{
 "metadata": {
  "name": "",
  "signature": "sha256:9eaab2b896a6bb6c961934db80d46f26a50e6de94b234af0dcf8aaeaefc72384"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 10:Open Channel Flow"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.2 Page no.572"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab 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",
      "#Given\n",
      "z2=0.5              #ft\n",
      "q=5.75              #(ft**2)/sec\n",
      "y1=2.3              #ft\n",
      "z1=0                #ft\n",
      "V1=2.5              #ft/sec\n",
      "\n",
      "#calculation\n",
      "#bernoulli equation\n",
      "a=y1+((V1**2)/(2*32.2))+z1-z2   #ft where a=y2+((V**2)/(2*g))\n",
      "#continuity equation\n",
      "from scipy.optimize import fsolve\n",
      "#Calculation\n",
      "b=(y1*V1)                       #(ft**2/sec) where b=(y2*V2)\n",
      "#From b and  bernouli eq.  f=y**3-1.90*y**2+0.513\n",
      "def f(y):\n",
      "    f1=y**3-1.90*y**2+0.513\n",
      "    return(f1)\n",
      "y=fsolve(f,2)\n",
      "L=y+z2\n",
      "print \"Surface Elevation is \",round(L,2),\"ft\"\n",
      "\n",
      "#Plot\n",
      "E=[3,2,1.51,2.4,3]\n",
      "Y=[2.9,1.8,1.01,0.5,0.4]\n",
      "a=plot(E,Y)\n",
      "xlabel(\"E  ft\") \n",
      "ylabel(\"Y (ft)\") \n",
      "plt.xlim((0,4))\n",
      "plt.ylim((0,4))\n",
      "show(a)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Surface Elevation is  2.23 ft\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEKCAYAAAAW8vJGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1MD8AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.3 Page no.579"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Given\n",
      "y=5.0                       #ft\n",
      "angle=40.0               #degree\n",
      "l=12.0                      #ft\n",
      "rate=1.4                  #ft per 1000 ft of length\n",
      "K=1.49\n",
      "\n",
      "#Calculation \n",
      "import math\n",
      "A=(l*y)+(y*y/math.tan(angle*math.pi/180))     #ft\n",
      "P=(l+(2*y/math.sin(angle*math.pi/180)))         #ft\n",
      "Rh=A/P\n",
      "S0=rate/10**3\n",
      "x=K*(A)*(Rh**(0.666667))*(S0**(0.5))             #where Rh=Q*n\n",
      "n=0.012\n",
      "Q=x/n                        #cfs\n",
      "\n",
      "#Result\n",
      "print \"The flowrate=\",round(Q,0),\"cfs\"\n",
      "V=Q/A                     #ft/sec\n",
