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+{
+ "metadata": {
+  "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 7  : Entrainment and Elutriation  from Fluidized Beds"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example 1, Page 179"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Entrainment from Fine Particle Beds with High Freeboard\n",
+      "\n",
+      "#Variable declaration\n",
+      "rhog=5.51;  #Density of gas in kg/m**3\n",
+      "rhos=1200;  #Density of solid in kg/m**3\n",
+      "dpbar=130;  #Average size of particles in micrometer\n",
+      "uo=0.61;    #Superficial gas velocity in m/s\n",
+      "g=9.80;     #Acceleration due to gravity in m/s**2\n",
+      "\n",
+      "#CALCULATION\n",
+      "#Assuming that freeboard in higher than TDH, computation of entrainment rate by Zenz & Weil's method\n",
+      "x=(uo**2)/(g*(dpbar*10**-6)*rhos**2);#Calculation of value of x-axis for Fig.(6), page 175\n",
+      "y=1.2;                               # Value of y-axis from Fig.(6)\n",
+      "Gsstar=y*rhog*uo;                    #Computation of rate of entrainment\n",
+      "\n",
+      "#OUTPUT\n",
+      "print '\\nRate of entrainment=%.2fkg/m**2s'%Gsstar\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "Rate of entrainment=4.03kg/m**2s\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example 2, Page 180\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Entrainment from Large Particle Beds with High Freeboard\n",
+      "\n",
+      "#Variable declaration\n",
+      "x=0.2;          #Fraction of fines in the bed\n",
+      "Gsstar=4.033320 #Rate of entrainment in kg/m**2s(from Exa.1)\n",
+      "\n",
+      "#CALCULATION\n",
+      "Gsstar1=x*Gsstar;#Rate of entrainment by Eqn.(3)\n",
+      "\n",
+      "#OUTPUT\n",
+      "print '\\nRate of entrainment=%.3fkg/m**2s'%Gsstar1\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "Rate of entrainment=0.807kg/m**2s\n"
+       ]
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example 3, Page 181\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Entrainment from Beds with a Wide Size Distribution of Solids\n",
+      "\n",
+      "#Variable declaration\n",
+      "rhog=5.51;                    #Density of gas in kg/m**3\n",
+      "rhos=1200;                    #Density of solid in kg/m**3\n",
+      "uo=0.61;                      #Superficial gas velocity in m/s\n",
+      "g=9.80;                       #Acceleration due to gravity in m/s**2\n",
+      "dp=[10,30,50,70,90,110,130];  #Diameter of particle in micrometer\n",
+      "p=[0.,0.0110,0.0179,0.0130,0.0058,0.0020,0.];\n",
+      "pi=3.142857;\n",
+      "dt=6;\n",
+      "\n",
+      "#CALCULATION\n",
+      "n=len(dp);\n",
+      "i=0;\n",
+      "x = [0,0,0,0,0,0,0]\n",
+      "while i<n:\n",
+      "    x[i]=(uo**2)/(g*(dp[i]*10**-6)*rhos**2);#Computation of value of x-axis for Fig.(6), page 175)\n",
+      "    i=i+1;\n",
+      "\n",
+      "y=[40,12,6,3.2,2.,1.3,1];#Value of y-axis corresponding to each value of x-axis\n",
+      "y1 = []\n",
+      "for i in range(n):\n",
+      "    y1.append(y[i]*p[i]);\n",
+      "i=0;\n",
+      "k=0;\n",
+      "\n",
+      "while i<n-2:\n",
+      "    y1[i]=(y[i]*p[i]);\n",
+      "    k=k+((0.5)*(dp[i+1]-dp[i])*(y1[i+1]+y1[i]));#Integration using Trapezoidal rule\n",
+      "    i=i+1;\n",
+      "rhosbar=k*rhog;#Computation of solid loading\n",
+      "te=(pi/4)*(dt**2)*rhosbar*uo;#Computation of total entrainment\n",
+      "\n",
+      "#OUTPUT\n",
+      "print '\\nSolid loading =%.1fkg/m**3'%rhosbar\n",
+      "print '\\nTotal Entrainment =%.0fkg/s'%te\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "Solid loading =32.4kg/m**3\n",
+        "\n",
+        "Total Entrainment =559kg/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example 4, Page 181\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#k* from Steady State Experiments\n",
+      "\n",
+      "#Variable declaration\n",
+      "dp=[40,60,80,100,120]; #Diameter of particle in micrometer\n",
