DC Python Tutorial for Juan to test.ipynb

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   "source": [
    "# DC Python Tutorial\n",
    " \n",
    "Hint: If you are typing a function name and want to know what the options are for completing what you are typing, just hit the tab key for a menu of options.\n",
    "\n",
    "Hint: If you want to see the source code associated with a function, you can do the following\n",
    "import inspect\n",
    "inspect.getsource(foo) \n",
    "\n",
    "Where \"foo\" is the function that you'd like to learn about. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "source": [
    "#Here we import packages that we will need for this notebook. You can find out about these packages in the Help menu.\n",
    "\n",
    "\n",
    "# although math is \"built in\" it needs to be imported so it's functions can be used.\n",
    "import math\n",
    "\n",
    "from scipy import constants, interpolate\n",
    "\n",
    "#see numpy cheat sheet https://www.dataquest.io/blog/images/cheat-sheets/numpy-cheat-sheet.pdf\n",
    "#The numpy import is needed because it is renamed here as np.\n",
    "import numpy as np\n",
    "\n",
    "import pandas as pd\n",
    " \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# sys and os give us access to operating system directory paths and to sys paths.\n",
    "import sys, os\n",
    "\n",
    "# If you place your GitHub directory in your documents folder and \n",
    "# clone both the design challenge notebook and the AguaClara_design repo, then this code should all work.\n",
    "# If you have your GitHub directory at a different location on your computer, \n",
    "# then you will need to adjust the directory path below.\n",
    "# add the path to your GitHub directory so that python can find files in other contained folders.\n",
    "path1 = '~'\n",
    "path2 = 'Documents'\n",
    "path3 = 'GitHub'\n",
    "path4 = os.path.join(path1, path2, path3)\n",
    "myGitHubdir=os.path.expanduser(path4)\n",
    "if myGitHubdir not in sys.path:\n",
    "    sys.path.append(myGitHubdir)\n",
    "\n",
    "# add imports for AguaClara code that will be needed\n",
    "# physchem has functions related to hydraulics, fractal flocs, flocculation, sedimentation, etc.\n",
    "from AguaClara_design import physchem as pc\n",
    "\n",
    "# pipedatabase has functions related to pipe diameters\n",
    "from AguaClara_design import pipedatabase as pipe\n",
    "\n",
    "# units allows us to include units in all of our calculations\n",
    "from AguaClara_design.units import unit_registry as u\n",
    "\n",
    "from AguaClara_design import utility as ut"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Resources in getting started with Python \n",
    "Here are some basic [Python functions](http://docs.python.org/3/library/functions.html) that might be helpful to look through. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transitioning From Matlab To Python\n",
    "\n",
    "**Indentation** - When writing functions or using statements, Python realises related blocks of code from the way they are indented\n",
    "\n",
    "**Suppressing Statements** - Unlike Matlab, you do not need a semi-colon to suppress a statement in Python;\n",
    "\n",
    "**Indexing** - Matlab starts at index 1 whereas Python starts at index 0. \n",
    "\n",
    "**Functions** - In Matlab, functions are written by invoking the keyword \"function\", the return parameter(s), the equal to sign, the function name and the input parameters. A function is terminated with \"end\". \n",
    "\n",
    "`function y = average(x)\n",
    "if ~isvector(x)\n",
    "    error('Input must be a vector')\n",
    "end\n",
    "y = sum(x)/length(x); \n",
    "end`\n",
    "\n",
    "In Python, functions can be written by using the keyword \"def\", followed by the function name and then the input parameters in paranthesis followed by a colon. A function is terminated with \"return\". \n",
    "\n",
    "`def average(x):\n",
    "   if ~isvector(x)\n",
    "   raise VocationError(\"Input must be a vector\")\n",
    "   return sum(x)/length(x); `\n",
    "  \n",
    "**Statements** - for loops and if statements do not require the keyword \"end\" in Python. The loop header in Matlab varies from that of Python. Check examples below:\n",
    "\n",
    "`s = 10;                                               \n",
    "H = zeros(s);                                                                  \n",
    "for c = 1:s                                          \n",
    "    for r = 1:s                                         \n",
    "        H(r,c) = 1/(r+c-1);                                                  \n",
    "    end\n",
    "end`\n",
    "\n",
    "\n",
    "`s = 10 \n",
    " H = []\n",
    " for (r in range(s)):\n",
    "  for (c in range(s)):\n",
    "   H[r][c].append(1/(r+c-1)`\n",
    "   \n",
    "   \n",
    "**Printing** - Use \"print\" in Python instead of \"disp\" in Matlab. \n",
    "\n",
    "**Matrices and Arrays** - In Matlab, it is common to use matrixes, but in Python, matrices are used primarily only for linear programming purposes. For this class, we will stay with using arrays. \n",
    "\n",
    "**Helpful Documents**\n",
    "\n",
    "[Numpy for Matlab Users](https://docs.scipy.org/doc/numpy-dev/user/numpy-for-matlab-users.html)\n",
    "\n",
    "[Stepping from Matlab to Python](http://stsievert.com/blog/2015/09/01/matlab-to-python/)\n",
    "\n",
    "[Python for Matlab Users, UC Boulder](http://researchcomputing.github.io/meetup_fall_2014/pdfs/fall2014_meetup13_python_matlab.pdf)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "---\n",
    "\n",
    "## Arrays and Lists\n",
    "\n",
    "Python has no native array type. Instead, it has lists, which are defined using [ ]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = [0,1,2,3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python has a number of helpful commands to modify lists, and you can read more about them [here](https://docs.python.org/2/tutorial/datastructures.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to use lists as arrays, numpy (numpy provides tools for working with **num**bers in **py**thon) provides an array data type that is defined using ( ). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a_array = np.array(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pint is compatible with NumPy, so it is possible to add units to arrays and perform certain calculations with these arrays. Refrain from using lists often because they do not handle units well. Additionally, use functions from NumPy if possible instead of function from the math package. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a_array_units = a_array * u.m"
   ]
  },
  {
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   "execution_count": 6,
