 lb/(ft**2)\n",
        "The net pressure force = 5.84 lb\n",
        "The net viscous/shear force = 5.84 lb\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.4 Page no.427"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#Given\n",
      "T=20.0                                       #degree C\n",
      "d=998.0                                     #kg/(m**3)\n",
      "kvis=1.004*(10**-6)                   #(m**2)/s where kvis=kinematic viscosity\n",
      "D=0.1                                        #m\n",
      "Q=0.04                                      #(m**3)/sec\n",
      "pgrad=2.59                                # kPa/m where pgrad is pressure gradient\n",
      "l=1                                         #m length\n",
      "#calculation\n",
      "import math\n",
      "from scipy import integrate\n",
      "stress=D*(pgrad*1000)/(4*l)           #N/(m**2)\n",
      "uf=(stress/d)**0.5                    #m/sec where uf is frictional velocity\n",
      "ts=5*kvis*1000/(uf)                   #mm where ts is the thickness of the viscous sublayer\n",
      "print \"The thickness of the viscous sublayer=\",round(ts,2),\"mm\"\n",
      "V=Q/(math.pi*(D**2)/4)               #m/s\n",
      "Re=V*D/kvis\n",
      "print \"The reynolds number=\",round(Re,0),\"hence the flow is turbulent.\"\n",
      "\n",
      "n=8.4                                #from turbulent flow velocity profile diagram\n",
      "#Q=(math.pi)*(R**2)*V\n",
      "R=1                                  #say                                        \n",
      "def f1(r):\n",
      "    return(1/R**2*(((1-r/R)**(1/n))*2*math.pi*r))\n",
      "q=integrate.quad(f1,0.0,R)\n",
      "q_=q[0]\n",
      "x=round(q_,2)/math.pi                          #x=V/Vc\n",
      "Vc=V/x\n",
      "print \"The approximate centerline velocity=\",round(Vc,2),\"m/s\"\n",
      "\n",
      "#C\n",
      "r=0.025                                     #m\n",
      "stress1=(2*stress*r)/D               #N/(m**2)\n",
      "#d(uavg)/dr=urate=-(Vc/(n*R))*((1-(r/R))**((1-n)/n)) where uavg=average velocity\n",
      "urate=-(Vc/(n*(D/2)))*((1-(r/(D/2)))**((1-n)/n))           #s**(-1)\n",
      "stresslam=-(kvis*d*urate)                                          #N/(m**2)\n",
      "stressratio=(stress1-stresslam)/stresslam\n",
      "\n",
      "#result\n",
      "print \"The ratio of teh turbulent to laminar stress at a point\\nmidway between the centreline and the pipe wall =\",round(stressratio,0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The thickness of the viscous sublayer= 0.02 mm\n",
        "The reynolds number= 507267.0 hence the flow is turbulent.\n",
        "The approximate centerline velocity= 6.04 m/s\n",
        "The ratio of teh turbulent to laminar stress at a point\n",
        "midway between the centreline and the pipe wall = 1219.0\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.5 Page no.435"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=4.0                         #mm\n",
      "V=50.0                      #m/sec\n",
      "l=0.1                      #m\n",
      "d=1.23                   #kg/(m**3)\n",
      "vis=1.79/100000    #N*sec/(m**2)\n",
      "Re=d*V*(D*10**-3)/vis\n",
      "#if flow is laminar\n",
      "f=64/Re\n",
      "pdiff=f*l*0.5*d*(V**2)/((D*10**-3)*1000)        #kPa\n",
      "\n",
      "#result\n",
      "print \"The pressure drop if the flow is laminar=\",round(pdiff,3),\"kpa\"\n",
      "\n",
      "#if flow is turbulent\n",
      "#roughness=0.0015 hence f=0.028\n",
      "f1=0.028\n",
      "pdiff1=f1*l*0.5*d*(V**2)/((D/1000)*1000)   #kPa\n",
      "print \"The pressure drop if flow is turbulent=\",round(pdiff1,3),\"kpa\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The pressure drop if the flow is laminar= 0.179 kpa\n",
        "The pressure drop if flow is turbulent= 1.076 kpa\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.6 Page no.446"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "A=[22,28,35,35,4,4,10,18,22]\n",
      "V=[36.4,28.6,22.9,22.9,200,200,80,44.4,36.4]\n",
      "g=32.2                        #ft/s**2  gravitational constant         \n",
      "SG=0.0765                      #spesific gravity\n",
      "hl=(0.2*(V[1]**2+V[2]**2+V[6]**2+V[7]**2)+0.6*V[5]**2+0.2*V[4]**2+4*V[3]**2)/(2*g)\n",
      "pdiff=SG*hl/144                          #psi\n",
      "Pa=SG*A[4]*V[4]*hl\n",
      "\n",
      "#result\n",
      "print \"The value of (p1-p9)=\",round(pdiff,3),\"psi\"\n",
      "print \"The horsepower supplied to the fluid by the fan=\",round(Pa,1)/550,\"hp\"\n",
      "\n",
      "#Plot\n",
      "V=[50,100,150,200,250,300]\n",
      "Pa=[0,10,25,62.3,120,220]\n",
      "a=plot(V,Pa)\n",
      "xlabel(\"q ft**3/s\") \n",
      "ylabel(\"d (ft)\") \n",
      "plt.xlim((0,300))\n",
      "plt.ylim((0,250))\n",
      "          \n",
      "show(a)\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of (p1-p9)= 0.297 psi\n",
        "The horsepower supplied to the fluid by the fan= 62.272 hp\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Q1NXVOb9ft26dc0ZUoLXPMAyys7OJi4tjzpw5zuPBcv46al+wnL8TJ044u83O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\nFBQiIuLW/wOZ1ZDRj1PfyAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.7 Page no.449"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "T=120.0                                #degree F\n",
      "D=8.0                                 #in\n",
      "vavg=10.0                             #ft/s\n",
      "roughness=0\n",
      "kvis=1.89*10**-4                      #(ft**2)/s\n",
      "Re=vavg*(D/12)/kvis\n",