      "Fr=V/(32.2*y)**(0.5)\n",
      "print \"Froude number=\",round(Fr,2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The flowrate= 917.0 cfs\n",
        "Froude number= 0.8\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.4 Page no.580"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "y=5                 #ft\n",
      "angle=40            #degree\n",
      "l=12                #ft\n",
      "rate=1.4            #ft per 1000 ft of length\n",
      "Q=10                #m**3/sec\n",
      "bw=l*1/3.281        #m where bw=bottom width \n",
      "\n",
      "#Calculation\n",
      "import math\n",
      "from scipy.optimize import fsolve\n",
      "#A=(l*y)+(y*y/math.tan(angle*math.pi/180)) ft**2\n",
      "#A=1.19*y**2+3.66*y           area interms of distance depth y, 1.19,3.66  are constant\n",
      "#Rh=1.19*y**2+3.66*y/((3.11*y+3.66)**2)\n",
      "#P=bw(2*y/math.sin(angle*math.pi/180)) m\n",
      "#Rh=A/P\n",
      "#Q=10=k*A*Rh**2/3*So**0.5/(n)\n",
      "n=0.03              #From table 10.1\n",
      "\n",
      "def f(y):\n",
      "    f1=((1.19*y**2+3.66*y)**5-515*(3.11*y+3.66)**2)  #digits used are costants which is used in the area equation.\n",
      "    return(f1)\n",
      "y=fsolve(f,2)\n",
      "\n",
      "#Result\n",
      "print \"The depth of the flow=\",round(y,1),\"m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The depth of the flow= 1.5 m\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.7 Page no.583"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Given\n",
      "S0=0.002\n",
      "n1=0.02\n",
      "z1=0.6               #ft\n",
      "n2=0.015\n",
      "n3=0.03\n",
      "z2=0.8               #ft\n",
      "#length of section 1 ,2,3\n",
      "l1=3.0               #ft\n",
      "l2=2.0               #ft\n",
      "l3=3.0               #ft\n",
      "#Area\n",
      "A1=l1*(z1)           #ft**2\n",
      "A2=l2*(y)            #ft**2\n",
      "A3=l3*(z1)           #ft**2\n",
      "#Pressure head\n",
      "P1=l1+z1             #ft\n",
      "P2=l2+(2*z2)         #ft\n",
      "P3=l3+z1             #ft\n",
      "Rh1=A1/P1            #ft\n",
      "Rh2=A2/P2            #ft\n",
      "Rh3=A3/P3            #ft\n",
      "y=z1+z2              #ft\n",
      "K=1.49\n",
      "\n",
      "#Calculation\n",
      "Q=K*(S0**(0.5))*((A1*(Rh1**(0.667))/n1)+(A3*(Rh3**(0.667))/n3)+(A2*(Rh2**(0.667))/n2))   #(ft**3)/sec\n",
      "\n",
