{
 "metadata": {
  "name": "",
  "signature": "sha256:48111e112fd64084e75ff1b319dc96b3d4269ed40b43b7a2ec8b550fc1c50ab6"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<figure>\n",
      "  <IMG SRC=\"https://raw.githubusercontent.com/mbakker7/exploratory_computing_with_python/master/tudelft_logo.png\" WIDTH=250 ALIGN=\"right\">\n",
      "</figure>\n",
      "\n",
      "# Exploratory Computing with Python\n",
      "*Developed by Mark Bakker*\n",
      "## Water Management Notebook 2: Manning's equation and emptying reservoir"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Exercise 1: <a name=\"back1\"></a>Manning's equation\n",
      "The average velocity of water flowing in a canal may be estimated with Manning's equation. Manning's equation for the average velocity $v$ is\n",
      "\n",
      "$v=\\frac{1}{n}R_h^{2/3}S^{1/2}$\n",
      "\n",
      "where $n$ is Manning's coefficient, $R_h$ is the hydraulic radius, and $S$ is the slope of the bottom of the canal. \n",
      "A detailed description of Manning's equation can be found <a href=\"http://en.wikipedia.org/wiki/Manning_formula\" target=\"_blank\"> here</a>.\n",
      "\n",
      "\n",
      "We will consider canals with a trapezoidal cross-section as shown below. The slope of the banks is 1:1.\n",
      "\n",
      "<img src= \"http://s16.postimg.org/r1x965vpx/channel.png\">\n",
      "\n",
      "Our goal in this exercise is to compute the water height $h$ for a given design discharge $Q_d$ given the width $w$, the roughness coefficient $n$, and the bottom slope $S$. This exercise consists of 6 steps."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 1*. Write a function that computes the hydraulic radius. The function should take two arguments: the height $h$ of the water above the bottom of the canal, and the width $w$ of the canal at the bottom (see Figure). The function should return the hydraulic radius. To test your function, the hydraulic radius for $h=2$ m, and $w=4$ m, is $R_h=1.2426$ m. (Note: in engineering practice it is, of course, ridiculous to give an answer with so many digits. But for testing code it is useful.)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 2*. Write a function that computes the average velocity in the canal. The function should take four arguments: the height $h$, the width $w$, the roughness coefficient $n$, and the bottom slope $S$. Inside the function, call the function for the hydraulic radius that you wrote for step 1. To test your function, the average velocity for $h=2$ m, $w=4$ m, $n=0.025$, $S=0.005$ is $v=3.2692$ m/s. Remember that `2/3=0`, while `2.0/3=0.666...`.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 3*. Write a function that computes the total discharge in the canal. The function should take four arguments: the height $h$, the width $w$, the roughness coefficient $n$, and the bottom slope $S$. Inside the function, call the function for the average velocity. To test your function, the total discharge for $h=2$ m, $w=4$ m, $n=0.025$, $S=0.005$ is $Q=39.23$ m$^3$/s."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 4*. Make a graph of total discharge $Q$ vs. the height of the water $h$, where $h$ varies from 1 to 4 m. Draw three lines for three different width $w=4$ m, $w=6$ m, $w=8$ m. Otherwise, use $n=0.025$, and $S=0.005$. Add a legend, labels on the axes, etc. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 5*. When you know the design discharge $Q_d$, you can find the corresponding water height $h$ from the graph you just produced. This is not very convenient though. Especially since the graph is for specific values of the roughness coefficient $n$ and the slope $S$. We want to find the water height that corresponds to a given $Q$. We need one additional function, let's call it `Qdiff` that computes the difference between the discharge computed with the discharge function you wrote in Step 3 and the design discharge you want. Inside the function, call the function for the total discharge that you wrote in Step 3. The input arguments of `Qdiff` are the height $h$, the width $w$, the roughness coefficient $n$, the bottom slope $S$, and the design discharge $Q_d$. `Qdiff` should return the difference between the design discharge and the discharge you compute with the specified values of $h$, $w$, $n$, and $S$. Test your `Qdiff` function. Use `fsolve` (see previous Notebook) to find the water height $h$ corresponding to the design discharge and the parameters of the canal $w$, $n$, $S$. Show that your code produces the correct result. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 6*. Compute the water height for $Q_d$ = 20, 40, 60, 80, 100 m$^3$/s, for $w=6$ m, $n=0.02$, $S=0.004$ and print them to the screen. \n",