      "g=32.2                                #ft/s**2 gravitational constant\n",
      "#Calculation\n",
      "import math\n",
      "#from this value of Re and roughness/D=0, and using Moody's chart\n",
      "f=0.022\n",
      "x=f*(vavg**2)/(D*2*32.2/12)            # x=hl/l\n",
      "#Dh=4*A/P=4*(a**2)/(4*a)=a\n",
      "y=(math.pi*((D/12)**2)*vavg)/(4)  # y=Vs/a**2 \n",
      "z=x*2*g/y**2                            #z=f/a**5\n",
      "f=0.023\n",
      "a=(f/z)**(0.2)\n",
      "\n",
      "#result\n",
      "print \"The duct size(a) for the square duct if the head loss per foot\\n remains the same for the pipe and the duct=\",round(a,3),\"ft\" "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The duct size(a) for the square duct if the head loss per foot\n",
        " remains the same for the pipe and the duct= 0.611 ft\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.8 Page no.451"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "T=60                          #degree F\n",
      "D=0.0625                  #ft\n",
      "Q=0.0267                 #(ft**3)/sec \n",
      "Df=0.5                     #in\n",
      "l1=15.0                    #ft\n",
      "l2=10.0                     #ft\n",
      "l3=5.0                      #ft\n",
      "l4=10.0                   #ft\n",
      "l5=10.0                   #ft\n",
      "l6=10.0                   #ft\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "V1=Q/(math.pi*(D**2)/4)            #ft/sec\n",
      "V2=Q/(math.pi*((Df/12)**2)/4)    #ft/sec\n",
      "d=1.94                                        #slugs/ft\n",
      "vis=2.34*10**-5                         #lb*sec/(ft**2)\n",
      "Re=d*V1*D/vis\n",
      "print \"The reynolds number =\",round(Re,3),\"hence the flow is turbulent\"\n",
      "\n",
      "#applying energy equation between points 1 and 2\n",
      "#when all head losses are excluded\n",
      "p1=(d*32.2*(l2+l4))+(0.5*d*((V2**2)-(V1**2)))         #lb/(ft**2)\n",
      "print \"a)The pressure at point 1 when all head losses are neglected=\",round(p1,3),\"lb/ft**2\"\n",
      "\n",
      "#if major losses are included\n",
      "f=0.0215\n",
      "hLmajor=f*(l1+l2+l3+l4+l5+l6)*(V1**2)/(D*2*32.2)\n",
      "p11=p1+(d*32.2*hLmajor)           #lb/(ft**2)\n",
      "\n",
      "#result\n",
      "print \"b)The pressure at point 1 when only major head losses are included=\",round(p11/144,1),\"psi\"\n",
      "\n",
      "#if major and minor losses are included\n",
      "KLelbow=1.5\n",
      "KLvalve=10\n",
      "KLfaucet=2\n",
      "hLminor=(KLvalve+(4*KLelbow)+KLfaucet)*(V1**2)/(2*32.2)\n",
      "p12=p11+(d*32.2*hLminor)#lb/(ft**2)\n",
      "print \"c)The pressure at point 1 when both major and minor head losses are included=\",round(p12/144,1),\"psi\"\n",
      "H=(p1/(32.2*1.94))+(V1*V1/(2*32.2))#ft\n",
      "\n",
      "#Plot\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "D=[0,15,15,25,25,30,30,40,40,50,50,60]\n",
      "P=[30.5,27.8,27.1,21.0,20.2,19.3,18.5,12.4,11.7,9.93,4.84,3.09]\n",
      "xlabel(\"distance along pipe from point  ft\") \n",
      "ylabel(\"P  hP\") \n",
      "plt.xlim((-0.5,60))\n",
      "plt.ylim((0,32))\n",
      "a=plot(D,P)\n",
      "plt.text(40,28, '-(a)no losses')\n",
      "plt.text(40,25, '-(c)including all losses')\n",
      "\n",
      "\n",
      "plt.text(0,30.5, '30.5')\n",
      "plt.text(15,27.8, '27.8')\n",
      "plt.text(15,27.1, '27.1')\n",
      "plt.text(25,21.0, '21.0')\n",
      "plt.text(25,20.2, '20.2')\n",
      "plt.text(30,19.3, '19.3')\n",
      "plt.text(30,18.5, '18.5')\n",
      "plt.text(40,12.4, '12.4')\n",
      "plt.text(40,11.7, '11.7')\n",
      "plt.text(50,9.93, '9.93')\n",
      "plt.text(50,4.84, '4.84')\n",
      "plt.text(60,3.09, '3.09')\n",
      "plt.text(0,22, 'pressure loss')\n",
      "plt.grid()\n",
      "\n",
      "D=[0,15,25,30,40,50,60]\n",
      "P=[10.7,10.7,6.37,6.37,2.07,2.07,2.07]\n",
      "xlabel(\"distance along pipe from point  ft\") \n",
      "ylabel(\"P  hP\") \n",
      "plt.xlim((-0.5,60))\n",
      "plt.ylim((0,32))\n",
      "a=plot(D,P)\n",
      "plt.text(0,10.7,  '10.7')\n",
      "plt.text(15,10.7, '10.7')\n",
      "plt.text(25,6.37, '6.37')\n",
      "plt.text(30,6.37, '6.37')\n",
      "plt.text(40,2.07, '2.07')\n",
      "plt.text(50,2.07, '2.07')\n",
      "plt.text(60,2.07, '2.07')\n",
      "plt.text(5,5, 'Elevation and Kinetic Energy')\n",
      "show(a)\n",
      "# 2nd plot\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "D1=[0,15,15,25,25,30,30,40,40,50,50,60,60]\n",
      "P1=[71.6,67,63,60,58,57,55,53,50,45,31,28,26]\n",
      "xlabel(\"distance along pipe from point 1 ft\") \n",
      "ylabel(\"Elevetion to Energy line H ft\") \n",
      "plt.xlim((0,60))\n",
      "plt.ylim((0,80))\n",
      "ax.annotate('slope due to pipe friction', xy=(8, 70), xytext=(15,75),\n",
      "            arrowprops=dict(facecolor='black', shrink=0.000),\n",
      "            )\n",
      "ax.annotate('sharp drop due to component loss', xy=(15, 65), xytext=(20,65),\n",
      "            arrowprops=dict(facecolor='black', shrink=0.000),\n",
      "            )\n",
      "ax.annotate('Energy line including all losses', xy=(35, 55), xytext=(40,53),\n",
      "            arrowprops=dict(facecolor='black', shrink=0.000),\n",
      "            )\n",
      "\n",
      "a1=plot(D1,P1)\n",
      "\n",
      "D1=[0,60]\n",
      "P1=[26,26]\n",
      "xlabel(\"distance along pipe from point 1 ft\") \n",
      "ylabel(\"Elevetion to Energy line H ft\") \n",
      "plt.xlim((0,60))\n",
      "plt.ylim((0,80))\n",