      "#Result\n",
      "print \"The flowrate=\",round(Q,1),\"ft**3/s\" \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The flowrate= 16.8 ft**3/s\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.8 Page no.584"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "aspratio=2       #asp ratio=aspect ratio=b/y\n",
      "\n",
      "#result\n",
      "print \"The aspect ratio=\",aspratio,\":1\"\n",
      "\n",
      "#Plot\n",
      "b=[0.5,1.2,2,5]\n",
      "q=[0.85,0.98,1,0.93]\n",
      "a=plot(b,q)\n",
      "xlabel(\"b/y  \") \n",
      "ylabel(\"q/qmax\") \n",
      "plt.xlim((0,5))\n",
      "plt.ylim((0.80,1.05))\n",
      "show(a)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The aspect ratio= 2 :1\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEPCAYAAACp/QjLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiYKBxERMfl/I7iv/evMN9AAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8481438>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.9 Page no.593"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Given\n",
      "w=100                    #ft\n",
      "y1=0.6                   #ft\n",
      "V1=18                   #ft/sec\n",
      "Fr1=V1/(32.2*y1)**0.5\n",
      "print \"The Froude number before the jump=\",round(Fr1,2)\n",
      "yratio=0.5*(-1+(1+(8*(Fr1**2)))**0.5)         #where yratio=y2/y1\n",
      "y2=y1*yratio        #ft\n",
      "print \"The depth after the jump=\",round(y2,2),\"ft\"\n",
      "#Q1=Q2, hence\n",
      "V2=(y1*V1)/y2              #ft/sec\n",
      "Fr2=V2/(32.2*y2)**0.5\n",
      "print \"The froude number after the jump=\",round(Fr2,2)\n",
      "Q=w*y1*V1#(ft**3)/sec\n",
      "hL=(y1+(V1*V1/(32.2*2)))-(y2+(V2*V2/(2*32.2)))       #ft\n",
      "Pd=62.4*hL*Q/550             #hp\n",
      "print \"Power dissipated within the jump=\",round(Pd,3),\"hp\"\n",
      "\n",
      "#Plot\n",
      "b=[1.54,1.2,0.8,0.6,0.4]\n",
      "P=[0,10,80,277,900]\n",
      "a=plot(b,P)\n",
      "xlabel(\"b (ft)\") \n",
      "ylabel(\"P  (hp)\") \n",
      "plt.xlim((0,1.6))\n",
      "plt.ylim((0,1000))\n",
      "show(a)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Froude number before the jump= 4.1\n",
        "The depth after the jump= 3.19 ft\n",
        "The froude number after the jump= 0.33\n",