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       "\\[\\begin{pmatrix}0 & 1 & 2 & 3\\end{pmatrix} meter\\]"
      ],
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       "$\\begin{pmatrix}0 & 1 & 2 & 3\\end{pmatrix}\\ \\mathrm{meter}$"
      ],
      "text/plain": [
       "<Quantity([0 1 2 3], 'meter')>"
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     },
     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "a_array_units"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to make a 2D array, you can use the same [command](https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[0,1,2],[3,4,5],[6,7,8]])\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indexing is done by row and then by column. To call all of the elements in a row or column, use a colon. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 7])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want a specific range of values in an array, you can also use a colon to slice the array, with the number before the colon being the index of the first element, and the number after the colon being **one greater** than the index of the last element."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_array[1:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For lists and 1D arrays, the `len()` command can be used to determine the length. Note that the length is NOT equal to the index of the last element because the indexes are zero based. The len function can be used with lists and arrays. For multiple dimension arrays the `len()` command returns the length of the first dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
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     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "len(a)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 11,
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     "data": {
      "text/plain": [
       "3"
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     "execution_count": 11,
     "metadata": {},
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   "source": [
    "len(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any higher dimension of array, `numpy.size()` can be used to find the total number of elements and `numpy.shape()` can be used to learn the dimensions of the array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
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     "execution_count": 12,
     "metadata": {},
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   "source": [
    "np.size(b)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a listing of the commands you can use to manipulate numpy arrays, refer to the [scipy documentation](https://docs.scipy.org/doc/numpy/reference/routines.array-manipulation.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes, it is helpful to have an array of elements that range from zero to a specified number. This can be useful, for example, in creating a graph. To create an array of this type, use `numpy.arange`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c = np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
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    "c"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Units\n",
    "\n",
    "Units are essential to engineering calculations. Units provide a quick check on all of our calculations to help reduce the number of errors in our analysis. Getting the right dimensions back from a calculation doesn't prove that the answer is correct, but getting the wrong dimensions back does prove that the answer is wrong! Unit errors from incorrect conversions are common when using apps that don't calculate with units. Engineering design work should always include units in the calculations. \n",
    "\n",
    "\n",
    "We use the pint package to add unit capabilities to our calculations in Python. We have imported the `pint.UnitRegistry` as 'u' and thus all of pint's units can be used by placing a 'u.' in front of the unit name. Meters are `u.m`, seconds are `u.s`, etc. Most units are simple values that can be used just like other terms in algebraic equations. The exception to this are units that have an offset. For example, in the equation PV=nRT, temperature must be given with units that have value of zero at absolute zero. We would like to be able to enter 20 degC into that equation and have it handle the units correctly. But you can't convert from degC to Kelvin by simply multiplying by a conversion factor. Thus for temperature the units have to be handled in a special way.\n",
    "\n",
    "Temperatures require use of the u.Quantity function to enter the value and the units of temperature separated by a ',' rather than by a multiplication symbol. This is because it doesn't make sense to multiply by a temperature unit because temperatures have both a slope and an intercept.\n",
    "\n",
    "You can find [constants that are defined in pint](https://github.com/hgrecco/pint/blob/master/pint/constants_en.txt) at the github page for pint.\n",
    "\n",
    "### Example problem and solution.\n",
    "Calculate the number of moles of methane in a 20 L container at 15 psi above atmospheric pressure with a temperature of 30 C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 1.62 mol of methane in the container.\n"
     ]
    }
   ],
   "source": [
    "# First assign the values given in the problem to variables.\n",
    "P = 15 * u.psi + 1 * u.atm\n",
    "T = u.Quantity(30,u.degC)\n",
    "V = 20 * u.L\n",
    "# Use the equation PV=nRT and solve for n, the number of moles.\n",
    "# The universal gas constant is available in pint.\n",
    "nmolesmethane = (P*V/(u.R*T.to(u.kelvin))).to_base_units()\n",
    "print('There are '+ut.sig(nmolesmethane,3)+' of methane in the container.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Functions \n",
    "\n",
    "If I were expecting to have to use the ideal gas law solved for number of moles in my future work as an engineer, I'd create a simple function so I can reuse it easily.\n",
    "\n",
    "- Function blocks begin with the keyword def followed by the function name and parentheses ( ).\n",
    "- Any input parameters or arguments should be placed within these parentheses. \n",
    "- The code block within every function starts with a colon (:) and is indented.\n",
    "- The statement return [expression] exits a function and returns an expression to the user. A return statement with no arguments is the same as return None.\n",
    "- (Optional) The first statement of a function can the documentation string of the function or docstring, writeen with apostrophes ' '.\n",
    "\n",
    "Below is an example of a function that takes three inputs, pressure, volume, and temperature, and returns the number of moles. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Creating a function is easy in Python\n",
    "def nmoles(P,V,T):\n",