      "a1=plot(D1,P1)\n",
      "\n",
      "ax.annotate('Energy line with no losses', xy=(10, 25), xytext=(10,10),\n",
      "            arrowprops=dict(facecolor='black', shrink=0.000),\n",
      "            )\n",
      "\n",
      "show(a1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The reynolds number = 45094.88 hence the flow is turbulent\n",
        "a)The pressure at point 1 when all head losses are neglected= 1547.821 lb/ft**2\n",
        "b)The pressure at point 1 when only major head losses are included= 21.3 psi\n",
        "c)The pressure at point 1 when both major and minor head losses are included= 30.5 psi\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nn3+Ol5cXV69e5cUXXwRyf5OvWrUqkZGRhIeH4+fnR2BgIMeOHeP69ev06NED\nPz8/goKCmDlzJgDjx483N1a3bt0aX19fWrdujYeHB15eXrzyyiv4+/ub95/zWI0bN+b999+nU6dO\n+Pn50alTJ5KTkwuMv3r16kydOpV27dqh1+sJCAigR48enDlzhnbt2pknpZ86dSqZmZkMGjQIX19f\nmjZtyiuvvELFihWL+iO1eTodjBkDP/xgqrYqzNPmp0+fpl27djRp0gRvb2/mzJkDmDpCNGnSBDs7\nOw4cOFDg9hs3bqRRo0Y0aNCAadOmFWU6iqJNFi2m7iNnOEuWLBFvb28rRlO8oqKirB1CsSmq3FJS\nRDp0EGnf3vR7QZKSkiQmJkZERK5fvy6enp5y+PBhOXLkiBw7dsx8B5ifjIwMqVevniQkJEh6err4\n+fnJ4cOHCzyWls+biLbz03Julr6U2/Qdh3oW4tFWrRr8978QGGh62nznzvzXq169Onq9HjB1n27c\nuDHnzp2jUaNGeHp63vMYe/bsoX79+ri7u2Nvb89TTz3Fjz/+WNSpKIqm2GzB8dRTTxEXF2ftMIqN\nlvuUF2VudnYweTJ8+SX06QMzZ977afPExERiYmJo0aJFofZ/9uxZ3NzczMu1a9fm7NmzBa6v5fMG\n2s5Py7lZms0WHIqSU9eu8L//mQZI7N8//6fNb9y4Qb9+/Zg9ezaOjo6F2q+6q1WUB2ezBYfW+1xr\nOb/iys3dHXbsgKpVISAg99Pmd+/epW/fvjzzzDP06tWr0PusVasWp0+fNi+fPn2a2rVrF7i+ls8b\naDs/LedmaWrOcaVEcXAwDZL47bfQvj3MmAFt256iefPm3L17l7Nnz1KqVClefvllLl26xIABA/jf\n//7HyJEj2bhxIy4uLrn25+rqytatW/H09MTe3p4rV66wefNmK2WnKCWDmo9DKbEOHTIN0/7VVz/y\nzDO98PPzIysri+PHjzN79mw2btxIVFQUd+7coXTp0lStWpXff/+dc+fOMXz4cNavX09ycjIrV67k\n008/5e7du1y/fp1t27bRuHFja6enKIVm6WunKjiUEu2xx+DoUdO/2Xr16sWoUaMYNWoUW7duxdXV\nleTkZEJCQjh69Og999erVy9Gjx5Nhw4dijlyRSk6aiKnP2m9PlLL+Vkzt5y9qlJSUnB1dQVMVVIp\nKSmF3rYgWj5voO38tJybpdlswaEoD+rGjRv07duX2bNnmweOzHa/OVIepkeWojyqiryq6vTp0zz7\n7LOcP3+ZRvKCAAAgAElEQVQenU7H888/n6uh8o8//sDd3Z3ly5fnaahUVVXKg8quqnJ2vkv37t3p\n0qULY8aMAaBRo0YYjUaqV69OUlIS7dq1y7eq6u7dvNsqSklS4quq7O3tmTlzJvHx8URHR/P5559z\n5MgRpk6dSmhoKMePH6dDhw5MnTq1qA+tPKIWLRL69h1K48ZeuS78PXv2ZOHChQAsXLgw3266IsLQ\noUPx8vIqVKExZMgQXF1d8fHxMb928OBBWrVqha+vLz179uT69et5trt9+zYtWrRAr9fj5eXFxIkT\nHyZVRbENxT2myZNPPik///yzNGzYUJKTk0XENLZQzkmWsuUMR8vjyohoOz9L5rZsmUjnztsFdFKq\nlJ84OemlenW9fPjhBklMvCgdOnSQBg0aSGhoqFy+fFlERM6ePStdu3YVEZHt27eLTqcTPz8/0ev1\notfrZcOGDQUeb/bs2XLgwIFc46gFBATItm3bRERkwYIF8q9//SvfbW/evCkiInfv3pUWLVrI9u3b\ni+QzKErq77JkssClPJdifY7jYRoqIyIicHd3JzExkdjY2FxTvGY3bqll217OZonjVasGGzaEAFms\nWmXk8GG4di2En36Cd981Urv223TqFEJgIPz0k5EaNaBduxDWr19v3l/2XCyFOV5WVhaVKlXK9f6J\nEycICgrCaDRSoUIFvv/+e95777082+/ZsweA5s2bk5mZyW+//UZGRobVz1fO5djYWJuKpyiXY2Nj\nbSqef7JsNBqJjIwETFNpW1xxlUjXr1+Xpk2byqpVq0RExMXFJdf7lSpVyrNNMYajPILu3BGJjhaZ\nMUOkXz+RGjVEXF1FevcW+fhjkZ07RW7ffvD9JiQk5LrjCAwMlNWrV4uIyPTp08XJySnf7TIzM8XP\nz08cHR1l3LhxD5WTouTH0tfOYulVlT38w6BBg8z1ytl96QGSkpKoVq1acRxaUczKlDE9IPjqq7Bi\nBZw9axrvqn9/+OMPGD0aKleG1q1h3DhYtQruMb1KgRYsWMD//d//ERAQwI0bNyhTpky+65UqVYrY\n2FjOnDnDtm3b8tyhKUpJUeQFhxTQ2FiYhsqctP6fSsv52WpuOh3UqQPh4fDpp7B/P6SkmEbfdXaG\nefOgcWOoV880D/oXX8DBg7knkuratSvNmjXjxIkT5teuXr3K5cuXyczMZMWKFeYq2b9zd3fH19eX\nkJAQzpw5w759+4o75Qdmq+euKGg5N0sr8oJj586dfPvtt0RFRWEwGDAYDGzcuJEJEybw888/4+np\nyZYtW5gwYUJRH1pRHpijo2nMq7ffhp9+Ms15vnYttG1rmgN9wADTXUmnTjBpEnh7dzbXLWd79dVX\nmTx5Mvv376datWq55q/PduHCBUQEo9HIrl27qFu3LgaDwTJJKkoRU0OOKMp9XLgA0dGwciVs2BCO\nyC+kpqZSu3Zt3n33XT7//HOSkpJwcnKiUaNGODk58e233+YaEysuLo5mzZrRoEEDSpUqxaBBgxg3\nbpy1U1M0wtLXTjU6rqLcx2OPQffupruTxMQlREYm0qNHD379c1z3Dh060KZNG27dusX+/fvZvXs3\nADVr1mT9+vUA+Pr6UqtWLezt7bGzs8vz8KuilCQ2O+SI1usjtZyflnO7csWY57WhQ4cyZ84cTp06\nxcyZMxkyZEi+2+7cuZOYmBg2bNjA559/zvbt24s52gen5XOn5dwszWYLDkUpKfbs2UPv3r0B6Nev\nn/l5jb+rUaMGAFWrVqV3794Frqcots5mC47sh160Ssv5aTk3F5eQPK/Vr1+frVu3ArBlyxY8PT3z\nrJOWlmYeiuTmzZts2rQp17AltkLL507LuVmaauNQlEKys4MDB8Jp1WorFy9ewM3Njffee4+vvvqK\nl156iTt37lCuXDm++uorgDwTRvXp0weAjIwMnn76aTp16mTNdBTlodlsryqj0ajpbwhazk+rud29\nC/36GTlyJISVK8HX19oRFT2tnjvQdm4lfnRcRdEqe3vTU+j//jd06AB/Ps+qKI8cm73jUBRbdugQ\n9OsHQUGmp9DLlrV2RMqjTN1xKEoJ4O1terL86lUIDITff7d2RIpiOTZbcGi9z7WW83tUcnNygmXL\nYPBgaNnSNFRJSfeonDvln7HZgkNRSgKdDl55BX78EV56CSZOhIwMa0elKMXrnm0cqamp/PHHH9Sv\nX98iQySoNg6lJEtNhYEDTQXHkiVQvbq1I1IeFTbTxjF//nyaNGnC6NGjadiwIT/++KPFglKUkqhq\nVdi40dRgHhAANjiiiKIUiQILjpkzZxIfH8/u3bvZvXs3U6ZMsWRcmq+P1HJ+j3Judnbw3numuT36\n9YPp06Ek3UQ/yudOKbwCC44yZcpQtWpVAOrWrcudO3csFpSilHRdusCePabG8759Tb2vFEUrCmzj\nqFq1KuHh4eZ6s2XLlvHUU08hIuh0OubMmVP0wag2DkVj7tyB116DTZtM83n4+Vk7IkWLLH3tLLDg\niIyMRKfTAeQJSKfTMXjw4KIPRhUcikZ9952p99XHH0NEhLWjUbTGZgoOa1BjVWmDyi1/8fGmaqug\nIJgzB8qVK9rYioI6dyWTzc0AeOzYMT755BMSExPJ+LODuk6nY8uWLcUenKJoSZMmpqfNhw+H1q1N\nVVd161o7KkV5cPe94/D19eXFF1+kadOm2NnZmTbS6fD39y/6YFRVlfIIEIHPPoPJk2H+fOjZ09oR\nKSWdzVVV+fv7s3//fssEowoO5RESHQ1hYaaHBt9/H0qr2XGUh2QzDwBeunSJixcv0qNHDz7//HOS\nkpK4dOmS+ae4ab3PtZbzU7kVTsuWsH8/HDgAHTtCcnKR7fqhqXOnFEaB33GaNm1q7lUF8Mknn5h/\n1+l0/K6GA1WUf6xqVdiwwVRt5e9vGqokONjaUSnKvdlsrypFedRs3Gjqqjt2LLz+umkARUUpDJtr\n47AkVXAoj7pTp6B/f6hZE77+GiwwtqiiATbTxmFtWq+P1HJ+KreH9/jjsG0b1KplGigxNrZYD5eH\nOndKYRRLwTFkyBBcXV3x8fExvzZp0iRq166NwWDAYDCwcePG4ji0opR4Dg5/ddcNDYUFC6wdkaLk\nVixVVdu3b8fR0ZFnn32WX3/9FYB3330XJycnXnvttYKDUVVVipLL4cOmUXZbtTIVJrb4tLlifZqo\nqgoKCqJSpUp5XleFgqI8GC8v0yi7aWmmuc1PnrR2RIpSiCFHitKnn37KokWLCAgIYPr06fnOKhgR\nEYG7uzuJiYno9Xr0er15fJnsOkotLOesb7WFeIpy+e85WjueolyOjY1lzJgxFj/+d9/BmDFG/P0h\nMjKEXr20lZ8llmfNmqWZ64nRaCQyMhIAd3d3LE4KkJaWJjNmzJCRI0fK3Llz5e7duwWtmq+EhATx\n9vY2L6ekpEhWVpZkZWXJW2+9JUOGDMmzTc5woqKiHuh4JY2W81O5FZ/oaJHHHxcZN07kAf9LFoq1\n8ytOWs7tHpfyYlFgG0dYWBhlypShTZs2bNiwAXd3d2bPnl3oAikxMZEePXqY2zgK855q41CU+7tw\nAZ55Bm7dgqVLoUYNa0ekWJvNjI575MgR84V92LBhNGvW7B8dKCkpiRp//oWvWrUqV48rRVEK77HH\nYP160/hWAQGmuT7atrV2VMqjpMDG8dI5Rlwr/YCjr4WHhxMYGMixY8dwc3NjwYIFvPHGG/j6+uLn\n58fWrVuZOXPmPfeRs75ci7Scn8qt+NnZwTvvmLrqDhgA06YVzdzmtpJfcdBybpZWYIkQFxeHk5OT\nefnWrVvmZZ1Ox7Vr1wrc6ZIlS/K8NmTIkH8Sp6Io+XjiCdMcH/37w65dsHChetpcKX5qyBFF0YD0\ndNP4VuvXmyaIMhisHZFiSZp4jkNRFMsqU8Y0He0HH0CnTvCf/1g7IkXLbLbg0Hp9pJbzU7lZz1NP\nmca6mj4dhgwx9bx6ELae3z+h5dwszWYLDkVRHk7jxqanze/cMQ1V8ttv1o5I0RrVxqEoGiUCX3wB\nkybBV19Br17WjkgpLqqNQ1GUIqHTwciRsG4djBkD48ZBRsa9t8lvZOtx48bRuHFj/Pz86NOnD1ev\nXi1w+8zMTAwGAz169CiqNBQbZLMFh9brI7Wcn8rNtjRvbprb/NAhaN8ekpIKXlev1+eZ8qBTp07E\nx8dz8OBBPD09mTJlSoHbz549Gy8vr1zTTtuKknjubJXNFhyKohSdKlVMXXVDQ01Pmxd0DfX19c0z\nsnVoaCilSpkuFS1atODMmTP5bnvmzBl++uknhg0bpqqcNc5mC47sESG1Ssv5qdxsU6lS8K9/QWQk\nhIebnjbPysq9zv3yW7BgAV27ds33vVdffZWPP/7YXMjYmpJ87myNbZ5hRVGKTWioqdfV6tXQuzdc\nvly47T744APKlCnDwIED87y3bt06qlWrhsFgUHcbjwCbLTi0Xh+p5fxUbrbPzQ22bgUPD1PVVUyM\n6fWuXbvSrFkzTpw4YV53xYoV1KpVi7fffpvXX3893/2tXbuWefPm4eDgQGhoKOvWraN58+aWSKXQ\ntHLubIHNFhyKohSvMmVg1iyYMsU05tV//gOdO3c2TxCU7cqVK5QrV47WrVvj4OCQ776+/PJL0tPT\nuXPnDps2bcLBwYHvv//eAlko1qCe41AUhaNHTXceTzwRzvbtv5Camkrt2rV59913mTJlCunp6Vy6\ndImaNWvSoUMH/u///o9z584xfPhw1q9fn2tfn3zyCVOmTOHixYtWyubRY+lrpyo4FEUBwNUV4uLg\n1q38J1pr164d06dPp2nTpvfcz5AhQwgICGDkyJHFGa6Sg3oA8E9ar4/Ucn4qt5Jr1y7jP9o+PT2d\ntWvX0r9//6IIp0hp/dxZks0WHIqilDwbNmzA39+fqlWrWjsUpRjZbMGh9T7XWs5P5VZyeXiE3HMm\nwftVhyxZsoTw8PAijqpoaP3cWZLNFhz5jZlz6dIlQkND8fT0pFOnTly5ciXPdseOHcNgMJh/nJ2d\nmTNnjiVDtznqs1QKo08faNkynPr1A4mPP4aLixtvvrmA5ctX4+bmRnR0NN26daNLly4AnDt3jm7d\nupm3v3nzJps3b6ZPnz7WSkGxFLEhOcOZPXu2HDhwQLy9vc2vjRs3TqZNmyYiIlOnTpU33njjnvvL\nzMyU6tWry6lTp4on4H8gKirKYsfatm2bRT9LS+ZmaVrOTURky5Yo+f13kcWLRV56SaRpU5Hy5UVa\ntBAZM0Zk2TKR06etHeXD0fK5s/Sl3GbvOPIbM2fNmjUMHjwYgMGDB7N69ep77mPz5s3Uq1cPNze3\nYouzJAgKClKfpVIoOp3pocCBA+Gzz0yDI54/bxqexNUVFi+Gpk1NDxCGhcHMmRAdbZr7Q3l02HR3\n3MTE3N0CK1WqxOU/x0cQESpXrmxezo/qFvgX9VkqRUUEfv8ddu2C3btNP8ePg5+faeKoVq0gMBBq\n1rR2pI8OS3fHLW2xIxUxnU53z6Gbs7sFTps2zYJRlUzqs1QehE4H9eqZfgYNMr124wbs3WsqRBYu\nhBEjoEKFvwqSVq1Arzc9ra6UfDZbVZVfn2tXV1eSk5MBSEpKolq1agVub+vdAq3dp7w4P0tr51ac\ntJwbPHx+jo7Qrh28+SasXQupqbB5M3TpAkeOwPDhULkytGljmlDqhx/uPS9IcTAajcyePRsfHx+8\nvb2ZPXt2nnUuX75M79698fPzo0WLFsTHxwNw+/ZtWrRogV6vx8vLi4kTJ1o2eBtjk3ccKTdSMCYa\nqZpelat3rrIifgUADQMbMvajsfQa2ovV81fTqE0j83t/N2vuLPTB+gLft7b4xHhS41Mtciw3Zzeq\nUz3Xaz179mThwoW88cYbLFy4kF73mFfUlrtYKrZJp4MGDUw/fzalcf26aVTe3btN42INHw4VK+a+\nK/HzA3v74okpISGB+fPns3fvXuzt7encuTPdu3enXr165nU+/PBDmjZtyqpVqzh27BgvvfQSmzdv\npmzZskRFRVG+fHkyMjJo06YNO3bsoE2bNsUTrI2zyTaOuJQ4uvftTurhVO5cu0NZl7I0CWtCzWY1\niZ4ZTdqFNMpXLU/LV1tSpkIZbl26xf4v99NmoukkZtzO4KeXfqLLZ12wL1dMf4UlyIapG8j4PYPM\nm5lUd63Oe++9x5NPPklYWBinTp3C3d2d5cuX4+Likmf8oZs3b1KnTh0SEhJwcnKyciaKloiY2kZy\ntpUkJJga37PbSVq1gnvcDD+QlStXsnHjRubPnw/A+++/j4ODA+PGjTOv0717dyZMmGAuEOrXr8/u\n3btz3W2npaXRtm1bFi5ciJeXV9EE9w+psapsJxzNSM9M58t9X/L+9vfp2qAr74W8h5uz6h2l2J6r\nV/+6K9m929Rjq3Ll3Hclvr5Q+iHqSo4ePcqTTz7J7t27KVu2LB06dKB58+a5qqzeeustbt26xYwZ\nM9izZw+tW7dmz549GAwGMjMz8ff35+TJk7z44ot89NFHRZj5P6OJsaoe9oGznFRdctEpY1eG0S1G\nc2L0CWo51UL/pZ4Jmydw5fa9z8HD0vK503JuYP38nJ1NE039+9+wYQNcvAjr1pnaT2JiTI3xlSpB\nSAhMnPhXe0phJCcn88Ybb9CpUye6dOmCwWDIM1vhhAkTuHLlCgaDgc8++wyDwYCdnR0AdnZ2xMbG\ncubMGbZt22b1z8qaiqXgeO655/JMeD916lRCQ0M5fvw4HTp0YOrUqcVxaOUeKjpU5P327xM3Io4L\naRfw/NSTmbtncidDdcJXbFOpUtC4MQwdCvPnQ3w8nD5tKjQcHEzPmmS3pTz7LHzxBcTGQkZG/vsb\nMmQI+/btY+vWrbi4uNCwYcNc7zs5ObFgwQJiYmJYtGgRqamp1K1bN9c6zs7OdOvWjX379hVX2rav\nuJ4sTEhIyPWkcsOGDSU5OVlERJKSkqRhw4Z5tinGcJR8HEo5JN2/6y4eszzku7jvJDMr09ohKcoD\ny8wUOXRI5KuvRJ57TqRRIxEnJ5F27UTefFNk3TqRCxdM66akpIiIyB9//CGNGjWSq1ev5trXlStX\n5M6dOyIi8tVXX8ngwYNFRCQ1NVUuX74sIiJpaWkSFBQkmzdvtkyChWDpa6fFelWlpKTg6uoKmLqC\npqSk5LteREQE7u7uALi4uKDX682Dk2XfGqrlollOPZzK2Bpj0bXSMe7ncUyKnMQLAS/wWvhrNhGf\nWlbLhV1u0gRSU400aAALFoRw6RLMm2ckPh5mzQohOhpefdXIjz++QkZGBvb29jz//PMcOHCAY8eO\nAdCwYUPi4+OZM2cOOp0OV1dXc8N5UlISffv2JSsri/LlyzNo0CDs7OwwGo1WyddoNJpnasy+XlpU\ncZVIf7/jcHFxyfV+pUqV8myTMxwtjysjYnv5ZWVlybJDy6Tu7LrS5dsuEpcc99D7srXcipKWcxPR\nbn6jRomMHh1l7TCKTTFeyvNlsQcAH+SBM8XydDodYU3COPLSEbrU70LHbzoy5MchnLl2xtqhKYpi\nYyxWcGQ/cAbc94Ez0P7Y+baaX3YPrOOjjlPDqQZ+c/2Y+MvEB+qBZau5FQUt5wbazq9BgxBrh6AZ\nxVJwhIeHExgYyLFjx3Bzc+Prr79mwoQJ/Pzzz3h6erJlyxYmTJhQHIdWiohzWWc+aP8BcSPiSL2Z\niuennsyKnqV6YCmKYrsPAOZsdNKikpbfofOHmLB5AodTD/NB+w8Y4D2AUrr8v3eUtNwehJZzA+3m\nN3o06HRG5swJsXYoxUITDwAq2uNdzZt1A9ex4MkFzIieQfN5zYlKiLJ2WIqiWIHN3nEotitLslgR\nv4I3t7xJo8caMbXDVHxcfe6/oaJYyejR4Olp+leL1B2HYvNK6UoxwHsAR146whP1nlA9sBTlEWOz\nBUf2wy5apYX8ytiV4eUWL3N81HGqO1bHb64fb/7yJus3rbd2aMVGC+ftXrSc34kTRmuHoBk2W3Ao\nJYdzWWc+7PAhB0ccJOVmCs+seobZ0bNJz0y3dmiKohQD1cahFLlfU35lwi8TOHrhKB+2/5D+TfoX\n2ANLUSxBtXEULfW/WSlyPq4+rB+4nvk95vPxro9pMb8FxkSjtcNSFKWI2GzBoeW6VtB2ftm5tfNo\nx57hexjbaixDfhxC9++6c+j8IesG9w9p+byBtvNTbRxFx2YLDkUbSulK8ZT3Uxx56QihdUPpsKgD\nQ9cM5ey1s9YOTVGUh6TaOBSLunr7KtN2TuPL/V8yImAE4wPH41zW2dphKRqn2jiKlrrjUCwqZw+s\npOtJeH7myZz/zVE9sBSlBLHZgkPLda2g7fwKk1vtirVZ8OQCNg/azH9P/hevz71YHr/c5u84tXze\nQNv5qTaOomOzBYfyaMjugfVVj6/4aOdHD90D68qVK/Tr14/GjRvj5eVFdHR0rvd//PFH/Pz8MBgM\n+Pv7s2XLFgCOHTuGwWAw/zg7OzNnzhybOZai2CSLTht1HzYWjmJhmVmZ8l3cd+Ixy0O6Le4mh1IO\nFXrbZ599Vv7zn/+IiMjdu3flypUrud6/ceOG+fe4uDipV69e3uNnZkr16tXl1KlTNnMspWiMGiUy\nZ461oyg+lr52qjsOxWaU0pUi3CecIy8doWPdjrRb2I5ha4bdtwfW1atX2b59O0OGDAGgdOnSODvn\nbnCvUKGC+fcbN27w2GOP5dnP5s2bqVevHm5ubjZxLEWxVTZbcGi5rhW0nd8/zc2htANjWo7h+Ojj\nPFb+MXzn+vLWlre4evtqvusnJCRQtWpVnnvuOZo2bcrw4cNJS0vLs97q1atp3LgxXbp0ybeKaOnS\npQwcOPCesa1YscJix7IGLf9dqjaOomOzBYeiuJR1YWrHqcS+EMu56+fw/MyTT//3aZ4eWBkZGRw4\ncICRI0dy4MABKlSowNSpU/Psr1evXhw5coS1a9cyaNCgXO+lp6ezdu1a+vfvf8+YMjMzLXYsRbFV\nNltwaHEWspy0nF9R5+bm7MbXT37Nz4N+ZsNvG/L