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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 15 : Non newtonian phenomena"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 15.1 - Page No :760\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "\n",
      "# Variables\n",
      "# given\n",
      "r = array([10, 20, 50, 100, 200, 400, 600, 1000, 2000])\n",
      "tau = array([2.2, 3.1 ,4.4, 5.8, 7.4, 9.8, 11.1, 13.9, 17.0])\n",
      "\n",
      "# Calculation and Results\n",
      "#tau = tau*(10**-4);\n",
      "plot(r,tau);\n",
      "plot(r,tau,'ro');\n",
      "suptitle(\"asic shear diagram for the fluid\")\n",
      "xlabel(\"Shear rate, S**-1 \")\n",
      "ylabel(\"Shear streets, Nm**-2 \")\n",
      "\n",
      "# the data falls nearly on a straight line\n",
      "# from the graph the slope and the intercept are\n",
      "slope = 0.3841;\n",
      "intercept = 9.17046;\n",
      "# from the relation tau = K*(-r)**n;\n",
      "K = math.exp(intercept);\n",
      "n = slope\n",
      "print \"K = \",K\n",
      "print \"n = \",n\n",
      "print \" The fluid is pseudo plastic, since the slope is less than 1 \"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "K = "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 9609.04383369\n",
        "n =  0.3841\n",
        " The fluid is pseudo plastic, since the slope is less than 1 \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['draw_if_interactive']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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pWoFtbVkWejnHa8yYSkRkKNU+Vvr888/Rt29fXL58GaGhobh69So2b95c7YmH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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x35cb850>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 15.2 - Page No :774\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "a = array([651, 1361, 2086, 5089, 7575, 11140, 19270, 25030])\n",
      "tau = array([3.71, 7.49, 11.41, 24.08, -35.21, 46.25, 77.50, 96.68])\n",
      "\n",
      "# from the graph\n",
      "betao = -4.3790154;\n",
      "beta1 = 0.8851;\n",
      "\n",
      "# Calculations\n",
      "K = math.exp(betao);\n",
      "n = beta1;\n",
      "plot(a,tau);\n",
      "suptitle(\"Capillary shear diagram for polyisobutylene L-80 in cyclohexane.\")\n",
      "xlabel(\"Pseudoshear rate\")\n",
      "ylabel(\"Wall shear stress \")\n",
      "\n",
      "# Results\n",
      "print \" The final rheological model_ is  tauw  =  %f*8*Uz,avg/do)**%f\"%(K,n);\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " The final rheological model_ is  tauw  =  0.012538*8*Uz,avg/do)**0.885100\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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f5ORJGDVK2ydECHH/SjSP5Nq1a8TFxeHv72/JmIok80hESWRkwCefwPvvwzPP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\nCCFEqUgiEUIIUSr/D5BULYf7jJs0AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3f00550>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 15.3 - Page No :774\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "# from Example  15.2 \n",
      "n = 0.8851;\n",
      "K = 0.01254;\n",
      "n = n;\n",
      "\n",
      "# Calculations\n",
      "K = K/((3*n+1)/(4*n));\n",
      "\n",
      "# Results\n",
      "print \"n = \",n\n",
      "print \"K  =  %f N/m**2\"%(K);\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "n =  0.8851\n",
        "K  =  0.012146 N/m**2\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 15.4 - Page No :775\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "a = array([10, 20, 50, 100, 200, 400, 600, 1000, 2000])\n",
      "tau = array([2.24, 3.10, 4.35, 5.77, 7.50, 9.13, 11.0, 13.52, 16.40])\n",
      "tau = tau*10**-4;\n",
      "betao = 8.96694;\n",
      "beta1 = 0.48452520;\n",
      "beta2 = 0.010923041;\n",
      "\n",
      "# Calculations\n",
      "# such a plot suggests a second order polynomila  of the type y = betao+beta1*x+beta2*x**2;\n",
      "# where y = ln(tauw) and x = ln(8*Uz,avg/do) = ln(a);\n",
      "# from the graph\n",
      "n = beta1+2.*beta2*a;\n",
      "phiw = ((3.*n+1.)/(4.*n))*(a);\n",
      "mu = tau/phiw;\n",
      "\n",
      "# Results\n",
      "\n",
      "print \" 8*Uz,avg/do     n         ((3*n+1)/4*n)    phiw            mu\"\n",
      "for i in range(9):\n",
      "    print \" %6.0f       %8.4f      %8.4f      %8.4f       %6.6f\"%(a[i],n[i],3*n[i]+1/4*n[i],phiw[i],mu[i])\n",
      "\n",
      "\n",
      "# Answer in book is wrong. Please calculate manually."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 8*Uz,avg/do     n         ((3*n+1)/4*n)    phiw            mu\n",
        "     10         0.7030        2.1090       11.0563       0.000020\n",
        "     20         0.9214        2.7643       20.4262       0.000015\n",
        "     50         1.5768        4.7305       45.4273       0.000010\n",
        "    100         2.6691        8.0074       84.3663       0.000007\n",
        "    200         4.8537       14.5612      160.3013       0.000005\n",
        "    400         9.2230       27.6689      310.8425       0.000003\n",
        "    600        13.5922       40.7765      461.0358       0.000002\n",
        "   1000        22.3306       66.9918      761.1954       0.000002\n",
        "   2000        44.1767      132.5301      1511.3182       0.000001\n"
       ]
      }
     ],
     "prompt_number": 24
    }
   ],
   "metadata": {}
  }
 ]
}