    "    return (P*V/(u.R*T.to(u.kelvin))).to_base_units()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try using the new function to solve the same problem as above. You can reuse the variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 1.62 mol of methane in the container.\n"
     ]
    }
   ],
   "source": [
    "print('There are '+ut.sig(nmoles(P,V,T),3)+' of methane in the container.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Density Function\n",
    "We will create and graph functions describing density and viscosity of water as a function of temperature. We will use the [scipy 1D interpolate function](https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html#d-interpolation-interp1d) to create smooth interpolation between the known data points to generate a smooth function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`density_water`, defined in `physchem`, is a function that returns a fluid's density at a given temperature. It has one input parameter, temperature (in Celsius)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The density of water at 20.00 celsius is 998.2 kg/m³.\n"
     ]
    }
   ],
   "source": [
    "# Here is an example of how you could define the function yourself if you chose.\n",
    "\n",
    "# Below are corresponding arrays of temperature and water density with appropriate units attached.\n",
    "\n",
    "# The 1d interpolation function willuse a cubic spline.\n",
    "Tarray = u.Quantity([0,5,10,20,30,40,50,60,70,80,90,100],u.degC)\n",
    "rhoarray = [999.9,1000,999.7,998.2,995.7,992.2,988.1,983.2,977.8,971.8,965.3,958.4]*u.kg/u.m**3\n",
    "def DensityWater(T):\n",
    "    \n",
    "    rhointerpolated=interpolate.interp1d(Tarray, rhoarray, kind='cubic')\n",
    "    rho=rhointerpolated(T.to(u.degC))\n",
    "    return rho*u.kg/u.m**3\n",
    "\n",
    "# You can get the density of water for any temperature using this function call.\n",
    "print('The density of water at '+ut.sig(u.Quantity(20,u.degC),4) +' is '+ut.sig(DensityWater(u.Quantity(20,u.degC)),4)+'.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "GraphTarray = np.linspace(0, 100, num=41, endpoint=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Pipe Database\n",
    "\n",
    "The `pipedatabase` file in the `AguaClara_design` has many useful functions concerning pipe sizing. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6.625 inch"
      ],
      "text/latex": [
       "$6.625\\ \\mathrm{inch}$"
      ],
      "text/plain": [
       "<Quantity(6.625, 'inch')>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The OD function in pipedatabase returns the outer diameter of a pipe given the nominal diameter, ND. \n",
    "pipe.OD(6*u.inch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.0 inch"
      ],
      "text/latex": [
       "$3.0\\ \\mathrm{inch}$"
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      "text/plain": [
       "<Quantity(3.0, 'inch')>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The ND_SDR_available function returns the nominal diameter of a pipe given an inner diameter and SDR, standard diameter ratio.\n",
    "\n",
    "ID = 3.068 * u.inch\n",
    "SDR = 40\n",
    "pipe.ND_SDR_available(ID,SDR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\\[\\begin{pmatrix}0.5 & 1.0 & 2.0 & 3.0 & 4.0 & 6.0 & 8.0 & 10.0 & 12.0 & 16.0 & 18.0 & 24.0 & 30.0 & 36.0 & 48.0 & 60.0 & 72.0\\end{pmatrix} inch\\]"
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       "<Quantity([  0.5   1.    2.    3.    4.    6.    8.   10.   12.   16.   18.   24.\n",
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     },
     "execution_count": 23,
     "metadata": {},
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   ],
   "source": [
    "pipe.ND_all_available()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Physchem\n",
    "The 'AguaClara_design' [physchem](https://github.com/AguaClara/AguaClara_design/blob/master/physchem.py) has many useful fluids functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Q=5*u.L/u.s\n",
    "D=100*u.mm\n",
    "nu=1*u.mm**2/u.s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From utility, use the sig function to display calulated values to a user specified number of significant figures. Use as `ut.sig(value, sigfig)`. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'63662'"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ut.sig(pc.re_pipe(Q,D,nu),5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a table of a few of the equations that are provided below as functions describing pipe flow and their physchem function counterparts. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Equation Name                         |                                                                                            Equation                                                                                           |                       Physchem function                      |\n",
    "|---------------------------------------|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:------------------------------------------------------------:|\n",
    "| Reynolds Number                       |                                                                                 $Re= \\frac{{4Q}}{{\\pi D\\nu }}$                                                                                |                 `re_pipe(FlowRate, Diam, Nu)`                |\n",
    "| Swamee-Jain Friction factor           |                ${\\rm{f}} = \\frac{{0.25}}{{{{\\left[ {\\log \\left( {\\frac{\\varepsilon }{{3.7D}} + \\frac{{5.74}}{{{{{\\mathop{\\rm Re}\\nolimits} }^{0.9}}}}} \\right)} \\right]}^2}}}$                |             `fric(FlowRate, Diam, Nu, PipeRough)`            |\n",
    "| Hagen Pousille laminar flow head loss |                                                   ${h_{\\rm{f}}} = \\frac{{32\\mu LV}}{{\\rho g{D^2}}} = \\frac{{128\\mu LQ}}{{\\rho g\\pi {D^4}}}$                                                   |                                                              |\n",
    "| Darcy Weisbach head loss              |                                                             ${h_{\\rm{f}}} = {\\rm{f}}\\frac{8}{{g{\\pi ^2}}}\\frac{{L{Q^2}}}{{{D^5}}}$                                                            |    `headloss_fric(FlowRate, Diam, Length, Nu, PipeRough)`    |\n",
    "| Diameter                              | $0.66\\left ( \\varepsilon ^{1.25}\\left ( \\frac{LQ^{2}}{gh_{f}} \\right )^{4.75}+\\nu Q^{9.4}\\left ( \\frac{L}{gh_{f}} \\right )^{5.2} \\right )^{0.04}$| `diam_swamee(FlowRate, HeadLossFric, Length, Nu, PipeRough)` |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "\n",
    "## Our First Graph!\n",
    "\n",