        "Power dissipated within the jump= 277.539 hp\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEMCAYAAADTfFGvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X1UVXWixvHvQbBMxdQS9KCSguLxBTQlLfVihiUFY6UU\nvVGaTdnMlGu6TbeZu9JmraRp1p1xaryrZdawelmo41zhpnLNmdDyDcvURkzJQAGBxpR8LQT2/WPn\nCVTkHODsfc7h+azFGoV9js+22edx//bvt7fDMAwDERERD4XYHUBERAKLikNERLyi4hAREa+oOERE\nxCsqDhER8YqKQ0REvOKz4pg9ezYRERGMHDnS/b1jx46RnJzMkCFDmDZtGjU1Ne6fLVq0iNjYWOLi\n4li/fr37+59++ikjR44kNjaWp556yldxRUTEQz4rjkceeYT8/Pwm38vKyiI5OZkDBw4wdepUsrKy\nACgqKmL58uUUFRWRn5/PvHnzOL+85IknnmDZsmUUFxdTXFx80XuKiIi1fFYckyZNomfPnk2+l5eX\nR2ZmJgCZmZmsXr0agNzcXDIyMggLCyM6OpqYmBi2b99OZWUlJ0+eJDExEYCHHnrI/RoREbGHpdc4\nqquriYiIACAiIoLq6moAjhw5QlRUlHu7qKgoKioqLvq+0+mkoqLCysgiInKBULv+YIfDgcPhaNf3\nExER73l75ylLzzgiIiKoqqoCoLKykj59+gDmmURZWZl7u/LycqKionA6nZSXlzf5vtPpbPb9DcPw\n+68XXnjB9gzBkjMQMiqncvr7V2tYWhxpaWlkZ2cDkJ2dzYwZM9zfz8nJoba2lpKSEoqLi0lMTCQy\nMpLw8HC2b9+OYRi8/fbb7teIiIg9fDZUlZGRwcaNGzl69Cj9+/fnxRdf5LnnniM9PZ1ly5YRHR3N\nihUrAHC5XKSnp+NyuQgNDWXJkiXuoaclS5bw8MMPc/bsWVJSUrjtttt8FVlERDzgMFp7ruJnHA5H\nq0+7rFRQUEBSUpLdMVoUCDkDISMoZ3tTzvbVms9OFYeISAfWms9O3XJERES8ouIQERGvqDhERMQr\nKg4REfGKikNERLyi4hAREa+oOERExCsqDhER8YqKQ0REvKLiEBERr6g4RETEKyoOERHxiopDRES8\nouIQERGvqDhERMQrKg5p4tw5mD8f6uvtTiIi/krFIU2EhcEHH0Bhod1JRMRfqTjkIqmp8L//a3cK\nEfFXKg65SFqaikNEmqfikIskJsLXX0Npqd1JRMQfqTjkIp06QUqKzjpE5NJUHHJJus4hIs1xGIZh\n2B2iPTgcDoJkV/zCqVPQrx+Ul0N4uN1pRMRXWvPZqTMOuaRu3eDGG2H9eruTiIi/UXFIszRcJSKX\noqEqadahQzB2LFRVmRfMRST4aKhK2tXAgeZ1jm3b7E4iIv5ExSGXpeEqEbmQikMuS8UhIhdScchl\njRsH33wDX31ldxIR8RcqDrmskBC4/XaddYjIj1Qc0iINV4lIY5qOKy06fRr69oWyMujRw+40ItKe\nNB1XfKJrV5g4EfLz7U4iIv5AxSEe0XCViJxnS3EsWrSI4cOHM3LkSO677z6+//57jh07RnJyMkOG\nDGHatGnU1NQ02T42Npa4uDjW6+ZJtrjjDli3Durq7E4iInazvDhKS0tZunQpO3fu5PPPP6e+vp6c\nnByysrJITk7mwIEDTJ06laysLACKiopYvnw5RUVF5OfnM2/ePBoaGqyO3eH17w8DBsCWLXYnERG7\nWV4c4eHhhIWFcebMGerq6jhz5gz9+vUjLy+PzMxMADIzM1m9ejUAubm5ZGRkEBYWRnR0NDExMRQW\nFlodW9BwlYiYQq3+A3v16sUvf/lLBgwYQJcuXbj11ltJTk6murqaiIgIACIiIqiurgbgyJEjjB8/\n3v36qKgoKioqLvneCxYscP86KSmJpKQkn+1HR5SaCg8+CK+8YncSEWmtgoICCgoK2vQelhfHwYMH\n+eMf/0hpaSk9evRg1qxZvPPOO022cTgcOByOZt+juZ81Lg5pf9dfD99+C8XFEBtrdxoRaY0L/1G9\ncOFCr9/D8qGqTz75hBtvvJHevXsTGhrKXXfdxdatW4mMjKSqqgqAyspK+vTpA4DT6aSsrMz9+vLy\ncpxOp9WxBXMV+R13aLhKpKOzvDji4uLYtm0bZ8+exTAMNmzYgMvlIjU1lezsbACys7OZMWMGAGlp\naeTk5FBbW0tJSQnFxcUkJiZaHVt+kJam4hDp6CwfqoqPj+ehhx5i7NixhISEMGbMGB577DFOnjxJ\neno6y5YtIzo6mhUrVgDgcrlIT0/H5XIRGhrKkiVLLjuMJb41dSrcfz8cPw49e9qdRkTsoFuOiNdS\nU+G++yAjw+4kItJWuuWIWELTckU6Np1xiNeOHIERI6C6GsLC7E4jIm2hMw6xRL9+MGgQbN5sdxIR\nsYOKQ1pFw1UiHZeKQ1pFxSHScak4pFVGj4YzZ2D/fruTiIjVVBzSKg6HVpGLdFQqDmk1DVeJdEya\njiutdvYsREZCSQn06mV3GhFpDU3HFUt16QJJSeaTAUWk41BxSJukpkJent0pRMRKGqqSNqmsBJfL\nXEXeubPdaUTEWxqqEsv17Ws+1Omjj+xOIiJWUXFIm2l2lUjHouKQNjtfHBopFOkYVBzSZvHxcO4c\n7NtndxIRsYKKQ9pMq8hFOhYVh7QLXecQ6Tg0HVfaxXffQUQEHDwI11xjdxoR8ZSm44ptrrwSbr4Z\n1q61O4mI+JqKQ9pNWpqGq0Q6Ag1VSbv5+msYMsT8X60iFwkMGqoSW/XpA8OGwcaNdicREV9ScUi7\n0uwqkeCn4pB2pVXkIsFPxSHtasQIszT27rU7iYj4iopD2pXDoeEqkWCn4pB2p+IQCW6ajivt7vvv\nzVXkBw6YM61ExH9pOq74hSuugFtu0SpykWCl4hCf0LPIRYKXhqrEJ/71L4iJMZ9FfuWVdqcRkeZo\nqEr8xrXXmlNzCwrsTiIi7U3FIT6j2VUiwUnFIT6jVeQiwcmW4qipqWHmzJkMGzYMl8vF9u3bOXbs\nGMnJyQwZMoRp06ZRU1Pj3n7RokXExsYSFxfH+vXr7YgsreByQWgo7NljdxIRaU+2FMdTTz1FSkoK\n+/btY8+ePcTFxZGVlUVycjIHDhxg6tSpZGVlAVBUVMTy5cspKioiPz+fefPm0dDQYEds8ZJWkYsE\nJ8uL49tvv+Wjjz5i9uzZAISGhtKjRw/y8vLIzMwEIDMzk9WrVwOQm5tLRkYGYWFhREdHExMTQ2Fh\nodWxpZVUHCLBx/LiKCkp4dprr+WRRx5hzJgxzJ07l9OnT1NdXU1ERAQAERERVFdXA3DkyBGioqLc\nr4+KiqKiosLq2NJKkyfD/v1QVWV3EhFpL6FW/4F1dXXs3LmT1157jXHjxvH000+7h6XOczgcOByO\nZt+juZ8tWLDA/eukpCSSkpLaI7K0QefOMG0arFkDc+bYnUZECgoKKGjjPHnLiyMqKoqoqCjGjRsH\nwMyZM1m0aBGRkZFUVVURGRlJZWUlfX64yZHT6aSsrMz9+vLycpxO5yXfu3FxiP9ITYVVq1QcIv7g\nwn9UL1y40Ov3sHyoKjIykv79+3PgwAEANmzYwPDhw0lNTSU7OxuA7OxsZsyYAUBaWho5OTnU1tZS\nUlJCcXExiYmJVseWNkhJgX/8A777zu4kItIeLD/jAHj11Ve5//77qa2tZfDgwbz11lvU19eTnp7O\nsmXLiI6OZsWKFQC4XC7S09NxuVyEhoayZMmSyw5jif/p3RsSEszySEmxO42ItJXuVSWWeOUV+Oor\n+O//tjuJiDTWms9OFYdY4osvIDkZDh8213eIiH/QTQ7Fbw0dat4ld9cuu5OISFupOMQSWkUuEjwu\nO1T19ddfs3LlSjZt2kRpaSkOh4OBAwcyefJkZs2a5Z4y6w80VOX/PvwQnn0WduywO4mInNeu1zjm\nzJnDwYMHmT59OomJifTt2xfDMKisrKSwsJD8/HxiYmJ444032iV8W6k4/N+5c+azyP/5T+jXz+40\nIgLtXBx79uxh1KhRl32xJ9tYRcURGDIy4OabYe5cu5OICPhwVlVtbS379u0jJCSEoUOH0rlz51aH\n9BUVR2B47z3IydHzyEX8hU+KY82aNTz++OMMGjQIgK+++orXX3+dFD9byaXiCAzHj8PAgeZND6+6\nyu40IuKT4hg6dChr1qwhJiYGgIMHD5KSksL+/ftbn9QHVByBIykJfvlLc5aViNjLJ+s4wsPD3aUB\nMGjQIMLDw71PJ/IDTcsVCWwtnnE8/vjjHD58mPT0dABWrlzJgAEDSE5OBuCuu+7yfUoP6IwjcBw4\nYJ51lJdDiFYSidjKJ0NVDz/8sPvNAQzDaHKTwbfeesvLmL6h4ggsQ4fCu+/C2LF2JxHp2HSvquDY\nlQ7hmWega1doxaMARKQd+aQ4vv76a5YuXUppaSl1dXXuP+jNN99sfVIfUHEElo0bYf582LnT7iQi\nHVtrPjtbfB7HT37yEyZPnkxycjIhPwxI63kY0lY33QSHDpnXORo9Ul5EAkCLZxwJCQnsCoBbmuqM\nI/Dcfz9MmgSPP253EpGOyyfTce+44w7WrFnT6lAizdG0XJHA1OwZR7du3dxDUqdPn6Zz586EhYWZ\nL3I4OHHihHUpPaAzjsBTUwMDBkBlpXmhXESs167XOE6dOtXmQCKXc/XV5nTcDRvgJz+xO42IeKrZ\noaqvvvqqxRcfPHiwXcNIx6PhKpHA0+xQ1T333MPp06dJS0tj7NixTZ7H8cknn5CXl0f37t3Jycmx\nOvMlaagqMH35