{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1 - Particulate Solids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 13 Example 1.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LvxW4JX0mA68BZpLdXXAFsGan69qGtr4TmJGma9M+YBvgRmA22bfrNerSPuAL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\ns2U4OJiZ2TL+Px67cyeePwvIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e970f93d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " The surface mean diameter is 21.668 um\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,title,xlabel,ylabel,show\n",
    "from sympy.mpmath import quad\n",
    "#Given size analysis of a powdered material\n",
    "d=[1,101]##diameter of the powdered particles\n",
    "x=[0,1]##mass fractions of the particles\n",
    "plot(d,x)\n",
    "title(\"size analysis of powder\")\n",
    "xlabel(\"particle size(um)\")\n",
    "ylabel(\"mass fraction(x)\")\n",
    "show()\n",
    "#d=100*x+1# # from the given plot\n",
    "#calculation of surface mean diameter\n",
    "def surface_mean_diameter(x0,x1):\n",
    "    ds=1/(quad(lambda x:1/(100*x+1),[x0,x1]))\n",
    "    return ds\n",
    "\n",
    "ds=surface_mean_diameter(0,1)##deduced surface mean diameter according to def.\n",
    "print\"\\n The surface mean diameter is %.3f um\"%(ds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 14 Example 1.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ztjghmJkZkHFCkLSPpAckzZb0tKTPpvOHSJosab6k+4qv2syaE4KZWdsyrVSW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\nCGZmlnJCMDMzAP4/NERYI8Yy/TcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e96009b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " tot_n1d12 =13513 \n",
      " tot_n1d13=423975\n"
     ]
    },
    {
     "data": {
      "image/png": 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Tbrblb+O3s3/LgtwFPHvBs5w/7PxQh2QCyKvKv/Ly+NOmTfxh4EBut76FqGf3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\njDHmCJYcjDHGHMGSgzHGmCP8P02N8o8m39UaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e95e57550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "the surface mean diameter is: 31.374 um\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,title,xlabel,ylabel,show\n",
    "\n",
    "#from given differential eq we get these functions\n",
    "#particle number distribution for the size range 0-10um\n",
    "\n",
    "\n",
    "#n=0.5*d**2#\n",
    "#const of integration is0 since at n=0,d=0\n",
    "\n",
    "#particle number distribution for the size range 10-100um\n",
    "#n=83-(0.33*(10**(5))*d**(-3))\n",
    "#c2=83,since at d=10um,n=50\n",
    "\n",
    "#number distribution plot for the powdered material of size range 0-100um\n",
    "def number_distribution(d):\n",
    "    if(d<=10):\n",
    "        n=0.5*d**2#\n",
    "    else:\n",
    "        n=83-(0.33*(10**(5))*d**(-3))#\n",
    "    return n    \n",
    "d=0#\n",
    "n=[]\n",
    "while(d<=100):\n",
    "    n.append(number_distribution(d))\n",
    "    d=d+1# \n",
    "plot(range(0,101),n)\n",
    "title(\"number_distribution_plot\")\n",
    "xlabel(\"diameter(um)\")\n",
    "ylabel(\"number distribution\")\n",
    "show()\n",
    "\n",
    "\n",
    "ps=[0, 6.2, 9.0 ,10.0, 11.4, 12.1, 13.6 ,14.7 ,16.0 ,17.5 ,19.7 ,22.7, 25.5, 31.5 ,100]\n",
    "def difference(i):\n",
    "    #ps=[0 6.2 9.0 10.0 11.4 12.1 13.6 14.7 16.0 17.5 19.7 22.7 25.5 31.5 10]#\n",
    "    #according to the given particle sizes particle sizes are in um\n",
    "    n1=number_distribution(ps[i])-number_distribution(ps[i-1])#\n",
    "    return n1\n",
    "def average(i):\n",
    "    da= (ps[i]+ps[i-1])/2#\n",
    "    return da\n",
    "tot_n1d12=0#\n",
    "tot_n1d13=0#\n",
    "i=1#\n",