    "We will use [matplotlib](https://matplotlib.org/) to create a graph of water density as a function of temperature. [Here](https://matplotlib.org/users/pyplot_tutorial.html) is a quick tutorial on graphing. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Poo5IClCiiwSrI10kKFLNfbMSHh8MngsjZ8NeXaOOqFaoyIsE/2Zmjcws0czm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\nN19ZTa5zO2Aj8EjYVfeQmdW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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa259eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a list of 100 numbers between 0 and 100 and then assign the units of degC to the array. \n",
    "# This array will be the x values of the graph.\n",
    "\n",
    "plotpoints=100\n",
    "GraphTarray = u.Quantity(np.array(np.linspace(0, 100, num=plotpoints, endpoint=True)),u.degC)\n",
    "\n",
    "# create a plot that shows both the original data values (plotted as points) \n",
    "# and the smooth curve that shows the density function.\n",
    "\n",
    "plt.plot(Tarray, rhoarray, 'o', GraphTarray, (DensityWater(GraphTarray)), '-')\n",
    "# For an x axis log scale use plt.semilogx(Tarray, rhoarray, 'o', xnew, f2(xnew), '-')\n",
    "# For a y axis log scale use plt.semilogy(Tarray, rhoarray, 'o', xnew, f2(xnew), '-')\n",
    "# For both axis log scale use plt.loglog(Tarray, rhoarray, 'o', xnew, f2(xnew), '-')\n",
    "\n",
    "plt.legend(['data', 'cubic'], loc='best')\n",
    "plt.xlabel('Temperature (degrees Celcius)')\n",
    "plt.ylabel('Density (kg/m^3)')\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Viscosity Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# dynamic viscosity\n",
    "def ViscosityDynamic(T):\n",
    "    Ttemp=T.to(u.kelvin).magnitude\n",
    "    mu=2.414*(10**-5)*u.Pa*u.s*10**((247.8)/(Ttemp-140))\n",
    "    return mu\n",
    "\n",
    "# kinematic viscosity\n",
    "def ViscosityKinematic(T):\n",
    "    nu=ViscosityDynamic(T)/(DensityWater(T))\n",
    "    return nu.to(u.mm**2/u.s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WjuavA13d/VR3Py18fCHegcmRDe7YnP89vz8fLt3Eb17R/s4iUrNi6VOYAzQDtJFwHXHh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\nUwyesUUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa5c36d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(GraphTarray, ViscosityKinematic(GraphTarray), '-')\n",
    "plt.xlabel('Temperature (degrees Celcius)')\n",
    "plt.ylabel('Viscosity (mm^2/s)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Design Challenge 1, learning Python, Jupyter, and some AguaClara Design Tools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1) \n",
    "Calculate the minimum inner diameter of a PVC pipe that can carry a flow of at least 10 L/s for the town of Ojojona. The population is 4000 people. The water source is a dam with a surface elevation of 1500 m. The pipeline connects the reservoir to the discharge into a distribution tank at an elevation of 1440 m. The pipeline length is 2.5 km. \n",
    "\n",
    "The pipeline inlet at the dam is a square edge with a minor loss coefficient (${K_e}$) of 0.5. The discharge at the top of the distribution tank results in a loss of all of the kinetic energy and thus the exit minor loss coefficient is 1. See the minor loss equation below.\n",
    "\n",
    "${h_e} = {K_e}\\frac{{{V^2}}}{{2g}}$\n",
    "\n",
    "The water temperature ranges from 10 to 30 Celsius. The roughness of a PVC pipe is approximately 0.1 mm. Use the fluids functions to calculate the inner pipe diameter.\n",
    "\n",
    "Report the critical design temperature, the kinematic viscosity (maximum viscosity will occur at the lowest temperature), and the minimum inner pipe diameter (in mm). Use complete sentences to report the results and use 2 significant digits (use the sig function)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The critical water temperature for this design is 10 degC.\n",
      "The kinematic viscosity of water is 1.3 mm²/s.\n",
      "The minimum pipe inner diameter is 97 mm.\n"
     ]
    }
   ],
   "source": [
    "SDR = 26\n",
    "Q = 10 * u.L/u.s\n",
    "delta_elevation = 1500 * u.m - 1440 * u.m\n",
    "L_pipe = 2.5 * u.km\n",
    "K_init = 1.5\n",
    "# The maximum viscosity will occur at the lowest temperature.\n",
    "T_crit = u.Quantity(10,u.degC)\n",
    "nu = ViscosityKinematic(T_crit)\n",
    "e = 0.1 * u.mm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2)\n",
    "Find the nominal diameter of a PVC pipe that is SDR26. SDR means standard diameter ratio. The thickness of the pipe wall is 1/SDR of the nominal diameter. The pipedatabase file has a useful function that returns nominal diameter given SDR and inner diameter.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The nominal diameter of the pipeline is 4.0 in (1.0e+2 mm).\n"
     ]
    }
   ],
   "source": [
    "SDR = 26\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 3) \n",
    "What is the actual inner diameter of this pipe in mm? Compare this with the [reported inner diameter for SDR-26 pipe](http://www.cresline.com/pdf/cresline-northwest/pvcpressupipeline_Re/CNWPVC-26.pdf) to see if our pipe database is reporting the correct value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The inner diameter of the pipe is 106 mm.\n",
      "Cresline reports the inner diameter is 106 mm.\n"
     ]
    }
   ],
   "source": [
    "pipeline_ID = pipe.ID_SDR(pipeline_ND,SDR)\n",
    "cresline_ID = 4.154*u.inch\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4) \n",
    "What is the maximum flow rate that can be carried by this pipe at the coldest design temperature?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum flow rate at 10 celsius is 0.013 m³/s.\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5) \n",
    "What is the Reynolds number and friction factor for this maximum flow? Assign these values to variable names so you can plot them later on the Moody diagram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Reynolds number and friction factor for the pipeline flow are 1.2e+5 and 0.022 respectively.\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6) \n",
    "Check to see if the fluids functions are internally consistent by calculating the head loss given the flow rate that you calculated and comparing that head loss with the elevation difference. Display enough significant digits to see the difference in the two values. Note that the Moody diagram has an accuracy of about ±5% for smooth pipes and ±10% for rough pipes [Moody, 1944](http://user.engineering.uiowa.edu/~me_160/lecture_notes/MoodyLFpaper1944.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The head loss is 60.5 m and that is close to the elevation difference of 60.0 m.\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7) \n",
    "How much more water (both volumetric and mass rate) will flow through the pipe at the maximum water temperature of 30 C? Take into account both the change in viscosity (changes the flow rate) and the change in density (changes the mass rate)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The increase in flow rate at 30 celsius is 2.4e-4 m³/s.\n",