pXmBvKJCq8hF7NDu6zi+/PJLcnJy2Lx5M4cOHQJg4MCBTJw4kYyMDPcdc/2BiiNw\nuVzwl79AYqLdSUQ6Hq0cD45d6XB+9Svo3Bl++1u7k4h0PD6Zjivia7rOIRJYVBxiuwkTzGschw/b\nnUREPKHiENt16gTTp8P779udREQ8oeIQv6DhKpHAoYvj4hdOnACnE44cge7d7U4j0nHo4rgErPBw\nGD8ePvjA7iQi0pJmi+Ps2bP84Q9/4Mknn+T11193P4tDxFc0XCUSGJodqkpPT6dz585MnDiRdevW\nER0dzeLFi63O5zENVQW+khK44QbzpoedOtmdRqRjaNcFgCNHjuTzzz8HoK6ujnHjxvHZZ5+1PaWP\nqDiCw4gRsHSpOUVXRHyvXa9xhIaGXvLXIr6k4SoR/9fsGUenTp246qqr3L8/e/YsXbp0MV+k53GI\nj2zZAj/9KfxwsisiPqZ7VQXHrnRo9fXQty8UFkJ0tN1pRIKfpuNKwOvUCVJSNFwl4s9sK476+npG\njx5NamoqAMeOHSM5OZkhQ4Ywbdo0ampq3NsuWrSI2NhY4uLiWL9+vV2RxSK6ziHi32wrjsWLF+Ny\nudzPNc/KyiI5OZkDBw4wdepUsrKyACgqKmL58uUUFRWRn5/PvHnzaGhosCu2WGDaNNi61VxNLiL+\nx5biKC8vZ+3atTz66KPusbW8vDwyMzMByMzMZPXq1QDk5uaSkZFBWFgY0dHRxMTEUFhYaEdssUj3\n7nDjjaCTSxH/ZEtxzJ8/n1deeYWQRs8Kra6uJiIiAoCIiAiqq6sBOHLkCFFRUe7toqKiqKiosDaw\nWE7DVSL+y/IFGu+//z59+vRh9OjRFBQUXHIbh8PhHsJq7ueXsmDBAvevk5KSSEpKakNSsVNqKixc\naM6y0ipykfZTUFDQ7Gevpywvji1btpCXl8fatWv57rvvOHHiBA8++CARERFUVVURGRlJZWUlffr0\nAcDpdFJWVuZ+fXl5OU6n85Lv3bg4JLANHGhOy922DW66ye40IsHjwn9UL1y40Ov3sHyo6qWXXqKs\nrIySkhJycnK4+eabefvtt0lLSyM7OxuA7OxsZsyYAUBaWho5OTnU1tZSUlJCcXExiYmJVscWG2i4\nSsQ/2b6O4/yw03PPPccHH3zAkCFD+Mc//sFzzz0HgMvlIj09HZfLxfTp01myZMllh7EkeKg4RPyT\nVo6L32pogH79zNuQDBpkdxqR4KSV4xJUQkLg9tt11iHib1Qc4tc0XCXifzRUJX7t9GlzdlVZGfTo\nYXcakeCjoSoJOl27wsSJkJ9vdxIROU/FIX5Pw1Ui/kVDVeL3ysogIQGqq0EPoxRpXxqqkqDUvz8M\nGGBOyxUR+6k4JCBouErEf6g4JCCoOET8h4pDAsL118O330Jxsd1JRETFIQEhJATuuENnHSL+QMUh\nAUPDVSL+QdNxJWCcOQORkXDoEPTsaXcakeCg6bgS1K66CiZP1ipyEbupOCSgaLhKxH4aqpKAUlEB\nI0eaq8jDwuxOIxL4NFQlQc/phOuug82b7U4i0nGpOCTgaLhKxF4qDgk4Kg4Re6k4JOCMGWM+4Gn/\nfruTiHRMKg4JOA6HVpGL2EnFIQEpNRVWrYKGBruTiHQ8Kg4JSMnJ5pnH/PmgWdgi1lJxSEC64gpY\nuxY++gh+8xu704h0LHoQpwSsq6+G//s/+Ld/g27d4D/+w+5EIh2DikMC2rXXwoYN5j2sunWDn//c\n7kQiwU/FIQGvX78fy6NrV5g92+5EIsFNxSFBITraLI+kJLM87rnH7kQiwUvFIUFjyBDzluvJyeYt\n2FNT7U4kEpw0q0qCyqhR8P77MGcO/P3vdqcRCU4qDgk648bBX/8K996ru+iK+IKKQ4LS5Mnwzjtw\n552wc6fdaUSCi4pDgtatt8Lrr0NKCuzda3cakeChi+MS1O68E86cMUukoABiYuxOJBL4VBwS9O6/\n37wN+y23wKZNMGCA3YlEApuKQzqExx5rWh6RkXYnEglcll/jKCsrY8qUKQwfPpwRI0bwpz/9CYBj\nx46RnJzMkCFDmDZtGjU1Ne7XLFq0iNjYWOLi4li/fr3VkSVIzJ8PDzxgrvP45hu704gELodhWHtT\n6qqqKqqqqkhISODUqVNcf/31rF69mrfeeotrrrmGZ599lpdffpnjx4+TlZVFUVER9913Hzt27KCi\nooJbbrmFAwcOEBLStPMcDgcW74oEIMOAX/0KPvzQXOcRHm53IhF7teaz0/IzjsjISBISEgDo1q0b\nw4YNo6Kigry8PDIzMwHIzMxk9erVAOTm5pKRkUFYWBjR0dHExMRQWFhodWwJEg4HvPyyudbjjjvM\nC+ci4h1br3GUlpby2WefccMNN1