0wKpduza1a9emWbNmAPTr148DBw4UuL+goCAy\nMjK4ePGi+bUNGzbg7+9P1apV7xnLk08+abFjWYOW/y7VnONFp7S1A1CUwvJ19eWnp3/il99/Yfzm\n8UzfPZ0P2n9AvUr1qFqjKlv2bsGjvgcr162kdr3aJFxOMG/7R8IfPO7+ODqdjkMHD5GRlcG1Ute4\ndvkaAPMXzqdjz465tslPJZdKuLm5cfz4cTw9Pdm8eTNNmjTJtc7JkyepW7cuOp3OXKhUqVLF/P6S\nJUsIDw8vqo9FUSzOZp8c1+rcx9m0nJ8lcsuSLJYeWspHOz/i6p2rpJ9N58LSC0imYP+YPY+FP8bN\nmJsAOAU6cfWXq9zYewOdnQ6dg47KvSrj8LiDaV93sjjz3hlq/6s2pcre+yb8wuELhPmHEfNVDJl3\nM6lXrx4LFixg2bJlALzwwgt89NFHLFq0CHt7exwdHZkxY4b5DuXmzZvUqVOHhIQEnJycivETejha\n/btUc44XLXXHoZRIpXSlGOgzkIE+ORqYP7rHBq/cZ4fjC3fc5euXszFjI2cGnGFim4mMbDYSh9IO\nvPDCC3/tavx4xo/Pf4cVKlTgwoULhTuYotgom73jUBRbduj8ISZsnkB8ajzvt3ufcJ9wNeeIDVNj\nVRUt9Zeeg52dXa4nez/6yPQVNiQkhP379xfpsWbNmsWtW7fMy926dePatWtFeoyHMWnSJKZPn37P\n12/fvk1oaCjvvfceAK1bt37o4y1cuJCkpCTz8vDhwzly5EihtjUajTg7O+c6Z9lPaRc372rerBu4\njsgnI5mzZw7+X/mz6eQmixxbUazNZgsOa/QnL1++PDExMeaf7OoGnU6HTqcr0mNNmzYtV///9evX\nU7FixSI9xsMoKM/szyA9PZ2+ffvSrFkz/v3vfwOwc+fOXOs+yLmLjIzk3Llz5uV58+bRuHHjQm/f\ntm3bXOesffv2hd62IJmZmQW+9/fc2rq3JXpoNG8FvcWon0YR+k0oB5IK7mVl6x6F5zgyMzMxGAz0\n6NEjzzoXLlygc+fO6PV6vL29iYyMzPX+vbZ9lNhswWGrNm3aRGBgIP7+/oSFhXHz5k02btxIWFiY\neR2j0Wj+w3rxxRdp1qwZ3t7eTJo0CYA5c+Zw8eJF2rVrR4cOHQBwd3fn0qVLAMyYMQMfHx98fHyY\nPXs2AImJiTRu3Jjnn38eb29vnnjiCW7fvp0nvrVr19KyZUuaNm1KaGgo58+fB0x3DEOGDKFdu3bU\nq1ePTz/91LzNBx98QMOGDQkKCuLYsWMF5n737l2eeuopGjZsyIcffmh+3dHR0Zx3SEgIkyZNonHj\nxjzzzDPmdfbv309ISAgBAQF07tyZ5ORkVq5cyb59+3j66adp2rQpt2/fznV3t3HjRvz9/dHr9XTs\n2DHfmPK7Pb/XZ3Xy5Em6dOlCQEAAwcHB5nwjIiIYMWIELVu25I033uDkyZO0bNkSX19f3n77bXND\n9pQpU/jxxx/Nx3r66adZu3Yt/bz6ET8ynt6NetPtu248/cPT9+2hpVjH7Nmz8fLyyvdL0meffYbB\nYCA2Nhaj0cjYsWPJyMgo1LaPFIsOcHIf1g7Hzs5O9Hq9+Wf58uUiIhISEiL79++X1NRUCQ4OlrS0\nNBERmTp1qrz33nuSkZEhjz/+uPn1ESNGyOLFi0VE5NKlSyIikpGRISEhIfLrr7+KiIi7u7tcvHjR\nfOzs5X379omPj4+kpaXJjRs3pEmTJhITEyMJCQlSunRpOXjwoIiIhIWFybfffpsnh8uXL5t/nzdv\nnowdO1ZERN555x1p3bq1pKeny4ULF6RKlSqSkZFhPt6tW7fk2rVrUr9+fZk+fXqe/b7zzjtSuXJl\neeqpp/K85+joKCIiUVFR4uzsLGfPnpWsrCxp1aqV7NixQ9LT06VVq1Zy4cIFERFZunSpDBkyJNdn\nm7rHrnwAAB4NSURBVC17+fz58+Lm5iaJiYl58sqWfbyc5+z333+/52fVvn17OXHihIiIREdHS/v2\n7UVEZPDgwdKjRw/JysoSEZFu3brJ0qVLRURk7ty55hy3bt0qvXr1EhGRK1euiIeHh2RmZuaK6/qd\n6zIpapJUnlZZXtnwiqTeTM0Tu2JZ2WNVnT59Wjp06CBbtmyR7t2751lv7ty5MnLkSBEROXnypDRo\n0MD83v22tSZLXzst3qvK3d2dihUrYmdnh729PXv27LF0CAUqV64cMTEx+b4nIkRHR3P48GECAwMB\n0xPAgYGB2NnZ0blzZ9asWUPfvn356aef+OSTTwBYtmwZ8+bNIyMjg6SkJA4fPoy3t3eBx9ixYwd9\n+vShXLlyAPTp04ft27fTs2dPPDw88PX1BcDf35/ExMQ8+zh9+jRhYWEkJyeTnp5O3bp1AVNVU7du\n3bC3t6dKlSpUq1aN5ORktm/fTp8+fShbtixly5alZ8+e+X6L1+l0tGnThl27dnHixAkaNGiQbw7N\nmzenZs2aAOj1ehITE3F2diY+Pt5815CZmWleJzvv/D7r4OBg6tSpA4CLi0u+xwsKCmLt2rW5XktM\nTMz3s7p58ya7du3K9cR2enq6Ob/+/fubv0lGR0ezZs0aAMLDw3n99dcBCA4OZuTIkVy4cIGVK1fS\nr18/SpXKfePuWMaRd0LeYUTACN7b9h6NPmvEa61eY0zLMZS3L59vHoplvPrqq3z88ccFticOHz6c\n9u3bU7NmTa5fv87y5csLve2jxOJVVTqdDqPRSExMzD0LDVutaw0NDTXXp8fHxzNv3jwAnnrqKZYv\nX05UVBQBAQFUqFCBhIQEpk+fzpYtWzh48CDdunUzV5nkV80EeXtHiIj5Yubg4GB+3c7OLtctdLbR\no0fz8ssvExcXx5dffpmrAb5MmTJ5ts/veAUJDg5m5syZdOnSheTk5HzXcXBwMJ+7nDE2adLE/LnF\nxcWxcePGXDnn9zn8E3//rDIzM8nKyqJSpUq52kTi4+PN65Uvf/+LutFo5Nlnn+Wbb74hMjLSPNhh\nflwdXfm86+fsHrqb2ORYGnzagHn755GRlfe82Qpb/X9XFDZtmkK1atUwGAwF/p1/+OGH6PV6zp07\nR2xsLC+99BLXr19n3bp19932UWKVNo6S+MHrdDpatmzJzp07OXnyJGB6mOvEiROAqZH2wIEDzJs3\nz/xU8LVr16hQoQIVK1YkJSWFDRs2mPdXvnz5PN9cdDodQUFBrF69mlu3bnHz5k1Wr15NUFBQoT+z\na9eumb/N52zYK+guIjg4mNWrV3P79m3zf5B7XbT79OnD66+/TufOnbl6Nf9BB/9+jIYNG5Kammqe\nt+Lu3bscPnwYACcnp3w/h5YtW7Jt2zbzXVV2+8/DEhGcnJzw8PBg5cqV5tfi4uLyXb9ly5bm9ZYu\nXZrrvYiICGbNmoVOp6NRo0b3PXaDKg1Y3n85qwasYvGvi/H5wofVR1eXyP8HJVlSUjxr1qzBw8OD\n8PBwtmzZwrPPPptrnZx3pPXq1cPDw4OjR4+ya9eu+277KLF4VZVOp6Njx47Y2dnxwgsvMHz48Fzv\nR0RE4O7uDkBsbCx6vd78JGv2t6HiWk5LS6NBgwbmxt4mTZowbNgwc2yHDh1izJgxhIeHc+fOHW7e\nvMnQoUOZOHEipUqVwmAwsH79ehYtWgTA5cuXqVGjBo0aNcLNzY2GDRuau5q++uqrBAcH89hjj5mH\npdixYwcVK1YkIiKC5s2bc/PmTbp164afnx+JiYmkpaXlerI3MTEx17LRaKRv377079+fSpUq0aBB\nA/PFXafTcfLkyVzr7969G1dXVwYMGICfnx8ODg7mqqH8Pp/s7UeMGEFKSgpt27blo48+Mhc0sbGx\nXLp0ybz+2bNncXR0xN7enpUrVzJ48GBu3LhB2bJlefXVVzl//jwBAQGMGDGC8uXLM3XqVK5cuQL/\n396dR0VxpW0AfxrCooASDYsjKgoCNvSGCFFEWYJIWFxw3KIBYWIwg6MzEzVmEiWREDUah6iTzCfC\nMDFRj0uiSEQl0gENiAqICioKCG6MqOwgNLzfHx06tCyCYtOU93cOR7q76tZ9utu61K2qewG89tpr\nCAsLw5QpU9C/f3+YmJhg9erVSvXJzs5GcnIyJBIJAPkQ5gsXLkRgYKDiyLZFy+OlS5di586diIiI\nQEVFBdzd3bFz504AwOXLlzF48GC4urrin//8J/z9/fHhhx8iICAAAwcOVJRnbGwMPp8PPp/f5v3v\n9PuVX4u1I9aizqwOq5JW4eOYj/Guw7sImx3WpfVV9biFutSnpx4PGfInvP/+nzBnjitSUn7B6tWr\nlY4YpVIp9PX1kZSUBGdnZxw8eBA5OTmwsLBAZGQkpkyZAkD+Xdq0aROCg4O79fn35GOpVKr4w7Bl\nf6lSKj2jQkR37twhIqL//e9/JBKJKCUlRfFaL1SHYdrVcqEDEdHu3bsVJ8SJiGpqasjCwoIqKyuf\nuXxZk4xis2Jp2JfDaPqe6ZR3P++56st0TiolmjmTaMgQIlNTookTpTRmjB/98gtRVNQ39M033xAR\n0f3798nX15eEQiHZ2dkpLnJRLktKfn5+qo7QKVXvO3t1Tx0eHk6bNm1SPG4dPjk5uRdqpDpczseF\nbKmpqSQSiUgoFNLkyZPpxo0bRES0adMmGjFiBEVFRfXIdmobamnjqY302sbXaHH8YrpdebtHyn1W\nXPjsOpKcnEzNzUQ3bxLt2UO0fDnR668T9e9PZG9P9N57RN9+S5SfT/TbxXV9hqobDpV2VdXW1qKp\nqQkGBgaoqanB8ePHsXbtWlVWgWG6ZOLEicjOzm7zfEdXsz2rflr9sMJ5BULsQ7D+1HoIvhZgicMS\nrHReiQE6vX9DKNfweMDw4fKfOXPkz9XXA9nZQFoaEB8PfPghUFcHvP46MH68/N9x4wA1HJOy16h0\nrKrCwkLMmDEDgHzynbfeekvRbw2wsaoYpriiGGuS1+Do9aP4h8s/EOoQCm1N7aevyPSo27eB9HT5\nT1qavGGxsFBuTKysgCeuxO41qt53skEOGUYN5ZTmYPXPq5F3Pw+fuX+GOXZz2CCKvaihAbhw4feG\nJD0dKC8HnJx+b0gcHYEObjd64dggh7/h8vXkALfzsWzPT2giRML8BMRMi8GW9C0Yt2MckgqSXvh2\n2WfXPm1teXfV0qXA998DBQVAbi4QGgrU1gKRkcCwYYCtLRASAkRHA5cuAc3NPVf/p3FycoJYLAaf\nz1fqyWntL3/5C0aPHg2RSKR0s3NUVBQEAgHs7OwUwxx1hs3HwTBqzNXcFWf+dAb7cvch9EgoLAZZ\nYMMbGyA2Ffd21V56pqbAtGnyHwCQyYCLF+VHIykpwMaNQGmp/Eik5ajk9deBQYNeTH2Sk5PRv39/\nyGQyTJw4EadOncLEiRMVr//000+4fv068vPzcebMGSxZsgTp6em4dOkSoqOjcfbsWWhpaWHq1Knw\n9fWFhYVFh9tiXVUM00c0NDVgx/kdiEiNwBuj3sA6t3