      "The increase in mass rate at 30 celsius is 0.19 kg/s.\n"
     ]
    }
   ],
   "source": [
    "Tmax = u.Quantity(30,u.degC)\n",
    "nuhot = ViscosityKinematic(Tmax)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8)\n",
    "Why is the flow increase due to this temperature change so small given that viscosity actually changed significantly (see the calculation below)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The viscosity ratio for the two temperatures was 0.62.\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The flow is turbulent and thus viscosity has little influence on the flow rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9)\n",
    "Suppose an AguaClara plant is designed to be built up the hill from the distribution tank. The  transmission line will need to be lengthened by 30 m and the elevation of the inlet to the entrance tank will be 1450 m. The rerouting will also require the addition of 3 elbows with a minor loss coefficient of 0.3 each. What is the new maximum flow from the water source?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The new maximum flow rate at 10 celsius is 0.012 m³/s.\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 10)\n",
    "How much less water will flow through the transmission line after the line is rerouted?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The reduction in flow is 1.3e-3 m³/s.\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11)\n",
    "The next big goal is to create the Moody diagram using the friction factor function. As a first step, modify the friction factor function from that takes the Reynolds number and dimensionless roughness (ε/D) as inputs. You should define the friction function with an if, else statements. \n",
    "\n",
    "Create a beautiful Moody diagram. Format the graph well by hiding the arguments, add axis labels, and show a legend that clearly describes each plot. The result should look like the picture of a graph at right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#returns the friction factor for pipe flow for both laminar and turbulent flows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12) \n",
    "\n",
    "Create a beautiful Moody diagram. Format the graph well by hiding the arguments, add axis labels, and show a legend that clearly describes each plot. The result should look like the picture of a graph on the right.\n",
    "\n",
    "Start by creating a numpy array of Reynolds numbers (note that start and stop are the log10 of 3500 and log10 of 10^8.\n",
    "logspace(start, stop[, num, endpoint, base, ...])\n",
    "![](Moody.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QQgjReaSwCyEzZ870Wg6l4+yaEhYZxdlX38Ctf3+TUy+eiTJMPjF5BzNYMOd5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489Tk8IcR2G9OxEwpzRLE89zKtJezlXXFYlf1uBmfGvb+DXt/dl+gh/nBu7e9YmZZ36pKsJhs2y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa6bce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eGraph = np.array([0,0.0001,0.0003,0.001,0.003,0.01,0.03,0.1])\n",
    "Gpoint = 50\n",
    "ReG = np.logspace(math.log10(3500), 8, Gpoint)\n",
    "ReLam = np.logspace(math.log10(670),math.log10(2100),Gpoint)\n",
    "fLam = np.zeros(Gpoint)\n",
    "\n",
    "for i in range(0,Gpoint):\n",
    "    fLam[i] = fofRe(ReLam[i],0)\n",
    "\n",
    "fG = np.zeros((len(eGraph),Gpoint))\n",
    "for j in range(0,len(eGraph)-1):\n",
    "    for i in range(0, Gpoint):\n",
    "        fG[j,i]=fofRe(ReG[i],eGraph[j])\n",
    "    \n",
    "mylegend = np.append(eGraph.astype('str'),[('laminar', 'Pipeline')])  \n",
    "\n",
    "#I'd like to be able to set font size. None of the commented code works. First set of code makes an additional plot. \n",
    "#I'd like to know how to name a plot in a figure and show it a second time with additional items graphed.\n",
    "\n",
    "#ax = plt.subplot(111, xlabel='x', ylabel='y')\n",
    "#for item in ([ax.xaxis.label, ax.yaxis.label] +\n",
    "#             ax.get_xticklabels() + ax.get_yticklabels()):\n",
    "#    item.set_fontsize(20)\n",
    "\n",
    "#from matplotlib.font_manager import FontProperties as FP\n",
    "#FP(size=40)\n",
    "\n",
    "#Set the size of the figure to make it big!\n",
    "plt.figure('ax',(10,8))\n",
    "\n",
    "for i in range(len(fG)):\n",
    "    plt.plot( ReG,fG[i,:], '-', linewidth = 4)\n",
    "\n",
    "#fig = plt.figure()  \n",
    "plt.plot(ReLam,fLam,'k-',linewidth=4)\n",
    "plt.plot(pipeline_Re,fPipe,'ko')\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.grid(b=True, which='major', color='k', linestyle='-', linewidth=0.5)\n",
    "#Set the grayscale of the minor gridlines. Note that 1 is white and 0 is black.\n",
    "plt.grid(b=True, which='minor', color='0.5', linestyle='-', linewidth=0.5)\n",
    "#The next 2 lines of code are used to set the transparency of the legend to 1. \n",
    "#The default legend setting was transparent and was cluttered.\n",
    "leg = plt.legend(mylegend, loc='best')\n",
    "leg.get_frame().set_alpha(1)\n",
    "plt.xlabel('Reynolds number', fontsize=20)\n",
    "plt.ylabel('Friction factor', fontsize=20)\n",
    "plt.grid(True)\n",
    "\n",
    "#save the file so we can use it in other documents.\n",
    "plt.savefig(\"Moody.png\")\n",
    "plt.show()  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 13) \n",
    "Researchers in the AguaClara laboratory collected the following head loss data through a 1/8\" diameter tube that was 2 m long. I pasted the data into two numpy arrays below. When working withdata it is better to use NumPy arrays rather than lists because arrays are more versatile for computation. If you want to do math on a homogeneous array of numeric data, then you're much better off using NumPy, which can automatically vectorize operations on complex multi-dimensional arrays. We already added the units to the NumPy arrays. Calculate the maximum and minimum Reynolds number for this data set. The temperature was 22 C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HL_data=np.array([0.251 ,0.241 ,0.231 ,0.221 ,0.212 ,0.202 ,0.192 ,0.182 ,0.172 ,0.162 ,0.153 ,0.143 ,0.133 ,0.123 ,0.113 ,0.103 ,0.093 ,0.083 ,0.073 ,0.063])*u.m\n",
    "Q_data=np.array([148 ,144 ,135.5 ,133.833 ,128.167 ,122.667 ,115.667 ,112.833 ,106.833 ,102 ,94.833 ,86.5 ,82.667 ,77 ,73.333 ,67 ,60.833 ,51.5 ,48.667 ,41.833])*u.mL/u.min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Reynolds number varied from 2.9e+2 to 1.0e+3.\n"
     ]
    }
   ],
   "source": [
    "D_tube = 1/8*u.inch\n",
    "L_tube = 2*u.m\n",
    "T_data = u.Quantity(22,u.degC)\n",
    "nu_data = ViscosityKinematic(T_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Re_data_max = max(pc.re_pipe(Q_data,D_tube,nu_data))\n",