+      "uo=0.381;              #Superficial gas velocity in m/s\n",
+      "\n",
+      "#CALCULATION\n",
+      "Gs=0.9;#Rate of entrainment in kg/m**2 s from Fig.3(a)\n",
+      "pb = [0.45,1.00,1.25,1.00,0.60];#Size distribution for bed particles from Fig.3(b)\n",
+      "pe=[1.20,2.00,1.25,0.45,0.10];  #Size distribution for entrained particles from Fig.3(b)\n",
+      "n=len(dp);\n",
+      "for i in range(n):\n",
+      "    pb[i] = pb[i]/100.\n",
+      "    pe[i] = pe[i]/100.\n",
+      "i=0;\n",
+      "ki = []\n",
+      "while i<n:\n",
+      "    ki.append((Gs*pe[i])/pb[i]);#Calculation of ki* using Eqn.(13)\n",
+      "    i=i+1;\n",
+      "\n",
+      "#OUTPUT\n",
+      "print '\\ndpi(micrometer)',\n",
+      "print '\\t100pb(dpi)(micrometer**-1)',\n",
+      "print '\\t100pe(dpi)(micrometer**-1)',\n",
+      "print '\\tki*(kg/m**2 s)'\n",
+      "\n",
+      "j=0;\n",
+      "while j<n:\n",
+      "    print '%f'%dp[j],\n",
+      "    print '\\t%f'%(100*pb[j]),\n",
+      "    print '\\t\\t\\t%f'%(100*pe[j]),\n",
+      "    print '\\t\\t\\t%f'%ki[j]\n",
+      "    j=j+1;\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "dpi(micrometer) \t100pb(dpi)(micrometer**-1) \t100pe(dpi)(micrometer**-1) \tki*(kg/m**2 s)\n",
+        "40.000000 \t0.450000 \t\t\t1.200000 \t\t\t2.400000\n",
+        "60.000000 \t1.000000 \t\t\t2.000000 \t\t\t1.800000\n",
+        "80.000000 \t1.250000 \t\t\t1.250000 \t\t\t0.900000\n",
+        "100.000000 \t1.000000 \t\t\t0.450000 \t\t\t0.405000\n",
+        "120.000000 \t0.600000 \t\t\t0.100000 \t\t\t0.150000\n"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example 5, Page 181\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Comparing Predictions for k*\n",
+      "\n",
+      "import math\n",
+      "\n",
+      "#Variable declaration\n",
+      "rhog=1.217;                                   #Density of gas in kg/m**3\n",
+      "myu=1.8E-5;                                   #Viscosity of gas in kg/m s\n",
+      "umf=0.11;                                     #Velocity at minimum fluidization condition in m/s\n",
+      "rhos=2000.0;                                  #Density of solid in kg/m**3\n",
+      "uo=1.0;                                       #Superficial gas velocity in m/s\n",
+      "g=9.80;                                       #Acceleration due to gravity in m/s**2\n",
+      "dp=[30,40,50,60,80,100,120];                  #Diameter of particle in micrometer\n",
+      "uti=[0.066,0.115,0.175,0.240,0.385,0.555,1.0];#Terminal velocity of particles in m/s\n",
+      "\n",
+      "#CALCULATION\n",
+      "n=len(dp);\n",
+      "i=0;\n",
+      "Ret = []\n",
+      "kistar1 = []\n",
+      "kistar2 = []\n",
+      "kistar3 = []\n",
+      "kistar4 = []\n",
+      "kistar5 = []\n",
+      "kistar6 = []\n",
+      "x1 = []\n",
+      "x2 = []\n",
+      "\n",
+      "while i<n:\n",
+      "    #Using Yagi & Aochi's correlation\n",
+      "    Ret.append((rhog*(uti[i])*dp[i]*10**-6)/myu)\n",
+      "    a =((myu*((uo-uti[i])**2))/(g*(dp[i]*10**-6)**2))*(0.0015*(Ret[i]**0.5)+(0.01*(Ret[i]**1.2)));\n",
+      "    kistar1.append(a)\n",
+      "    #Using Wen & Hasinger's correlation\n",
+      "    a=(((1.52E-5)*((uo-uti[i])**2)*rhog)/(g*dp[i]*10**-6)**0.5)*(Ret[i]**0.725)*((rhos-rhog)/rhog)**1.15;\n",
+      "    kistar2.append(a)\n",
+      "    #Using Merrick & Highley's correlation\n",
+      "    a=uo*rhog*(0.0001+130*math.exp(-10.4*((uti[i]/uo)**0.5)*((umf/(uo-umf))**0.25)));\n",
+      "    kistar3.append(a)\n",
+      "    #Using Geldart's correlation\n",
+      "    a=23.7*uo*rhog*math.exp(-5.4*(uti[i]/uo));\n",
+      "    kistar4.append(a)\n",
+      "    #Using Zenz & Weil's procedure\n",
+      "    a=(uo**2)/(g*(dp[i]*10.0**-6)*rhos**2);#Computation of value of x-axis for Fig.(6), page 175)\n",
+      "    x1.append(a)\n",
+      "    y1=[12.2,8.6,6.4,4.9,2.75,1.8,1.2];#Value of y-axis corresponding to each value of x-axis\n",