UwNzTv7WoxnSgrA86c+b176+xZeYPT+lyJ\nnR3wynP+Cd9631lbW4vJkycjLi4OfD5fsUxoaCjc3Nww57erAmxsbCCVSpGamopjx44hOjoaABAR\nEQEdHR2sWLGiw+2pbVcVwzDKtDW18WfHP+Na2DVYvGqBsf83Fn879jc8qH3Q21VjOvDaa4CPDxAR\nASQlAQ8fAvv3A87OQEYGMG8e8OqrgJub/Gquw4eB3wa07rbm5maIxWKYmJjAzc1NqdEA5DfkDhs2\nTPHYzMwMd+7cgUAgQGpqKh4+fIja2lokJCTg1q1bnW5LbRsOLve1AtzOx7K9WAY6Bgh3Dcfl9y6j\nXlYPm+02WH9qPeoa656+8lOoQ74XRR2yaWoCAgGweDEQEwPk5QHFxcCqVfLzKNu3y6/WsrAAFiwA\ntm0Dzp8HGhufXraGhgays7Nx69YtpKSktJu3vR4dGxsbrFq1ClOmTIG3tzckEkmbgTvbbKurgRmG\nUS+m+qb4l8+/cDr4NM7fPQ+rbVbYmblTrQdRZNp69VVg6lQgPBw4dkx+VHLkCODuDuTkAEFB8mVc\nXICVK4GDB4FWk2a2MXDgQPj4+ODcuXNKzw8dOhQlJSWKx7du3cLQoUMBAMHBwTh37hx++eUXGBoa\nwtrauvNKq/R2w6dQs+owTJ+SXpJOk2InEX87nw5fOayYW4Tp+yoqiE6cIFq3jujNN4kGDSIaPpxo\nzhyiLVvk+86WOWtqa2vJxcWFkpKSlMpISEggb29vIiJKS0sjJycnxWulpaVERHTz5k2ysbGhioqK\nTuujVntq1nAwzPNpbm6m+KvxZLvdllxiXCitJK1b6xcXF5Orqyvx+XyytbXtcGiVpUuXkqWlJQmF\nQsrMzCQioitXrihNqjVgwIAeG5qlJ3ApW3Mz0dWrRHFxRKGh8n2nvr4+6ejokI6ODvn7+xORfGKq\nlnG4iIgEAgFpaWmRrq6uYhyuK1eukJ6eHunq6pKuri7p6ek9NZta7anBxqriBJat98maZBSTGUNm\nX5rRzL0z6cr9K11a78CBA5SVlUVERFVVVWRlZUW5ublKy7T+yzU9PV3pL9cWTU1NZGpqSsXFxc+Z\npOdwORsAlWZj5zgYhoM0NTSxSLII18KuwWmoEybGTkTokVDcreqkcxzAoEGDIBbL7xHR19fHmDFj\ncOfOHaVlDh8+jMDAQADym87Ky8tRWlqqtExSUhIsLCyUruLpbVzOBkCl2dS24WgZg56ruJyPZVMf\n/bT6YaXzSlwNuwp9bX3YfW2HNclrUPW4qt3lW+crKipCVlYWnJyclJZp77LOJy/f3LNnD+bPn99z\nQXoAl7O1popsattwMAzTcwb1G4RNUzYhc3EmisqLMHrraGzL2IaGpoZ2l6+ursasWbMQFRWlmNis\nNXriss7Ws0Y2NDQgPj5eaW53dcKy/e5Zs6ltw6EO11y/SFzOx7KprxGGI/DfGf/FsQXHkJCfAP52\nPvZe2otmkg+qJJVK0djYiICAACxYsADTp09vU0Znl3UCwNGjRzF27FgYGRm9+EDdwOVsAFSajY1V\nxTAvIZGpCEffOoqThSex8sRKbErbhAi3CJRVlGH2wtkYOmoo/N72w42HN9qsO85tHL6J/gbjpoxD\n1rks9NPvh2qtalQ/rAYA7IjbAQ9/j3bX7U23K25zNhsAhISEgM/nY/ny5e2+7u/vj23btmHu3LlI\nT0+HoaEhTExMFK/v3r0b8+bN69K22FhVDPOSa6Zm7Lu8Dxt/3Yh7ufdw56s70P7D73OADPIdBNkj\n+U2FA5zlk0uV7S9DbV4tNLQ1YDTfCDrDdORlPW5G8SfFGL5mODR01atDo76gnrPZCpYVgMfjQSgU\nKrqfIiMjUVxcDAB49913AQBhYWFITEyEnp4eYmNjYW9vDwCoqanBiBEjUFhYCIMuzFjFGg6GYZg+\njs3H8Zu+3pf8NFzOx7L1XVzOx+Vsqqa2DQfDMAyjnlhXFcMwTB/HuqoYhmEYtaa2DQfX+yO5nI9l\n67u4nI/L2VRNbRsOhmEYRj2xcxwMwzB9HDvHwTAMw6g1tW04uN4fyeV8LFvfxeV8XM6maiptOBIT\nE2FjY4PRo0djw4YNnS6bnZ2tolr1Di7nY9n6Li7n43I2VVNZw9HU1KQYJyU3Nxe7d+9GXl5eh8uX\nl5erqmq9gsv5WLa+i8v5uJxN1VTWcGRkZMDS0hLm5ubQ0tLC3LlzcejQIVVtnmEYhukhKms42pt9\n6vbt2x0uX1RUpIJa9R4u52PZ+i4u5+NyNlVT2eW4Bw4cQGJiInbs2AEA2LVrF86cOYOtW7f+XplW\ns1ExDMMwXafKy3FVNpHTk7NPlZSUwMzMTGkZdg8HwzCM+lNZV5WDgwPy8/NRVFSEhoYG7N27F/7+\n/qraPMMwDNNDVHbE8corr2Dbtm3w8vJCU1MTQkJCMGbMGFVtnmEYhukhKr2Pw9vbG1evXsX169ex\nevXqDpfrzv0e6i44OBgmJiYQCASK5x4+fAhPT09YWVlhypQpffYywZKSEri5ucHW1hZ2dnb46quv\nAHAnX319PZycnCAWi8Hn8xXfWa7kA+SXyUskEvj5+QHgTjZzc3MIhUJIJBI4OjoC4E42QH5p8axZ\nszBmzBjw+XycOXNGpfnU7s7x7t7voe4WLVqExMREpefWr18PT09PXLt2DR4eHli/fn0v1e75aGlp\nYcuWLbh8+TLS09Oxfft25OXlcSafrq4ukpOTkZ2djZycHCQnJ+PUqVOcyQcAUVFR4PP5igtTuJKN\nx+NBKpUiKysLGRkZALiTDQCWLVuGN998E3l5ecjJyYGNjY1q85Ga+fXXX8nLy0vx+PPPP6fPP/+8\nF2v0/AoLC8nOzk7x2Nramu7du0dERHfv3iVra+veqlqPmjZtGp04cYKT+WpqasjBwYEuXbrEmXwl\nJSXk4eFBJ0+eJF9fXyLiznfT3NycysrKlJ7jSrby8nIaOXJkm+dVmU/tjji6e79HX1RaWgoTExMA\ngImJCUpLS3u5Rs+vqKgIWVlZcHJy4lS+5uZmiMVimJiYKLrluJLvr3/9K7744gtoaPy+G+BKNh6P\nhzfeeAMODg6KWwC4kq2wsBBGRkZYtGgR7O3t8c4776Cmpkal+dSu4XjZ7uXg8Xh9PnN1dTUCAgIQ\nFRUFAwMDpdf6ej4NDQ1kZ2fj1q1bSElJQXJystLrfTXfkSNHYGxsDIlE0uFl8H01GwCcPn0aWVlZ\nOHr0KLZv347U1FSl1/tyNplMhszMTLz33nvIzMyEnp5em26pF51P7RqOrtzv0deZmJjg3r17AIC7\nd+/C2Ni4l2v07BobGxEQEICFCxdi+vTpALiVr8XAgQPh4+OD8+fPcyLfr7/+isOHD2PkyJGYN28e\nTp48iYULF3IiGwAMGTIEAGBkZIQZM2YgIyODM9nMzMxgZmaGcePGAQBmzZqFzMxMmJqaqiyf2jUc\nL8P9Hv7+/oiLiwMAxMXFKXa4fQ0RISQkBHw+H8uXL1c8z5V8ZWVliitT6urqcOLECUgkEk7ki4yM\nRElJCQoLC7Fnzx64u7vj22+/5US22tpaVFVVAQBqampw/PhxCAQCTmQDAFNTUwwbNgzXrl0DACQl\nJcHW1hZ+fn6qy/fCzp48h59++omsrKzIwsKCIiMje7s6z2Xu3Lk0ZMgQ0tLSIjMzM4qJiaEHDx6Q\nh4cHjR49mjw9PenRo0e9Xc1nkpqaSjwej0QiEYnFYhKLxXT06FHO5MvJySGJREIikYgEAgFt3LiR\niIgz+VpIpVLy8/MjIm5kKygoIJFIRCKRiGxtbRX7EC5ka5GdnU0ODg4kFAppxowZVF5ertJ8ajV1\nLMMwDKP+1K6rimEYhlFvrOFgGIZhuoU1HAzDMEy3sIaDYRiG6RbWcLxkwsPDsXnzZgDA2rVr8fPP\nP3e47KFDh9RunDCpVKoYkE/Vzp8/j2XLlvVIWfv27QOfz4eHh0ePlNdT4uPjnzqw6M2bN7F79+4u\nlffVV1+Bz+djwYIFavl9Yp4NazheMq3vJv3kk0863XH98MMPyM3NVUW1+oSxY8ciKiqqR8rauXMn\noqOj2zTcMpmsR8p/Vn5+fli1alWnyxQWFuL777/vUnlff/01kpKSsGvXLvZ94hDWcLwEPvvsM1hb\nW8PFxQVXr15VNB5BQUE4cOAAAOCDDz6Ara0tRCIRVqxYgbS0NMTHx2PFihWwt7dHQUEBduzYAUdH\nR4jFYsyaNQt1dXWKcpYtWwZnZ2dYWFgoygSADRs2QCgUQiwWK4Ylv3HjBry9veHg4IBJkybh6tWr\nbeqckZGBCRMmwN7eHs7OzoqbnVp7+PAhpk+fDpFIhPHjx+PixYsA5EdVwcHBcHNzg4WFhdL0xOvW\nrYONjQ1cXFwwf/58xdFXa0FBQQgNDcW4ceNgbW2NhIQEAMpHO+Hh4Vi4cCEmTJgAKysrREdHK9b/\n4osv4OjoCJFIhPDw8Dblf/rppzh9+jSCg4OxcuVKxMXFwd/fHx4eHvD09MSjR486zBUYGIhJkybB\n3NwcBw8exPvvvw+hUAhvb+92Gx1XV1csX74cEokEAoEAZ8+e7fS9+89//oOlS5d2+rl+8MEHSE1N\nhUQi6bQhDQ0NRUFBAaZOnYrIyEjF90kikaCgoKDD9Zg+4IXdIcKohXPnzpFAIKC6ujqqrKwkS0tL\n2rx5MxERBQUF0YEDB6isrExpJM2Kigql11s8ePBA8ftHH31EW7duJSKiwMBAmj17NhER5ebmkqWl\nJRHJb+ScMGEC1dXVEREpbkhyd3en/Px8IiJKT08nd3f3NvWurKwkmUxGREQnTpyggIAAIiJKTk5W\njOQaFhZGn376KRERnTx5ksRiMRERrV27lpydnamhoYHKyspo8ODBJJPJKCMjg8RiMT1+/Jiqqqpo\n9OjRiveitaCgIPL29iYiovz8fDIzM6P6+nqlba9du5bEYjHV19dTWVkZDRs2jO7cuUPHjh2jxYsX\nExFRU1MT+fr6UkpKSpttuLq60vnz54mIKDY2lszMzBTvT2e5XFxcSCaT0YULF6hfv36UmJhIREQz\nZsygH3/8sd3ttNQnJSVFMUpzR9uIjY2lsLAwIur4c5VKpYr34WnMzc0V35snv09M36WyGQCZ3pGa\nmoqZM2dCV1cXurq67Q7fYmhoCF1dXYSEhMDX1xe+vr6K16jV/aEXL17ERx99hIqKClRXV2Pq1KkA\n5N1fLcMbjBkzRjEqZ1JSEoKDg6Grq6vYTnV1NdLS0vDHP/5RUW5DQ0ObOpWXl+Ptt9/G9evXwePx\n0NjY2GaZ06dP4+DBgwAANzc3PHjwAFVVVeDxePDx8YGWlhYGDx4MY2Nj3Lt3D6dPn8b06dOhra0N\nbW1t+Pn5dTjA3+zZswEAlpaWGDVqFK5cuaL0Oo/Hw7Rp06CjowMdHR24ubkhIyMDqampOH78OCQS\nCQD5kBfXr1+Hi4tLu9tp4enpCUNDw6fm8vb2hqamJuzs