      "Make a graph for $h$ vs $Q_d$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"#ex1answer\">Answers to Exercise 1</a>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Polynomial fit\n",
      "The function `polyfit` may be used to fit a polynomial through a set of data. Given a set of $x$ and $y$ values, `polyfit` computes the parameters $p$ of a polynomial of degree $N$ that goes through the data\n",
      "\n",
      "$f(x) = p_0 x^N + p_1 x^{N-1} + ... + p_{N-1}x + p_N$ \n",
      "\n",
      "Once you have computed the parameters $p_n$, you can evaluate the polynomial using the `polyval` function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([1,3,4,6,8,9])\n",
      "y = np.array([1,4,2,6,5,7])\n",
      "p = np.polyfit(x,y,5)\n",
      "print p\n",
      "x2 = np.linspace(0,10,100)\n",
      "y2 = np.polyval(p,x2)\n",
      "plt.plot(x,y,'bo')\n",
      "plt.plot(x2,y2)\n",
      "plt.ylim(-1,8)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  3.01587302e-02  -7.90873016e-01   7.68174603e+00  -3.36662698e+01\n",
        "   6.42880952e+01  -3.65428571e+01]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "(-1, 8)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAEACAYAAABBDJb9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1048d20d0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When the degree of the polynomial is equal to the number of data points minus one, the polynomial goes exactly through the data points as shown above where there are 6 data points and a polynomial of degree 5 (hence, 6 $p$ values) is fitted through the data. Higher order polynomials often wiggle through the data and may give unreasonable values outside the range of the data. A smoother polynomial is obtained when the degree of the polynomial is smaller than the number of data points minus 1. The best fit is obtained by computing the parameters such that the sum of squared differences between the fitted line and the data is minimized. For example, let's fit a polynomial of order 3 through the data of the previous example"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([1,3,4,6,8,9])\n",
      "y = np.array([1,4,2,6,5,7])\n",
      "p = np.polyfit(x,y,3)\n",
      "print 'the values of p are:',p\n",
      "x2 = np.linspace(0,10,100)\n",
      "y2 = np.polyval(p,x2)\n",
      "plt.plot(x,y,'bo')\n",
      "plt.plot(x2,y2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the values of p are: [ 0.00943775 -0.16406679  1.47407525 -0.22559713]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10731fa90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAEACAYAAABBDJb9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCUhPFgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1072dec50>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "***\n",
      "###Exercise 2. <a name=\"back2\"></a>Emptying a reservoir \n",
      "Consider a reservoir filled with water that is emptied by opening a gate at the bottom of the reservoir. \n",
      "The water level in the reservoir is measured with a pressure transducer on the bottom of the reservoir while it is being emptied. \n",
      "The rate of change of the water level $h$ in the reservoir is theoretically related to the water level in the reservoir as\n",
      "\n",
      "$\\frac{\\text{d}h}{\\text{d}t} = \\alpha \\sqrt{h-h_0}$\n",
      "\n",
      "where $\\alpha$ and $h_0$ are constants. Rearrangement of the differential equation gives\n",
      "\n",
      "$\\frac{1}{\\sqrt{h-h_0}}\\text{d}h = \\alpha \\text{d}t$\n",
      "\n",
      "and integration gives\n",
      "\n",
      "$\\sqrt{h-h_0} = 2\\alpha t + \\beta$\n",
      "\n",
      "where $\\beta$ is a constant of integration. Rearrangment gives\n",
      "\n",
      "$ h = 4\\alpha^2 t^2 + 4\\beta\\alpha t + \\beta^2 + h_0$\n",
      "\n",
      "Hence, $h$ vs. $t$ is a parabola.\n",
      "\n",
