{
 "metadata": {
  "name": "",
  "signature": "sha256:38873375f358fa0dcf49ba785f6ed30d427f72b9198eb1e335390fde0490d638"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "import pylab as pl\n",
      "import math\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import csv\n",
      "# number of the grid points \n",
      "\n",
      "ymax = 31;\n",
      "\n",
      "# material properties \n",
      "\n",
      "rho = 1000.0;\n",
      "mu = 0.00102;\n",
      "nu = mu / rho ; \n",
      "\n",
      "#dimensions of the computational domain\n",
      "l = 0.5 ;\n",
      "h = 1 ;\n",
      "w = 1.0 ;\n",
      "\n",
      "# define Reynolds number\n",
      "\n",
      "Re = 2000 ;\n",
      "\n",
      "# compute the average velocity\n",
      "\n",
      "ua = (Re*nu)/(2.0*h);\n",
      "\n",
      "# compute the pressure drop\n",
      "\n",
      "dp = (12.0*mu*l*ua)/(h*h);\n",
      "\n",
      "# compute the volume flow rate \n",
      "\n",
      "Q = (w*dp*h*h*h)/(12.0*mu*l);\n",
      "\n",
      "# create the grid \n",
      "\n",
      "dy = h/(ymax-1.0)\n",
      "\n",
      "y = np.zeros(ymax)\n",
      "\n",
      "y[0] = 0.0\n",
      "\n",
      "for i in range(1,ymax):\n",
      "    y[i] = y[i-1]+dy\n",
      "      \n",
      "# compute the analytical solution\n",
      "u =np.zeros(ymax)\n",
      "\n",
      "#define the boundary conditions...define them inside the loop\n",
      "u[0] = 0.0\n",
      "u[ymax-1] = 0.0\n",
      "const = dp/(2.0*mu*l )\n",
      "\n",
      "for j in range(1,ymax-1):\n",
      "    u[j] = const * y[j]*(h-y[j])\n",
      "   \n",
      "\n",
      "print ua\n",
      "\n",
      "plt.plot(u,y,'x')\n",
      "plt.ylabel('Position [m]')\n",
      "plt.xlabel('Velocity [m/s]')\n",
      "plt.title('1D laminar velocity profile in a channel ')\n",
      "plt.show()\n",
      "\n",
      "\n",
      "    \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "0.00102\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HAGiajizLlUWpyaO0tNTGxsamVCAQOMra7ujoKGAorr8geQCApuqIW6+3RCVm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\nPAAAQGH/DzHVDrxjXFBYAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cf6b190>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}