7NDc3AwvLy8AgEAgQFFRUbtlz5s3DwDg\n4uKCyspKVFRUdLiNJzO297l29J51xfOsy6gP1nBwHI/HU/rP+uR/XCKCpqYmMjIy8PPPP2P//v3Y\ntm2bou+99TmRoKAgHD58GAKBAHFxcZBKpYrXtLW122zjyW0D8mHKDQ0NkZWV1Wm9P/74Y3h4eOCH\nH37AzZs34erq2u5yHe2IWtdHU1MTMpnsqe9FZ1oPPd6Rlvdq9erVWLx4cZfL5vF40NPTU3ruabk0\nNDSgpaWlVL+unh9pqeeT22hvNNX2Ptfn0VdHpGWUsXMcHDdp0iT8+OOPqK+vR1VVFY4cOdJmmZqa\nGpSXl8Pb2xtffvklLly4AAAwMDBAZWWlYrnq6mqYmpqisbERu3bteupOwNPTE7GxsYpzIY8ePcKA\nAQMwcuRI7N+/H4B8Z5STk9Nm3crKSvzhD38AAMTGxrZbvouLC7777jsA8vMPRkZGMDAwaHcHx+Px\n4OzsjPj4eDx+/BjV1dVISEhoNwMRYd++fSAi3LhxAwUFBbC2tm6zzKFDh/D48WM8ePAAUqkUjo6O\n8PLyQkxMDGpqagDI55e5f/9+p+/Tk/XtTq6u2Lt3LwDg1KlTMDQ0xIABA9rdhr6+fpfKMzAwaHN0\n0tX1Wn+fmL6LHXFwnEQiwZw5cyASiWBsbKyYf7kFj8dDVVUVpk2bhvr6ehARtmzZAgCYO3cu3nnn\nHWzduhX79u3DunXr4OTkBCMjIzg5OaG6ulqpnCd/9/LyQnZ2NhwcHKCtrQ0fHx9ERETgu+++w5Il\nSxAREYHGxkbMmzcPQqFQqV4rV65EYGAgIiIi4OPj0275LSfBRSIR9PT0FCODdjQXgYODA/z9/SEU\nChXzwA8cOLDNcjweD8OHD4ejoyMqKyvx73//G9ra2krl8ng8CIVCuLm5oaysDGvWrIGpqSlMTU2R\nl5eH8ePHA5DvLHft2gUjI6MOP6Mn69vVXE9m7Kgh19XVhb29PWQyGWJiYp55Gy2/i0QiaGpqQiwW\nY9GiRZ1eotx6/Se/T6NGjepwPUa9sUEOmZdKTU0N9PT0UFtbi8mTJ2PHjh0Qi8VKyyxatAh+fn6Y\nOXNmh+V88skn0NfXx9///vcXXeXn4ubmhs2bN8Pe3r63q8JwCDviYF4qixcvRm5uLurr6xEUFNSm\n0egO1l/PvKzYEQfDMAzTLezkOMMwDNMtrOFgGIZhuoU1HAzDMEy3sIaDYRiG6RbWcDAMwzDdwhoO\nhmEYplv+Hxp2XRumWCodAAAAAElFTkSuQmCC\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/52H7RfVjYZGXfB59FAYMKPxe0abBTZtgzpy8GtamTZUTrxCVLTo6mujo6MoO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\nrvgfIHgLBUAjJl4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.9 Page no.453"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "T=140.0                           #degree F\n",
      "sw=53.7                           #lb/(ft**3)\n",
      "vis=8*10**-5                    #lb*sec/(ft**2)\n",
      "l=799                               #miles\n",
      "D=4.0                              #ft\n",
      "Q=117.0                          #(ft**3)/sec\n",
      "V=9.31                            #ft/sec\n",
      "#energy equation=> hp=hL=f*(l/D)*((V**2)/(2*g))\n",
      "f=0.0125\n",
      "hp=f*(l*5280/D)*((V**2)/(2*32.2))        #ft,  in book ,calculation  mistake\n",
      "Pa=sw*Q*round(hp,2)/550                                  #hp\n",
      "\n",
      "#Result\n",
      "print \"The horsepower required to drive the system=\",round(Pa,3),\"hp\"\n",
      "\n",
      "#Plot\n",
      "import matplotlib.pyplot as plt\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "D=[2,3,4,5,6]\n",
      "P=[3.2*10**6,0.8*10**6,0.202*10**6,0.15*10**6,0.1*10**6]\n",
      "xlabel(\"D  ft\") \n",
      "ylabel(\"P  hP\") \n",
      "plt.xlim((0,6))\n",
      "plt.ylim((0,4*10**6))\n",
      "ax.plot([4], [0.202*10**6], 'o')\n",
      "ax.annotate('(4ft,2.02*10**5 hp)', xy=(4,0.25*10**6))\n",
      "a=plot(D,P)\n",
      "show(a)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The horsepower required to drive the system= 202694.35 hp\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Wq1XaNRoNzGYzAMBsNsPPz6/tANzd4enpidraWlRXV3fo0z5WXV0d1Go13Nzc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\nAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.10 Page no.454"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=4.0                        #in\n",
      "l=20                           #ft\n",
      "n=4.0                         #number of 90 degree elbows\n",
      "h=0.2                        #in\n",
      "T=100                      #degree F \n",
      "\n",
      "#calculation\n",
      "import math\n",
      "#energy equation between the inside of the dryer and the exit of the vent pipe\n",
      "p1=(h/12)*62.4         #lb/(ft**2)\n",
      "KLentrance=0.5\n",
      "KLelbow=1.5\n",
      "sw=0.0709              #lb/(ft**3)\n",
      "f=0.022                  #assumption\n",
      "#hence,\n",
      "V=((p1/sw)*2*32.2/(1+(f*l/(D/12))+KLentrance+(n*KLelbow)))**0.5       #ft/sec\n",
      "Q=V*(math.pi*((D/12)**2)/4)          #(ft**3)/sec\n",
      "\n",
      "#result\n",
      "print \"The flowrate=\",round(Q,2),\"ft**3/s\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The flowrate= 0.9 ft**3/s\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.11 Page no.456"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "             \n",
      "D=1.0                      #ft\n",
      "l=300.0                    #ft\n",
      "f=0.02                     #moody factor\n",
      "z1=90.0                   #ft\n",
      "g=32.2                     #ft/s**2, gravitational constant\n",
      "sw=62.4                    #lb/ft**3, specific heat\n",
      "import numpy\n",
      "#calculation\n",
      "from scipy.optimize import fsolve\n",
      "#energy equation between the surface of the lake and the outlet of the pipe\n",
      "#p1=V1=p2=z2=0  V2=V\n",
      "a=f*l/(D*2*g)                       #a=hl/V**2\n",
      "b=Pa*550/(sw*math.pi*(D**2)/4)    #b=ht/V\n",
      "#from bernouli eq.  f=0.109*V**3-90*V+561\n",
      "def f(V1):\n",
      "    f=0.109*V1**3-90*V1+561\n",
      "    return(f)\n",
      "V1=fsolve(f,10)\n",
      "def f1(V2):\n",
      "    f1=0.109*V2**3-90*V2+561\n",
      "    return(f)\n",
      "V2=fsolve(f,20)\n",
      "\n",
      "Q1=(math.pi*(D**2)/4)*V1         #(ft**3)/sec\n",
      "Q2=(math.pi*(D**2)/4)*V2        #(ft**3)/sec\n",
      "print \"The possible flowrates are=\",round(Q1,1),\"ft**3/s\" \"and \",round(Q2,1),\"ft**3/s\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The possible flowrates are= 5.166 ft**3/sand  19.537 ft**3/s\n"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.12 Page no.457"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "roughness=0.0005                #ft\n",
