{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Mass Balance for a Mixer"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem Statement"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Import the Sympy symbolic algebra package, and initialize printing of mathematics."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import display\n",
      "from sympy import *\n",
      "init_printing()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Stream Variables"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "var('S1 W1 W2 S3 W3')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}S_{1}, & W_{1}, & W_{2}, & S_{3}, & W_{3}\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAAaBAMAAABshlyMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nNYjnmhR/384db1L65SblNmL/A/zU+CcTYtD8AAAAAElFTkSuQmCC\n",
       "prompt_number": 2,
       "text": [
        "(S\u2081, W\u2081, W\u2082, S\u2083, W\u2083)"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Equations"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Mass Balances"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mbal = [Eq(0, S1 - S3),\n",
      "        Eq(0, W1 + W2 - W3 )]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Feed composition specifications"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Specify compositions of the inlet streams"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "comp = [Eq(S1, 0.77*(S1 + W1)),\n",
      "        Eq(S3, 0.186*(S3 + W3))]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Production rate specification"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prod = [Eq(S3 + W3, 200)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eqns = mbal + comp + prod\n",
      "\n",
      "for eq in eqns:\n",
      "    display(eq)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$0 = S_{1} - S_{3}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGoAAAARBAMAAADH6iSmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
       "text": [
        "0 = S\u2081 - S\u2083"
       ]
      },
      {
       "latex": [
        "$$0 = W_{1} + W_{2} - W_{3}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAARBAMAAABZfOFDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJdjLNVN0iZu+7\nq0QgoRR7AAACSElEQVQ4EX1TPWzTQBT+XNs4f3UsYKjEEEsIhBA/VsVeoyIELFRiRvWUdmuXCkZP\nEKhQMiAxJhtCDMkCqlgITEzgDgyIxVLFCi1Fpa1SwjvfnR3HTt9w9973vfdd/N0FOHntHNKhNQfh\n9PtnltF8miaAYyjcGn7G9/1NPNzvRGNLmGmNzf9ygLkQuD+GU3kMZe4C6j9AD6KxUg+qF2XJ0ra5\nMOnLUMThOZRsKf7mwioHKgGMHcmJvRZAaXZghgluuDzPoWSTcgTMHAI/OVANYP6VnNirHrSuC3F0\nBErhHCoe3gPu/AHEd9ZsmFSlouzjxaKD2yOgFM6h4q4NFNd2oUnTHOjkOtR6FDZrK/TgtG3FpYvo\ns5pCCifU7EeLU/G6DpV8Pk1a85tAWwjHNCUnto2FWp+c0C/7ApfCMaW2pj3ByW0Fa8qAOXERl4Ca\nk7WisqOh6rFLMHwxJYVjqtDSD4hTlhsUjxZY2xfLxR678bPoAlUbxvjlTR1cR9mno4Uw2bT8tl63\nCYipclikN5uKq88tbNB3UpwnP/soseemspMbjYDB6uEqCu9alGV+cUJlX+ncS2D9FRNQ3tCftIcp\njxUjoQ3I5+ipZIQTCgV3ZISld/vAikuJcpOtj3EmcohSGSVyr+KzKiOcUJiV7XLv0jd+4gVdHk7d\n+CoZuZsOmRmyKiOcUCWbNYzGFhVXOLC4Okrk5BnhpGcLP5IilZHD7U4KyRZGT2DmeKe+9OBDtp8j\nT/DamsRxvHjhyJ3QUR4OtydQuDf/Df8Ba4ukcLBd8cUAAAAASUVORK5CYII=\n",
       "text": [
        "0 = W\u2081 + W\u2082 - W\u2083"
       ]
      },
      {
       "latex": [
        "$$S_{1} = 0.77 S_{1} + 0.77 W_{1}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMQAAAARBAMAAABwex7EAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\npjq9FSb5kPgfKFd68+35P+Ozy8jYagS6AAAAAElFTkSuQmCC\n",
       "text": [
        "S\u2081 = 0.77\u22c5S\u2081 + 0.77\u22c5W\u2081"
       ]
      },
      {
       "latex": [
        "$$S_{3} = 0.186 S_{3} + 0.186 W_{3}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANoAAAARBAMAAABJHK+fAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n92cAAAAASUVORK5CYII=\n",
       "text": [
        "S\u2083 = 0.186\u22c5S\u2083 + 0.186\u22c5W\u2083"
       ]
      },
      {
       "latex": [
        "$$S_{3} + W_{3} = 200$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIUAAAARBAMAAAABA3JaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text": [
        "S\u2083 + W\u2083 = 200"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solve and Display Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "soln = solve(eqns)\n",
      "soln"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{Bmatrix}S_{1} : 37.2, & S_{3} : 37.2, & W_{1} : 11.1116883116883, & W_{2} : 151.688311688312, & W_{3} : 162.8\\end{Bmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAxMAAAAaBAMAAAA+kxw2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n",
       "prompt_number": 9,
       "text": [
        "{S\u2081: 37.2, S\u2083: 37.2, W\u2081: 11.1116883116883, W\u2082: 151.688311688312, W\u2083: 162.8}"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for (k,v) in soln.items():\n",
      "    print \"{:s} = {:6.2f} kg/day\".format(k,float(v))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "S1 =  37.20 kg/day\n",
        "W3 = 162.80 kg/day\n",
        "W1 =  11.11 kg/day\n",
        "S3 =  37.20 kg/day\n",
        "W2 = 151.69 kg/day\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}