      "*Step 1*. The raw data of the experiment is provided in the file `emptying_reservoir.csv`. A `csv` file is an ascii file that you can open in a standard editor (csv stands for comma separated values). Load the column labeled as 'Pressure' from the data file. Note the units of pressure. Pressure measurements include both air pressure and the pressure caused by the water column. Note: if you want to specify one colomn to read with the `usecols` keyword, put square brackets around the column number to make it a list. This may be a bit confusing, but `usecols` expects a sequence. `(3)` is not a sequence, it is just the number 3, while `[3]` is a sequence as it is the data type list. Alternatively, the somewhat funny syntax `(3,)` is a tuple and would work. If you want to read more than one column, for example columns 2 and 3, you can type either `(2,3)` (which is a tuple of two values) or `[2,3]` (which is a list of two values)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 2* The pressure transducer starts recording pressures before the start of the experiment (when the reservoir is openened and starts to empty) and is removed after a bit more than an hour. The pressure is recorded for some time after the pressure transducer is removed from the reservoir. Plot the pressure and determine at what index the experiment starts and at what index the experiment ends. Zooming is, unfortunately, not yet supported for inline graphs in IPython notebooks (v.1.0). Use the `xlim` and `ylim` functions to zoom in on the beginning and end of the experiment to determine the index of the beginning and end of the experiment. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 3*. Create a new array that only contains the pressure data during the experiment. Make a graph for pressure against time. Set time equal to zero at the beginning of the experiment and determine the time between measurements from the data file."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 4*. Fit a parabola through the data using polyfit. Plot in one graph the data of the experiment and the fitted polynomial. Do you get a nice fit?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Step 5*. Write a Python function for the change of water level with time $\\text{d}h/\\text{d}t$ based on the parabola of Step 4. Plot $\\text{d}h/\\text{d}t$ vs. $t$ based on the parabola. Next, compute the derivative numerically using the measured water levels during the experiment. Plot the numerical derivative based on the data on the same graph. Do you still get a good match between the model and the data?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"#ex2answer\">Answers to Exercise 2</a>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Answers to the exercises"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name=\"ex1answer\">Answers to Exercise 1</a>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 1\n",
      "def Rh(h,w):\n",
      "    A = (w * h) + (h * h)        # m^2, is the cross sectional area of the flow\n",
      "    P = w + 2 * h * np.sqrt(2.)     # m, is the wetted perimeter of the channel\n",
      "    rv = A / P\n",
      "    return rv\n",
      "Rh(2,4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "1.2426406871192852"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 2\n",
      "def Vavg(h,w,n,S):\n",
      "    rv = Rh(h,w)**(2.0/3) * np.sqrt(S) / n\n",
      "    return rv\n",
      "Vavg(2,4,0.025,0.005)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "3.2692041364531312"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 3\n",
      "def Qtot(h,w,n,S):\n",
      "    A = (w+h) * h\n",
      "    return A * Vavg(h,w,n,S)\n",
      "Qtot(2,4,0.025,0.005)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "39.230449637437573"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 4\n",
      "h = np.linspace(1,4,100)\n",
      "Q = Qtot(h,4,0.025,0.005)\n",
      "plt.plot(h,Q,label='w=4')\n",
      "Q = Qtot(h,6,0.025,0.005)\n",
      "plt.plot(h,Q,label='w=6')\n",
      "Q = Qtot(h,8,0.025,0.005)\n",
      "plt.plot(h,Q,label='w=8')\n",
      "plt.legend(loc='best')\n",
      "plt.xlabel('h (m)')\n",
      "plt.ylabel('Q (m$^3$/s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.text.Text at 0x1075963d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAY8AAAEPCAYAAAC6Kkg/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1078a1950>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 5\n",
      "def Qdiff(h,w,n,S,Qd):\n",
      "    Qt = Qtot(h,w,n,S)\n",
      "    return Qd - Qt\n",
      "from scipy.optimize import fsolve\n",