    "Re_data_min = min(pc.re_pipe(Q_data,D_tube,nu_data))\n",
    "print('The Reynolds number varied from '+ut.sig(Re_data_min,2)+' to '+ut.sig(Re_data_max,2)+'.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 14) \n",
    "Plot the data (as data points and NOT AS A CONTINUOUS LINE) and the theoretical value of head loss in a straight tube (as a curve) on a graph. For the theoretical value assume that minor losses were negligible. Make the y axis have units of cm and the x axis have units of mL/s. \n",
    "\n",
    "A couple of hints.\n",
    "* You can use the linspace command to create a set of flows to calculate the theoretical head loss for the plot. Linspace removes the units (this is a bug) and so you will need to reattach the correct units of flow.\n",
    "* When you create the theoretical head loss array you can use the np.zeros function to create an array of zeroes of the correct size before calculating each value of the array in a for loop. The array of zeroes needs to have units attached to it BEFORE asigning values to the elements of the array in the for loop.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "K_array = np.zeros(len(Q_data)-1)\n",
    "V_data = Q_data/(math.pi*(D_tube**2)/4)\n",
    "\n",
    "for i in range(0,len(Q_data)-1):\n",
    "    K_array[i]=2*u.g_0*(HL_data[i]-pc.headloss_fric(Q_data[i],D_tube,L_tube,nu_data,0*u.mm))/V_data[i]**2\n",
    "\n",
    "K = np.mean(K_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LG17KqasoaKxCtkstpjNHTJdT1MeQetK0+dWAsLsg/G6o0cy18V0mhxKG1nqa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\nlThgmJlZJQ4YZmZWyUPtfjYqR1CoJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbc47ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qpoint = 50\n",
    "\n",
    "# linspace removes the units (this is a bug) and so I need to reattach the units.\n",
    "QGraph = np.linspace(min(Q_data), max(Q_data), Qpoint)*Q_data[0].units\n",
    "\n",
    "HL_major_theory = np.zeros(Gpoint)*u.m\n",
    "HL_total_theory = np.zeros(Gpoint)*u.m\n",
    "\n",
    "\n",
    "for i in range(0,Qpoint):\n",
    "    HL_major_theory[i] = pc.headloss_fric(QGraph[i],D_tube,L_tube,nu_data,0*u.mm)\n",
    "    HL_total_theory[i] = pc.headloss(QGraph[i],D_tube,L_tube,nu_data,0*u.mm,K)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(Q_data.to(u.mL/u.s),HL_data.to(u.m),'o')\n",
    "plt.plot(QGraph.to(u.mL/u.s),HL_major_theory.to(u.m), '-',linewidth=2)\n",
    "plt.plot(QGraph.to(u.mL/u.s),HL_total_theory.to(u.m), '-',linewidth=2)\n",
    "\n",
    "leg=plt.legend(['data','theoretical major losses','theoretical total losses'], loc='best')\n",
    "leg.get_frame().set_alpha(1)\n",
    "plt.xlabel('Flow rate (mL/s)')\n",
    "plt.ylabel('Head loss (m)')\n",
    "plt.show()  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The theoretical model doesn't fit the data very well. We assumed that major losses dominated. But perhaps we were wrong. So let's try a more sophisticated approach where we fit major and minor losses to the data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xdata [  2.46666667e-06   2.40000000e-06   2.25833333e-06   2.23055000e-06\n",
      "   2.13611667e-06   2.04445000e-06   1.92778333e-06   1.88055000e-06\n",
      "   1.78055000e-06   1.70000000e-06   1.58055000e-06   1.44166667e-06\n",
      "   1.37778333e-06   1.28333333e-06   1.22221667e-06   1.11666667e-06\n",
      "   1.01388333e-06   8.58333333e-07   8.11116667e-07   6.97216667e-07] Len: 20 type: <class 'numpy.ndarray'>\n",
      "ydata [ 0.251  0.241  0.231  0.221  0.212  0.202  0.192  0.182  0.172  0.162\n",
      "  0.153  0.143  0.133  0.123  0.113  0.103  0.093  0.083  0.073  0.063] Len: 20 type: <class 'numpy.ndarray'>\n",
      "popt: 0.00333338705892\n"
     ]
    },
    {
     "data": {
      "image/png": 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AdWZL0Vatgssug/POg2rV4KOPggWnlEREQhdmIkkGVkZtZ7MXycDMGgFtgJlR\nxbea2XwzG21mNUsTpFQcaXNzaDd4Oo37v027wdNJm5sDO3bAiBHB/FiTJsEDD8C8eXD66bEOVyRh\nxPWkjWZ2IDAB6OPuGyPFzwJHAq2BVcBjRRzb08wyzCxj7dq15RKvhCd/ipOcDbk4wRQno0e8ybo2\nJwVTmpxwAsyfD/fcA/vtF+twRRJKmE9t5QANorbrR8qKxcyqECSRse4+Mb/c3b+PqvMc8FZhx7v7\nSGAkQEpKipcocok70VOc7Jf3C7fNGEfPLybyU7UDYMwY6NFDi02JxEiYiWQW0NTMGhMkkO7AFcU5\n0MwMeB5Y4u5DC+yr5+6rIptdgYVlF7LEq/wpTk5bPoeHpj3D7zas5t/HnsOgs65lzlXFuqxEJCSh\nJRJ332ZmvYF0IAkY7e6LzKxXZP8IM6sLZAAHAzvMrA/QAjgO6AEsMLN5kbe8292nAI+YWWvAgW+A\nG8M6B4kfxyblcsMbT9F5yccsPTSZ7pf/nc8bHkdyjeqxDk0k4YU6IDHyD/+UAmUjol6vJujyKug/\nQKH9FO7eoyxjlDi3Ywf8859MHNYfz/2Zx9tdwYjfX8wv+1alepUk+nZoFusIRRKeRrZL/PryS7jx\nRpg5kyrt2/Purfcz/qs8tm7IJbngwlQiEjNKJBJ/Nm8OFpp64olgHMiLL8If/8i5Zpwb69hE5DeU\nSCS+vPkm9O4N336rkekiFURcjyORBJKdDd26QefOcNBB8MknGpkuUkEokUhMTZq1gmEX3MzmJkex\n5a0pLLq1P8yZA6eeGuvQRKSYlEgkZj4aM5mjLmzPbW8/y6z6LTjnuuFcfMgZpC3STAQiFYkSiZS/\n9euhVy9OuzaVGj/9j16pA7j24vvJrlGX3LztDEnPjHWEIlICutku5ccdXn4Z7rwT1q1j9AmdefzU\nK/lpv/13qZY/il1EKga1SKR8fPUVtG8PV10FRx4JGRm8cNFtv0kiAEdotLpIhaJEIuHKzYWBA+G4\n44Lp3UeMgBkzoE0b+nZoRvUqSbtU12h1kYpHXVsSnqlTgzEhy5YFs/MOGQJ16uzcnT8qfUh6Jt9t\nyOUIjVYXqZCUSKTs5eRAnz4wfjw0awbTp8NZZxVaNbVNshKHSAWnri0pO9u2BdOaHH00vPUWPPRQ\nMF9WEUlERCoHtUikbMycCb16BfdBOnaEp5+GJk1iHZWIlAO1SKR01q8Plro9+WRYswb+/W+YMkVJ\nRCSBKJEeh1pgAAANO0lEQVTIXkmbk83fLhvAD/WPZPs/R5J1+fWwZAlcfLGWvBVJMEokUmLvj5/O\nEV3P477XB5N9yOF0vvpxLjzyItKWbop1aCISA6EmEjPraGaZZpZlZv0L2X+0mX1mZr+Y2V+Kc6yZ\nHWpm75rZfyO/a4Z5DhJl82bo148zLvsDR61ZzoAOvena41EW1WmiqU1EElhoicTMkoDhQCeCddgv\nN7MWBar9CNwGPFqCY/sD77t7U+D9yLaEyR0mToTmzeGRR5hwTHva3/BPXm3dEbdfLyFNbSKSmMJs\nkZwEZLn7MnffCowDukRXcPc17j4LyCvBsV2AMZHXY4DUsE5AgKVL4fzz4aKLoGZN+M9/GHZFf37c\n/5DfVNXUJiKJKcxEkgysjNrOjpSV9tg67r4q8no1UAcpe1u2wN/+BsccEywyNXRosE5Iu3aa2kRE\ndlGhx5G4u5uZF7bPzHoCPQEaNmxYrnFVeO+8E0xtsnQpXHYZPPYYJP/6fwBNbSIi0cJMJDlAg6jt\n+pGy0h77vZnVc/dVZlYPWFPYG7j7SGAkQEpKSqHJRgpYuRLuuAMmTICjjoJ334Vzzim0qqY2EZF8\nYXZtzQKamlljM6sKdAcml8Gxk4GrI6+vBiaVYcyJKS8PHn00uJn+9tvB1Cbz5xeZREREooXWInH3\nbWbWG0gHkoDR7r7IzHpF9o8ws7pABnAwsMPM+gAt3H1jYcdG3now8LqZXQ+sAC4N6xwSwiefBCPT\nFy0Kbqo/9RQ0bhzrqESkAjH3yt/rk5KS4hkZGbEOI26kzc3huQmfc92kZ7ho4XR+rpvM/iOGQ+fO\nGpUuIjuZ2Wx3T9lTvQp9s11KLi3jWxbc8w9e+WAM1fN+YfjvL+H506/g3oYppCqJiMheUCJJJJ99\nRvOLryL1uyw+/d1x3HvOTSw9LHimYUh6pm6ei8heUSJJBGvWQP/+8MILHHxgLW7p3I+3jz51l24s\njUoXkb2lRFKZbd8erJE+cGAwT9Zdd9Fj/9PJKiRnaFS6iOwtzf5bWc2YASkpwcDCE04IHuf9xz/o\n3bm1RqWLSJlSIqls1qyBa6+Fdu3ghx/g9deDgYXNmwPBQMJB3VqSXKM6BiTXqM6gbi11f0RE9pq6\ntiqLbdt+7cb6+Wfo1y94feCBv6mqUekiUpaUSCqDTz+FW26BL78MRqM/9RQcfXSsoxKRBKGurYrs\n++/hmmvg1FNh3bpgvfRp05RERKRcKZFURNu2Ba2OZs3glVeCR3u1XrqIxIi6tuJE2tyc4k3LHt2N\nde65vyYUEZEYUYskDqTNzWHAxAXkbMjFgZwNuQyYuIC0uVGz7hfWjZWeriQiIjGnRBIHhqRnkpu3\nfZey3LztDEnPLLwb66uv1I0lInFDXVtxoKjpSY5YmAEn3BEMJlQ3lojEKSWSOHBEjerkRCWTw35a\nz4APX+CihdOhQQMYPx66dVMLRETikrq24kDfDs2oXiWJpB3buSZjMtNH3siFiz8m89rewdNYF12k\nJCIicUstkjiQ2iaZWnNmUndgX5quXsbMpils+sdjnNP19FiHJiKyR0oksfbdd9C3L6e98go0bAjj\nx9NW3VgiUoGE2rVlZh3NLNPMssysfyH7zcyGRfbPN7PjI+XNzGxe1M/GyHrumNn9ZpYTte+8MM8h\nNFu3wpAhwc3zCRPgnnvUjSUiFVJoLRIzSwKGA+cC2cAsM5vs7oujqnUCmkZ+2gLPAm3dPRNoHfU+\nOcAbUcc97u6PhhV76KZNg9tug8zMYJ30xx+HI4+MdVQiInslzBbJSUCWuy9z963AOKBLgTpdgBc9\n8DlQw8zqFahzNrDU3VeEGGvo0ubmcFG/V3in2SnQoQObf/4F3n4bJk1SEhGRCi3MRJIMrIzazo6U\nlbROd+DVAmW3RrrCRptZzcI+3Mx6mlmGmWWsXbu25NGXoTdnZJF9ez/GDr2W05fP4R9nXM0pVz5J\nWr1WMY1LRKQsxPXjv2ZWFegM/Duq+FngSIKur1XAY4Ud6+4j3T3F3VNq164deqyFcocJEzjx/Hb0\n/mQs05r+nvZ/+ifP/v4SNnpSMHJdRKSCC/OprRygQdR2/UhZSep0Aua4+/f5BdGvzew54K2yCrhM\nLVoU3AeZPp31tRtx2xWD+aLBsbtUKWpEu4hIRRJmi2QW0NTMGkdaFt2ByQXqTAauijy99Xvgf+6+\nKmr/5RTo1ipwD6UrsLDsQy+F9evh9tuhVSuYNw+eeYYbbx/5myQCwYh2EZGKLrRE4u7bgN5AOrAE\neN3dF5lZLzPrFak2BVgGZAHPATfnH29mBxA88TWxwFs/YmYLzGw+cBZwR1jnUCLbt8OoUXDUUfD0\n09CzJ3z9Ndx0E38+rwXVqyTtUr16lST6dtC8WSJS8Zm7xzqG0KWkpHhGRkZ4H/DZZ3DrrTB7Npx2\nGgwbBq1b71Kl2OuNiIjECTOb7e4pe6qnke2lsWoV9OsHL70EycnBNO/duxc6oDC1TbISh4hUSnH9\n1Fbcyh+VftRR8NprcPfdwRohl1+uUekiknDUIimpqVOhT5/g/seFFwaj0ps0iXVUIiIxoxZJcWVl\nBYnjvMjUXlOmwOTJSiIikvDUIilC/s3xDWt+pP+ciVwxYwJJ+1WFRx4JHu+tWjXWIYqIxAUlkkKk\nzc1hwMQFnLXgI+59fyR1N/9IWsuz2e/RR+j0h+NjHZ6ISFxRIinEkPRMcvO202TdStYceCg3pw5g\nTnJzkudsoNMfYh2diEh8USIpRP7UJSN+fzHDT76UHfsk7VIuIiK/0s32QuRPXZKXVGVnEokuFxGR\nXymRFKJvh2aa0kREpJjUtVWI/BHomtJERGTPlEiKoClNRESKR11bIiJSKkokIiJSKkokIiJSKkok\nIiJSKkokIiJSKgmxQqKZrQVWhPgRhwE/hPj+ZUmxhkOxhkOxhqO4sf7O3WvvqVJCJJKwmVlGcZaj\njAeKNRyKNRyKNRxlHau6tkREpFSUSEREpFSUSMrGyFgHUAKKNRyKNRyKNRxlGqvukYiISKmoRSIi\nIqWiRLIHZtbRzDLNLMvM+heyv6+ZzYv8LDSz7WZ2aGTfN2a2ILIvI+Q4R5vZGjNbWMR+M7NhkfOY\nb2bHR+3b7TnGINYrIzEuMLMZZtYqal+5fafFjPVMM/tf1DVwb9S+ePte4+JajXxeAzP7wMwWm9ki\nM7u9kDpxcc0WM9a4uGaLGWvZX7Purp8ifoAkYClwJFAV+BJosZv6FwLTo7a/AQ4rp1hPB44HFhax\n/zxgKmDA74GZe3OO5RTrKUDNyOtO+bGW93dazFjPBN4q7bVTHrEWqBuzazXyefWA4yOvDwK+Lvj9\nxMs1W8xY4+KaLWasZX7NqkWyeycBWe6+zN23AuOALrupfznwarlEVoC7fwz8uJsqXYAXPfA5UMPM\n6lHycww9Vnef4e7rI5ufA/XDjGd3ivG9FiXuvtcCYnatArj7KnefE3m9CVgCFFy3IS6u2eLEGi/X\nbDG/16Ls9feqRLJ7ycDKqO1sivhDMbP9gY7AhKhiB94zs9lm1jO0KIunqHMp9jnGyPUE/yvNF0/f\nab5TIt0aU83smEhZ3H6v8XatmlkjoA0ws8CuuLtmdxNrtLi4ZvcQa5les1rYquxcCHzq7tH/IzzV\n3XPM7HDgXTP7KvK/RikGMzuL4C/lqVHF8fadzgEauvtmMzsPSAOaxjCe4oiba9XMDiRIaH3cfWPY\nn1caxYk1Xq7ZPcRa5tesWiS7lwM0iNquHykrTHcKdBW4e07k9xrgDYKmY6wUdS4lOcdyY2bHAaOA\nLu6+Lr88zr5T3H2ju2+OvJ4CVDGzw4jT7zUiLq5VM6tC8I/dWHefWEiVuLlmixFr3Fyze4o1lGu2\nPG4AVdQfghbbMqAxv958OqaQeocQ9E0fEFV2AHBQ1OsZQMeQ421E0TeFz2fXG5dflOQcyznWhkAW\ncEqB8nL/TosRa11+HY91EvBt5DuOu+81zq5VA14EnthNnbi4ZosZa1xcs8WMtcyvWXVt7Ya7bzOz\n3kA6wRMNo919kZn1iuwfEanaFZjm7j9FHV4HeMPMIPgDesXd3wkrVjN7leBpjMPMLBu4D6gSFecU\ngqdgsoCfgWt3d45hxVnMWO8FagHPRL6/bR5MMFeu32kxY70YuMnMtgG5QHcP/obG4/cKcXCtRrQD\negALzGxepOxugn+Q4+2aLU6s8XLNFifWMr9mNbJdRERKRfdIRESkVJRIRESkVJRIRESkVJRIRESk\nVJRIRESkVJRIRESkVJRIRESkVJRIRGLAzE6MTJpXzcwOiKwdcWys4xLZGxqQKBIjZvYQUA2oDmS7\n+6AYhySyV5RIRGLEzKoCs4AtBHM0bY9xSCJ7RV1bIrFTCziQYCW7ajGORWSvqUUiEiNmNplgFbrG\nQD137x3jkET2imb/FYkBM7sKyHP3V8wsCZhhZu3dfXqsYxMpKbVIRESkVHSPRERESkWJRERESkWJ\nRERESkWJRERESkWJRERESkWJRERESkWJRERESkWJRERESuX/ARYEoMX5J3ImAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbbb9c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([  3.33338706e-03,   8.44643791e+00])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "\n",
    "PipeRough = 0.1*u.mm\n",
    "\n",
    "def func(FlowRate, Diam, KMinor):\n",
    "    \n",
    "    a = pc.headloss(FlowRate, Diam, L_tube, nu, PipeRough, KMinor)\n",
    "    a = list(a)\n",
    "    b=[]\n",
    "    #print(a, type(a))\n",
    "    for i in range(len(a)):\n",
    "        b.append(a[i].magnitude)\n",
    "    return b\n",
    "cubicmeter_to_mL = (1* u.m**3/u.mL).to_base_units().magnitude\n",
    "xdata = Q_data.to(u.m**3/u.s).magnitude\n",
    "print('xdata',xdata, \"Len:\", len(xdata), \"type:\", type(xdata))\n",
    "                 \n",
    "ydata = HL_data.to(u.m).magnitude\n",
    "print('ydata',ydata, \"Len:\", len(ydata), \"type:\", type(ydata))\n",
    "\n",
    "plt.plot(xdata*cubicmeter_to_mL, ydata, 'o', label='data')\n",
    "\n",
    "# The xdata and y data are in mL (1 cm^3) and cm, so the bounds on diam must also be in cm. \n",
    "# 1/16 in diam = 0.15875 cm\n",
    "# 1/4 in diam = 0.635 cm\n",
    "# The second set of bounds are for K minor, and limit it to being 0 to 10. \n",
    "popt, pcov = curve_fit(func, xdata, ydata, bounds=[[0.0015875, 0.],[0.00635,20]])\n",
    "print(\"popt:\", popt[0])\n",
    "\n",
    "plt.plot(xdata*cubicmeter_to_mL, func(xdata, *popt), 'r-', label='fit')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "popt\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "analyze the flow data (perhaps from a data file)\n",
    "In any case illustrate data analysis from a ProCoDA file.\n",
    "figure out how to refer to a figure and format it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.33 mm'"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dtube=popt[0]*u.m\n",
    "ut.sig(Dtube.to(u.mm),3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Qi3llPXr0ZHTHMewpfYX5no0p47UjbYW3VaugQgXTRpGRjFUQoviRpFBEdOpk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\ngAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc133860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "def func(x, a, b, c):\n",
    "    return a * np.exp(-b * x) + c\n",
    "\n",
    "# define the data to be fit with some noise\n",
    "\n",
    "xdata = np.linspace(0, 4, 50)*u.s\n",
    "xdata=xdata\n",
    "y = func(xdata, 2.5*u.m, 1.3/u.s, 0.5*u.m)\n",
    "y_noise = 0.2 * np.random.normal(size=xdata.size)*u.m\n",
    "ydata = y + y_noise\n",
    "plt.plot(xdata, ydata, 'b-', label='data')\n",
    "xdata=xdata.magnitude\n",
    "\n",
    "\n",
    "# Fit for the parameters a, b, c of the function `func`\n",
    "\n",
    "popt, pcov = curve_fit(func, xdata, ydata)\n",
    "plt.plot(xdata, func(xdata, *popt), 'r-', label='fit')\n",
    "\n",
    "# Constrain the optimization to the region of ``0 < a < 3``, ``0 < b < 2``\n",
    "# and ``0 < c < 1``:\n",
    "\n",
    "popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 2., 1.]))\n",
    "plt.plot(xdata, func(xdata, *popt), 'g--', label='fit-with-bounds')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4062990816394629"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, b, c=popt\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.18826138635417"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44417596293188483"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\\[\\begin{pmatrix}3.0 & 2.748286302970369 & 2.521916520049668 & 2.3183388871108725 & 2.1352585656199032 & 1.9706117739592803 & 1.8225425233518422 & 1.6893816961391266 & 1.5696282305733054 & 1.4619322000273578 & 1.3650795958830646 & 1.2779786425612145 & 1.1996474904295433 & 1.129203147856134 & 1.0658515276443141 & 1.0088784956470285 & 0.957641820655752 & 0.9115639348186997 & 0.870125422979789 & 0.8328591675466294 & 0.7993450828852825 & 0.769205379885004 & 0.7421003073125559 & 0.7177243219502945 & 0.6958026443457432 & 0.6760881613471651 & 0.6583586405088272 & 0.6424142249652018 & 0.6280751805349616 & 0.6151798696588846 & 0.603582929332793 & 0.5931536324961865 & 0.5837744144052446 & 0.57533954737867 & 0.5677539489773804 & 0.560932110183199 & 0.554797131494387 & 0.5492798560723586 & 0.5443180901679341 & 0.5398559020393487 & 0.5358429914590387 & 0.5322341227019363 & 0.5289886146236118 & 0.5260698820801412 & 0.5234450235203336 & 0.5210844501014337 & 0.5189615521474862 & 0.5170523991905006 & 0.5153354702131142 & 0.513791411051902\\end{pmatrix} meter\\]"