+      "    kistar5.append(y1[i]*rhog*uo)\n",
+      "    #Using Gugnoni & Zenz's procedure\n",
+      "    a=(uo-uti[i])/((g*dp[i]*10**-6)**0.5);#Computation of value of x-axis for Fig.(6), page 175)\n",
+      "    x2.append(a)\n",
+      "    y=[5.8,5.4,3.2,2.8,1.3,0.6,0];#Value of y-axis corresponding to each value of x-axis\n",
+      "    kistar6.append(y[i]*rhog*uo)\n",
+      "    i=i+1;\n",
+      "\n",
+      "i=0;\n",
+      "print 'dp(micrometer)',\n",
+      "print '\\tYagi & Aochi',\n",
+      "print '\\tWen & Hashinger',\n",
+      "print '\\t\\tMerrick & Highley',\n",
+      "print '\\tGeldart et al.',\n",
+      "print '\\t\\tZenz & Well',\n",
+      "print '\\t\\tGugnoni & Zenz'\n",
+      "while i<n:\n",
+      "    print '\\n%f'%dp[i],\n",
+      "    print '\\t%f'%kistar1[i],\n",
+      "    print '\\t%f'%kistar2[i],\n",
+      "    print '\\t\\t%f'%kistar3[i],\n",
+      "    print '\\t\\t%f'%kistar4[i],\n",
+      "    print '\\t\\t%f'%kistar5[i],\n",
+      "    print '\\t\\t%f'%kistar6[i],\n",
+      "    i=i+1;\n",
+      "\n",
+      "#Note: There is huge deviation of the calculated answer and the answer given in the textbook for the correlation of Merrick & Highley.  There is a contradiction in the correlation used in the problem and the one given in page 179. \n",
+      "#We tried to retrieve the original paper i.e. D.Merrick and J.Highley, AICHE J., 6, 220(1960). But the effort was not fruitful.\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "dp(micrometer) \tYagi & Aochi \tWen & Hashinger \t\tMerrick & Highley \tGeldart et al. \t\tZenz & Well \t\tGugnoni & Zenz\n",
+        "\n",
+        "30.000000 \t2.571188 \t1.092184 \t\t32.451340 \t\t20.195582 \t\t14.847400 \t\t7.058600 \n",
+        "40.000000 \t2.965958 \t1.564720 \t\t19.546385 \t\t15.500369 \t\t10.466200 \t\t6.571800 \n",
+        "50.000000 \t3.240381 \t1.938471 \t\t11.993076 \t\t11.210646 \t\t7.788800 \t\t3.894400 \n",
+        "60.000000 \t3.289995 \t2.154988 \t\t7.713841 \t\t7.892113 \t\t5.963300 \t\t3.407600 \n",
+        "80.000000 \t2.852535 \t2.120728 \t\t3.447977 \t\t3.606955 \t\t3.346750 \t\t1.582100 \n",
+        "100.000000 \t1.883718 \t1.521994 \t\t1.600171 \t\t1.440318 \t\t2.190600 \t\t0.730200 \n",
+        "120.000000 \t0.000000 \t0.000000 \t\t0.332158 \t\t0.130271 \t\t1.460400 \t\t0.000000\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example 6, Page 190\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Entrainment from a Short Vessel Ht<TDH\n",
+      "import math\n",
+      "\n",
+      "#Variable declaration\n",
+      "dpbar=60.0;   #Average size of particles in micrometer\n",
+      "rhog=1.3;     #Density of gas in kg/m**3\n",
+      "rhos=1500.0;  #Density of solid in kg/m**3\n",
+      "umf=0.003;    #Velocity at minimum fluidization condition in m/s\n",
+      "uo=0.503;     #Superficial gas velocity in m/s\n",
+      "g=9.80;       #Acceleration due to gravity in m/s**2\n",
+      "Hf=2.0;       #Height at which the cyclone inlet is to be located in m\n",
+      "\n",
+      "#CALCULATION\n",
+      "y=(uo**2)/(g*(dpbar*10**-3)*rhos**2);#Calculation of value of y-axis for Fig.(6), page 175\n",
+      "x=1;#Value of x-axis from Fig.(6), page 175\n",
+      "Gsstar=x*rhog*uo;#Computation of rate of entrainment\n",
+      "Gsuo=5.0;#Ejection rate pf particles in kg/m**2 s from Fig.(11), page 188\n",
+      "a=0.72/uo;#From Fig.(12), page 189\n",
+      "Gs=Gsstar+(Gsuo-Gsstar)*math.exp(-a*Hf);\n",
+      "p=((Gs-Gsstar)/Gsstar)*100.0;\n",
+      "\n",
+      "#OUTPUT\n",
+      "print '\\nRate of entrainment from short bed=%.3fkg/m**2s'%Gs\n",
+      "print '\\nThis entrainment is %f percent higher than it would be if the gas exit were at the TDH'%p\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "Rate of entrainment from short bed=0.902kg/m**2s\n",
+        "\n",
+        "This entrainment is 37.955972 percent higher than it would be if the gas exit were at the TDH\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file