      "Q=2.0                            #(ft**3)/sec\n",
      "pd=0.5*144                      #lb/ft**2  where pd=pressure drop\n",
      "l=100                           #ft\n",
      "d=0.00238                      #slugs/(ft**3)\n",
      "vis=3.74*(10**(-7))            #lb*sec/(ft**2)\n",
      "\n",
      "#calculation\n",
      "x=Q/(math.pi/4)                #where x =V*(D**2)\n",
      "#energy equation with z1=z2 and V1=V2\n",
      "D=0.404*f**(1/5)\n",
      "#Calculation\n",
      "y=(l*d*(x**2)*0.5/(pd))       #where y=(D**5)/f\n",
      "f=0.027                        #using reynolds number, roughness and moody's chart\n",
      "D=((l*d*(x**2)*0.5/(pd))*f)**(0.2)\n",
      "\n",
      "#Result\n",
      "print \"The diameter of the pipe should be =\",round(D,3),\"ft\"\n",
      "\n",
      "#Plot\n",
      "q=[0.1,0.5,2,3]\n",
      "d=[0.06,0.09,0.196,0.225]\n",
      "a=plot(q,d)\n",
      "xlabel(\"q ft**3/s\") \n",
      "ylabel(\"d (ft)\") \n",
      "plt.xlim((0,3))\n",
      "plt.ylim((0,0.25))\n",
      "          \n",
      "show(a)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The diameter of the pipe should be = 0.196 ft\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lBT/88INT+6kUNR87OdR+7FpaWvDwww/j8ccfx6JFizq9rvbj19P+qf34tRs+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\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.13 Page no.458"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "T=60.0                       #degree F\n",
      "kvis=1.28*(10**(-5))         #(ft**2)/sec\n",
      "l=1700.0                     #ft\n",
      "roughness=0.0005             #ft\n",
      "Q=26.0                       #(ft**3)/sec\n",
      "n=4.0                        #number of flanged 45 degree elbows\n",
      "z1=44.0                      #ft\n",
      "\n",
      "#Calculation\n",
      "#V=31.1/D*2                   #where V=Q/A\n",
      "#f=0.0052*D**5-0.00135*D      #eleminating V\n",
      "\n",
      "#calculation\n",
      "#assume f=0.052               #(moody chart) hit and trial method\n",
      "from scipy.optimize import fsolve\n",
      "def f(D):\n",
      "    f=0.0052*D**5-0.00135*D-0.052\n",
      "    return(f)\n",
      "D=fsolve(f,1)\n",
      "\n",
      "#result\n",
      "print \"Pipe Diameter is \",round(D,1),\"ft\"\n",
      "\n",
      "#Plot\n",
      "l=[300,1000,1700,2000]\n",
      "d=[1.2,1.45,1.63,1.72]\n",
      "a=plot(l,d)\n",
      "xlabel(\"l ft\") \n",
      "ylabel(\"d (ft)\") \n",
      "plt.xlim((0,2000))\n",
      "plt.ylim((0,1.8))\n",
      "show(a)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "DPipe Diameter is  1.6 m\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gAACYIigAAKYICqCXhg8f3uX7Tz31lJKTk3X33XervLxcBw4c6OfKAGsRFEAv\ndff9Oc8884wqKyv18ssv680339T+/fv7uTLAWgQFcBV++9vf6siRI5o3b55Wr16td955Rw899JAy\nMjJ05MiRYJcHBAQrs4FeGjFihO97tC514403aufOnRo9erQKCgqUk5OjBQsWBKFCwBqMKIAA428v\nDDYEBRBg3KsCgw1BAQTQiBEjdObMmWCXAQQUQQH0UncjhUvfz8vL05/+9CdNmTKFyWwMGkxmAwBM\nMaIAAJgiKAAApggKAIApggIAYIqgAACYIigAAKYICgCAKYICAGDq/wCLwfuGk/zGOgAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8554780>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.14 Page no.462"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=1              #ft\n",
      "f=0.02\n",
      "z1=100           #ft\n",
      "z2=20            #ft\n",
      "z3=0             #ft\n",
      "l1=1000          #ft\n",
      "l2=500           #ft\n",
      "l3=400           #ft\n",
      "\n",
      "#Calculation\n",
      "from scipy.optimize import fsolve\n",
      "import math\n",
      "#V1+V2=V3                      #from eq of continuity ,because diameter are same\n",
      "#V1**2+0.4*V3**2=322          #from energy eq..........(1)\n",
      "#0.5*V2**2+0.4*V3**2=64.4     for fluid flowing B to c.........(2)\n",
      "# V1**2+0.5*V2**2=258          #...............(3)\n",
      "#From b and  bernouli eq.  f=V**4-460*V**2+3748\n",
      "def f(V2):\n",
      "    f1=V2**4-460*V2**2+3748\n",
      "    return(f1)\n",
      "V2=fsolve(f,2)\n",
      "V1=math.sqrt(258-0.5*V2**2)       #from eq 3\n",
      "A=(math.pi/4*(D**2))              #  ft**2, area\n",
      "Q1=V1*A\n",
      "Q2=V2*A\n",
      "Q3=Q1-Q2\n",
      "print \"Flow out of A reservoir =\",round(Q1,1), \"(ft**3)/sec\"\n",
      "print \"Flow  into B reservoir =\",round(Q2,2), \"(ft**3)/sec\"\n",
      "print \"Flow  into C reservoir =\" ,round(Q3,1),\"(ft**3)/sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Flow out of A reservoir = 12.5 (ft**3)/sec\n",
        "Flow  into B reservoir = 2.26 (ft**3)/sec\n",
        "Flow  into C reservoir = 10.3 (ft**3)/sec\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.15 Page no.467"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=60.0                 #mm\n",
      "pdiff=4                  #kPa\n",
      "Q=0.003               #(m**3)/sec\n",
      "d=789                 #kg/(m**3)\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "vis=1.19*(10**(-3))   #N*sec/(m**2)\n",
      "Re=d*4*Q/(math.pi*D*vis)\n",
      "#assuming B=dia/D=0.577, where dia=diameter of nozzle, and obtaining Cn from Re as 0.972\n",
      "Cn=0.972\n",
      "B=0.577\n",
      "dia=((4*Q/(Cn*math.pi))/((2*pdiff*1000/(d*(1-(B**4))))**0.5))**0.5\n",
      "\n",
      "#result\n",
      "print \"Diameter of the nozzle=\",round(dia*1000,1),\"mm\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Diameter of the nozzle= 34.1 mm\n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}