      "h50 = fsolve(Qdiff,3,args=(4,0.025,0.005,50))\n",
      "print 'design discharge is 50'\n",
      "print 'computed water height is ',h50\n",
      "print 'discharge computed with Qtot is ',Qtot(h50,4,0.025,0.005)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "design discharge is 50\n",
        "computed water height is  [ 2.28088116]\n",
        "discharge computed with Qtot is  [ 50.]\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 6\n",
      "w = 6.0\n",
      "n = 0.02\n",
      "S = 0.004\n",
      "h = np.zeros(5)\n",
      "Qd = np.arange(20,101,20)\n",
      "for i in range(5):\n",
      "    h[i] = fsolve(Qdiff,1,args=(w,n,S,Qd[i]))\n",
      "print 'Design discharge is ',Qd\n",
      "print 'Corresponding water height is ',h\n",
      "plt.plot(Qd,h,'b-o')\n",
      "plt.xlabel('Design discharge (m$^3$/d)')\n",
      "plt.ylabel('Water height (m)')\n",
      "plt.title('w=6 m, n=0.02, S=0.004')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Design discharge is  [ 20  40  60  80 100]\n",
        "Corresponding water height is  [ 1.03196415  1.54829374  1.95427027  2.29943954  2.60427215]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<matplotlib.text.Text at 0x1079fc150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEfCAYAAACqKwpQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiIiIiIiIiIiIiIJOD/AUK5iUf/BI6oAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107996910>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"#back1\">Back to Exercise 1</a>\n",
      "\n",
      "<a name=\"ex2answer\">Answers to Exercise 2</a>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 1\n",
      "head = np.loadtxt('emptying_reservoir.csv',skiprows=54,usecols=[1],delimiter=\";\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 2\n",
      "plt.subplot(211)\n",
      "plt.plot(head)\n",
      "plt.xlim(170,190)\n",
      "plt.ylim(1115,1120)\n",
      "plt.subplot(212)\n",
      "plt.plot(head)\n",
      "plt.xlim(325,335)\n",
      "plt.ylim(1040,1080)\n",
      "print 'Data from index 184 to 332'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Data from index 184 to 332\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEGCAYAAACD7ClEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107996110>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 3\n",
      "headnew = head[184:332]\n",
      "print len(headnew)\n",
      "time = np.arange(0,len(headnew)*30,30)\n",
      "plt.plot(time,headnew)\n",
      "plt.xlabel('time (seconds')\n",
      "plt.ylabel('head (cm)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "148\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.text.Text at 0x107d55510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAEPCAYAAACHuClZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107953590>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 4\n",
      "a = np.polyfit(time,headnew,2)\n",
      "hfit = np.polyval(a,time)\n",
      "plt.plot(time,headnew,'b',label='data')\n",
      "plt.plot(time,hfit,'r',label='parabola')\n",
      "plt.xlabel('time (seconds')\n",
      "plt.ylabel('head (cm)')\n",
      "plt.legend(loc='best')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<matplotlib.legend.Legend at 0x107cdc250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAEPCAYAAACHuClZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIiIiIiIpIe/w/F6FYeGenJoQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106337290>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Step 5\n",
      "def dhdt(t):\n",
      "    return 2*a[0]*t + a[1]\n",
      "dhdtnum = (headnew[1:] - headnew[:-1]) / 30.0\n",
      "plt.plot(0.5*(time[1:]+time[:-1]), dhdtnum,label='numerical 1') \n",
      "dhdtnum2 = (headnew[2:] - headnew[:-2]) / 60.0\n",
      "plt.plot(time[1:-1],dhdtnum2,'r',label='numerical 2')\n",
      "dhdtpoly = dhdt(time)\n",
      "plt.plot(time,dhdtpoly,'k',label='parabola')\n",
      "plt.legend(loc='best')\n",
      "plt.xlabel('time (seconds')\n",
      "plt.ylabel('head (cm)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<matplotlib.text.Text at 0x107dbbf90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZkAAAEPCAYAAACQmrmQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107dba2d0>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"#back2\">Back to Exercise 2</a>"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}