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       "$\\begin{pmatrix}3.0 & 2.748286302970369 & 2.521916520049668 & 2.3183388871108725 & 2.1352585656199032 & 1.9706117739592803 & 1.8225425233518422 & 1.6893816961391266 & 1.5696282305733054 & 1.4619322000273578 & 1.3650795958830646 & 1.2779786425612145 & 1.1996474904295433 & 1.129203147856134 & 1.0658515276443141 & 1.0088784956470285 & 0.957641820655752 & 0.9115639348186997 & 0.870125422979789 & 0.8328591675466294 & 0.7993450828852825 & 0.769205379885004 & 0.7421003073125559 & 0.7177243219502945 & 0.6958026443457432 & 0.6760881613471651 & 0.6583586405088272 & 0.6424142249652018 & 0.6280751805349616 & 0.6151798696588846 & 0.603582929332793 & 0.5931536324961865 & 0.5837744144052446 & 0.57533954737867 & 0.5677539489773804 & 0.560932110183199 & 0.554797131494387 & 0.5492798560723586 & 0.5443180901679341 & 0.5398559020393487 & 0.5358429914590387 & 0.5322341227019363 & 0.5289886146236118 & 0.5260698820801412 & 0.5234450235203336 & 0.5210844501014337 & 0.5189615521474862 & 0.5170523991905006 & 0.5153354702131142 & 0.513791411051902\\end{pmatrix}\\ \\mathrm{meter}$"
      ],
      "text/plain": [
       "<Quantity([ 3.          2.7482863   2.52191652  2.31833889  2.13525857  1.97061177\n",
       "  1.82254252  1.6893817   1.56962823  1.4619322   1.3650796   1.27797864\n",
       "  1.19964749  1.12920315  1.06585153  1.0088785   0.95764182  0.91156393\n",
       "  0.87012542  0.83285917  0.79934508  0.76920538  0.74210031  0.71772432\n",
       "  0.69580264  0.67608816  0.65835864  0.64241422  0.62807518  0.61517987\n",
       "  0.60358293  0.59315363  0.58377441  0.57533955  0.56775395  0.56093211\n",
       "  0.55479713  0.54927986  0.54431809  0.5398559   0.53584299  0.53223412\n",
       "  0.52898861  0.52606988  0.52344502  0.52108445  0.51896155  0.5170524\n",
       "  0.51533547  0.51379141], 'meter')>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.66765607424578777"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func(2,*popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.40629908,  1.18826139,  0.44417596])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Possible additional tutorial topics\n",
    "* [integration](https://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FusionTables enables you to access the raw data through a SQL-formatted URL. This is actually how we pull the data from FusionTables over to the website for display. Here's an example URL for getting data for Moroceli: https://www.googleapis.com/fusiontables/v2/query?sql=SELECT%20*%20FROM%201Sk13vckXZIuOaokQ6tbOkHjRAthBFF7FkgsGaSjD%20WHERE%20plant%3D%27Moroceli%27%20AND%20rawWaterTurbidity%20%3E%200%20ORDER%20BY%20timeFinished%20DESC%20LIMIT%20100&key=AIzaSyAAWkBly-1cwH3rbyLIhoZtJAY3RUHrViM  If you look at the URL carefully, you can see that a whole SQL Query s boiled in, as well as an API key to specify which table to pull from. This (as you can see by going to it in a browser) is displayed to you in a JSON, which is natively compatible with many Python parsers. Alternatively, if you were wanting to make many different requests using a Python library, you could use the one made by Google here. I believe the restrictions are such that anyone who has the API key can view the data (makes sense 'cause there is no login on the website) but only logged-in users can actually change, add and delete data.\n",
    "\n",
    "Let me know if you need more direction! Here's a sample codebase I found using the Python library if you happen to go that way. It might be more distracting than helpful to use the Python library... If you want to just use the URL, here's a small code snippet that works to pull and parse the data: \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['*meta-instance-id*', '*meta-model-version*', '*meta-ui-version*', '*meta-submission-date*', '*meta-is-complete*', '*meta-date-marked-as-complete*', 'collectionMethod', 'deviceID', 'timeStarted', 'timeFinished', 'nFilters', 'needspH', 'location', 'location:Accuracy', 'plant', 'purpose', 'timeCollected', 'dateCollected', 'flowRate', 'CDCPos', 'rawWaterTurbidity', 'settledWaterTurbidity', 'settledWaterTurbidityCheck', 'filteredWaterTurbidity', 'filteredWaterTurbidityCheck', 'filteredWaterTurbidity1', 'filteredWaterTurbidity2', 'coagulantDose', 'coagulantCheck', 'chlorineDose', 'entranceWaterLevel', 'entranceWaterLevel1', 'entranceWaterLevel2', 'backwashed', 'whichFilters', 'backwashTime', 'backwashDate', 'backwashDuration', 'backwashDurationCheck', 'backwashTime1', 'backwashDate1', 'backwashDuration1', 'backwashDurationCheck1', 'backwashTime2', 'backwashDate2', 'backwashDuration2', 'backwashDurationCheck2', 'whichFilters', 'backwashTime', 'backwashDate', 'backwashDuration', 'backwashDurationCheck', 'backwashTime1', 'backwashDate1', 'backwashDuration1', 'backwashDurationCheck1', 'backwashTime2', 'backwashDate2', 'backwashDuration2', 'backwashDurationCheck2', 'repairsDoneOther', 'ToDoDescription', 'comments', 'instanceID', 'acidDosingChemical', 'backwashCheck1', 'newStock', 'entranceWaterLevelAfterBackwash1', 'backwashCheck2', 'coagulantDoseSuggestion', 'stockCoagulantCheck', 'stockChlorineCheck', 'stockChlorineConcentration', 'phoneNumber', 'filteredWaterTurbidity3', 'filteredWaterTurbidity4', 'HClDose', 'entranceWaterLevel3', 'entranceWaterLevel4', 'entranceWaterLevelAfterBackwash2', 'backwashCheck3', 'backwashCheck4', 'entrancepH', 'entranceTemp', 'entranceConductivity', 'flocpH', 'flocTemp', 'flocConductivity', 'distributionpH', 'distributionTemp', 'distributionConductivity', 'stockCoagulantConcentration', 'stockHClCheck', 'backwashTime3', 'backwashDuration3', 'entranceWaterLevelAfterBackwash3', 'backwashTime4', 'backwashDuration4', 'entranceWaterLevelAfterBackwash4', 'setlledWaterTurbidityCheck']\n"
     ]
    }
   ],
   "source": [
    "import urllib.request, json \n",
    "with urllib.request.urlopen(\"https://www.googleapis.com/fusiontables/v2/query?sql=SELECT%20*%20FROM%201Sk13vckXZIuOaokQ6tbOkHjRAthBFF7FkgsGaSjD%20WHERE%20plant%3D%27Moroceli%27%20AND%20rawWaterTurbidity%20%3E%200%20ORDER%20BY%20timeFinished%20DESC%20LIMIT%20100&key=AIzaSyAAWkBly-1cwH3rbyLIhoZtJAY3RUHrViM\") as url:\n",
    "    data = json.loads(url.read().decode())\n",
    "    print(data['columns'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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