BdXU1ERAQAERERVFdXA3DkyBHGjx/vfk1UVBQVFRWXfL8FCxa4\nf52UlERSUpLPskvgcjjgtdfg4YfNWVd5eebzPUQ6goKCAgoKCtr0HrYVx6lTp7j77rtZvHgx3bt3\nb/Izh8OBw+Fo9rXN/axxcYhcTkgIvPmmubr8nntg5UoIC7M7lYjvXfiP6oULF3r9HrYsADx37hx3\n3303Dz74IDNmzADMs4yqqioAKisr6dOnDwBOp5OysjL3a8vLy3E6ndaHlqATGgrvvQe1tebZR329\n3YlEAoPlxWEYBnPmzMHlcvH000+7v5+WlkZ2djYA2dnZ7kJJS0sjJyeH2tpaSkpKKC4uJjEx0erY\nEqQ6d4ZVq+DIEXjiCT2/XMQTls+q+vjjj5k8eTKjRo1yDzktWrSIxMRE0tPTOXz4MNHR0axYsYKr\nr74agJdeeok333yT0NBQFi9ezK233nrxjmhWlbTByZPmNN0JE+C//su8DiLSEbTms9Py4vAVFYe0\n1fHjMGUKpKXBiy/anUbEGq357NTKcZEf9OwJ69f/+PzyZ5+1O5GIf1JxiDTSp4+5MHDSJLM85s2z\nO5GI/1FxiFzA6TTLY/Jk8/nlP6xLFZEfqDhELuG66+CDD8xrHl27wsyZdicS8R8qDpFmxMXBunXm\nszy6dIHbb7c7kYh/0BMARS4jIQFyc80Fgh9+aHcaEf+g4hBpwfjx5i1J0tNh61a704jYT8Uh4oGk\nJMjOhhkzYNcuu9OI2EvFIeKhlBRYsgSmT4d9++xOI2IfXRwX8cLdd5uPoJ02DTZuhEGD7E4kYj0V\nh4iXHnqo6fPLo6LsTiRiLRWHSCs88QScOvVjefzwFACRDkHFIdJK//7vZnkkJ5tTdXv1sjuRiDV0\nd1yRNjAMeOYZ+Phj2LABLniYpYjf023Vg2NXJMAYBjz+OOzfD2vXwlVX2Z1IxHMqjuDYFQlA9fXm\nzRC/+QZWr4YrrrA7kYhnVBzBsSsSoOrqYNYsCAmB5cvNZ5qL+LvWfHZqAaBIOwkNhZwc84L57NnQ\n0GB3IhHfUHGItKMrroD/+R8oLYUnnzSvf4gEGxWHSDu76ip4/3349FPz8bMqDwk2usYh4iPHjpk3\nRxw3Dm67zbxF++DB5jUQEX+hi+PBsSsSRL7+2rwx4q5d5tc338CoUWaJxMeb/ztihKbwin1UHMGx\nKxLEjh+HPXt+LJJdu8z1H9HRTcskIQEiIuxOKx2BiiM4dkU6mNpa+OKLpmWya5d5of3CMomNhU6d\n7E4swUTFERy7IoJhQHl50yLZvRuqqmD48B+LJCEBRo6Ebt3sTiyBSsURHLsi0qwTJ5oOde3eDXv3\nmrd2b1wmCQnQty84HHYnFn+n4giOXRHxSl2deZ2kcZl89pn5swvLZOhQrWiXplQcwbErIm1mGFBZ\n2bRMdu2CsjJwuZqWyahREB5ud2Kxi4ojOHZFxGdOnYLPP/+xSHbtgn/+05zB1bhM4uOhf38NdXUE\nKo7g2BURS9XXQ3Fx0zLZtQu+/75pkSQkwLBh0Lmz3YmlPak4gmNXRPxCdfXFZVJaal4naVwm8fHQ\ns6fdaaW1VBzBsSsifuvMGXMWV+My2bMHeve+eM1JdLSGugKBiiM4dkUkoDQ0wFdfXbzm5OTJpmcl\nCQnmGhQ95Mq/qDiCY1dEgsLRo02Hunbvhi+/hJiYpmcm8fFwzTV2p+24VBzBsSsiQeu776Co6OJp\nwuHhTcskIQEGDdKdhK0Q1E8AzM/PJy4ujtjYWF5++WW747RaQUGB3RE8Egg5AyEjKGdjV14JY8aY\nT0j8059g40aoqYFNm2DOHPM+XO+8A7fcAldfDTfdZD4Qa+lS2LEDzp7V36c/CIg1pPX19fzsZz9j\nw4YNOJ1Oxo0bR1paGsOGDbM7mtcKCgpISkqyO0aLAiFnIGQE5WyJwwHXXWd+3Xnnj98/ftw8I9m9\nG7ZsMW9Pv38/OBwF9O6dxJVXYslXly7mdRlvz34C5b97awREcRQWFhITE0N0dDQA9957L7m5uQFZ\nHCLimZ49zQdhNf7sra2F3/wGfv5zc9jrwq+zZy/9/e++Mxc/Hj3a/M9b+goL865w9u41y6+9Csyf\nZqgFRHFUVFTQv39/9++joqLYvn27jYlExA6dO5sPvWr0cWAJw4Bz5zwrqPNfx46Z12nO//7ECfPB\nXq0pre+/N/e9pXK56y547DHf/30ExMXxVatWkZ+fz9KlSwF455132L59O6+++qp7G4c/1bGISADx\ntgYC4ozD6XRSVlbm/n1ZWRlRUVFNtgmA/hMRCQoBMatq7NixFBcXU1paSm1tLcuXLyctLc3uWCIi\nHVJAnHGEhoby2muvceutt1JfX8+cOXN0YVxExCYBccYBMH36dPbv389rr71Gdnb2Zddz/OIXvyA2\nNpb4+Hg+O/9EGwu1tObk3XffJT4+nlGjRnHTTTexZ88eyzOC52tjduzYQWhoKH/7298sTPcjT3IW\nFBQwevRoRowYYdsUyJZyHj16lNtuu42EhARGjBjBX/7yF8szzp49m4iICEaOHNnsNnYfP9ByTn85\nhjz5+wT7jyFPcnp1DBkBpK6uzhg8eLBRUlJi1NbWGvHx8UZRUVGTbdasWWNMnz7dMAzD2LZtm3HD\nDTf4XcYtW7YYNTU1hmEYxrp16yzP6GnO89tNmTLFuP32242//vWvfpnz+PHjhsvlMsrKygzDMIx/\n/etffpnzhRdeMJ577jl3xl69ehnnzp2zNOemTZuMnTt3GiNGjLjkz+0+fs5rKac/HEOG0XJOw7D/\nGDKMlnN6ewwFzBkHNF3PERYW5l7P0VheXh6ZmZkA3HDDDdTU1FBdXe1XGSdMmECPHj3cGcvLyy3L\n501OgFdffZWZM2dy7bXXWp4RPMv53nvvcffdd7snTFxjw42PPMnZt29fTpw4AcCJEyfo3bs3oRY/\nx3XSpEn0vMw90O0+fs5rKac/HEPQck6w/xiClnN6ewwFVHFcaj1HRUVFi9tY+X8qTzI2tmzZMlJS\nUqyI1oSnf5e5ubk88cQTgD1Tnj3JWVxczLFjx5gyZQpjx47l7bfftjqmRznnzp3L3r176devH/Hx\n8SxevNjqmC2y+/hpDbuOIU/4wzHkCW+PoYC4OH6ep3/pxgVTc638j+XNn/Xhhx/y5ptvsnnzZh8m\nujRPcj799NNkZWW5b4J24d+rFTzJee7cOXbu3Mnf//53zpw5w4QJExg/fjyxsbEWJDR5kvOll14i\nISGBgoICDh48SHJyMrt376Z79+4WJPScncePt+w8hjzhD8eQJ7w9hgKqODxZz3HhNuXl5TidTr/K\nCLBnzx7mzp1Lfn5+i6e6vuBJzk8//ZR7770XMC/srlu3jrCwMEunQnuSs3///lxzzTV06dKFLl26\nMHnyZHbv3m1pcXiSc8uWLfz6178GYPDgwVx33XXs37+fsWPHWpazJXYfP96w+xjyhD8cQ57w+hhq\nx+svPnfu3Dlj0KBBRklJifH999+3eHF869atll808yTjoUOHjMGDBxtbt261NFtjnuRs7OGHHzZW\nrVplYUKTJzn37dtnTJ061airqzNOnz5tjBgxwti7d6/f5Zw/f76xYMECwzAMo6qqynA6ncY333xj\naU7DMIySkhKPLo7bcfw0drmc/nAMnXe5nI3ZdQydd7mc3h5DAXXG0dx6jtdffx2An/70p6SkpLB2\n7VpiYmLo2rUrb731lt9lfPHFFzl+/Lh73DMsLIzCwkK/y+kPPMkZFxfHbbfdxqhRowgJCWHu3Lm4\nXC6/y/n888/zyCOPEB8fT0NDA7/73e/o1auXpTkzMjLYuHEjR48epX///ixcuJBz5865M9p9/Hia\n0x+OIU8OMPsJAAACWUlEQVRy+ouWcnp7DAXEvapERMR/BNSsKhERsZ+KQ0REvKLiEBERr6g4RETE\nKyoOES+Vlpa2eFO785555hkKCgoA+Oijjxg+fDhjxoxh27ZtrFu3zr1dXl4ev/3tb30RV6TdqThE\nfOTkyZNs2rTJfafRd999l+eff56dO3fyxRdfsHbtWve2qamprFq1yj1FUsSfqThEWqGuro4HHngA\nl8vFrFmzOHv27EXb5ObmcssttwDwxhtvsHLlSv7zP/+T++67jxdeeIHly5czevRoVq5cicPhYMKE\nCaxfv97qXRHxmopDpBX279/Pk08+SVFREeHh4SxZsuSibTZv3uy+ncijjz5KWloav//973nvvfd4\n8cUXuffee/nss8+YNWsWAImJiWzatMnS/RBpDRWHSCv079+fCRMmAPDAAw/w8ccfX7TNoUOH6Nu3\nb5PvnV9va1zihnf9+vWjtLTUN4FF2pGKQ6QVGt8x1jCMZu8g29DQ0OzrLrWtP9+JVuQ8FYdIKxw+\nfJht27YB5kNwJk2adNE2AwcOpKqqqsn3zp9lhIeHc/LkySY/q6ysZODAgT5KLNJ+VBwiXnI4HAwd\nOpQ///nPuFwuvv32W/fN9hqbOHEin3zyyUWvBZgyZQpFRUXui+NgPkVw8uTJvt8BkTbSTQ5FfOTU\nqVNMmTKFHTt2tLhtQ0MDY8aM4ZNPPrH8cbIi3tIZh4iPdOvWjSlTpvDhhx+2uO3777/PzJkzVRoS\nEHTGISIiXtEZh4iIeEXFISIiXlFxiIiIV1QcIiLiFRWHiIh4RcUhIiJe+X/W0eKMLsKjQwAAAABJ\nRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}