    "for i in range(1,15):\n",
    "        tot_n1d12=tot_n1d12+difference(i)*(average(i))**2\n",
    "        tot_n1d13=tot_n1d13+difference(i)*(average(i))**3\n",
    "\n",
    "print\"\\n tot_n1d12 =%d \\n tot_n1d13=%d\"%(tot_n1d12,tot_n1d13)\n",
    "def surface_area(j):\n",
    "    s=(difference(j)*(average(j))**2)/tot_n1d12\n",
    "    return s\n",
    "\n",
    "j=0#\n",
    "\n",
    "\n",
    "plot(0,0)\n",
    "su=[0]\n",
    "for j in range(1,15):\n",
    "    su.append(su[j-1]+surface_area(j))\n",
    "plot(ps[0:15],su)\n",
    "\n",
    "title(\"surface area and mass distribution plot\")\n",
    "xlabel(\"diameter(um)\")\n",
    "ylabel(\"surface area or mass distribution\")\n",
    "\n",
    "#mass distribution plot\n",
    "def mass_distribution(k):\n",
    "    x=(difference(k)*(average(k))**3)/tot_n1d13#\n",
    "    return x\n",
    "\n",
    "ma=[0]#\n",
    "k=0#\n",
    "plot(0,0)\n",
    "for k in range(1,15):\n",
    "    ma.append(ma[k-1]+mass_distribution(k))\n",
    "plot(ps[0:15],ma)\n",
    "show()\n",
    "#evaluating surface mean diameter\n",
    "def surface_mean_diameter():\n",
    "    e=0#\n",
    "    for l in range(1,15):\n",
    "        n=(mass_distribution(l)/average(l))#\n",
    "        e=e+n#\n",
    "    \n",
    "    d=1/e#\n",
    "    return d\n",
    "print\"\\nthe surface mean diameter is: %.3f um\"%(surface_mean_diameter())\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 32 Example 1.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " degree of mixing is :\n",
      "\n",
      "    0.89015\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZBU47LY0JOeUUuOqq1Jj+k5/A9Ol5R2fV1LuUkyLil5J2Bj4E1gN+EhH3l3Jp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\nw8zMuuT/A0V/e9OnX9eGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e96125d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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thI6eUGbOTCOyX37Zq/dVyi9/Cffem16eXt5qUdnHoUgaDRwM/IQ0TcrBgNeG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\nmVlJOKGYmVlJ/H+dC+bYHMazpwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e95ea3910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,title,xlabel,ylabel,show\n",
    "p=0.20##components analysed represents 20 percent of the mixture by mass\n",
    "#for a completely unmixed system\n",
    "so=p*(1-p)#\n",
    "#for a completely random mixture :\n",
    "n=100##Each of the sample removed contains 100 particles\n",
    "sr=p*(1-p)/n#\n",
    "s=[0.025, 0.006, 0.015, 0.018 ,0.019]\n",
    "time_secs=[30, 60 ,90 ,120 ,150]\n",
    "print\"\\n degree of mixing is :\\n\"\n",
    "b=[]\n",
    "def degree_of_mixing():\n",
    "    for i in range(0,5):\n",
    "        b.append((so-s[(i)])/(so-sr))\n",
    "    print \"    %0.5f\"%b[(i)]##b is the degree of mixing\n",
    "\n",
    "    return b#\n",
    "\n",
    "plot(time_secs,degree_of_mixing())\n",
    "title(\"degree of mixing curve\")\n",
    "xlabel(\"time_secs\")\n",
    "ylabel(\"degree_of_mixing\")\n",
    "show()\n",
    "#plot of sample variance vs time(secs)\n",
    "plot(time_secs,s)\n",
    "title(\"sample variance curve\")\n",
    "xlabel(\"time_secs\")\n",
    "ylabel(\"sample variance\")\n",
    "show()\n",
    "#from the graph the maxima is at 60 secs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 39 Example 1.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " required density is = 2377 kg/m**3\n",
      "\n",
      "required density is by newton law =1195 kg/m**3\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols,solve\n",
    "#maximum size of the particle(mm)\n",
    "d_max=0.065#\n",
    "#minimum size of the particle(mm)\n",
    "d_min=0.015#\n",
    "#density of quartz(kg/m**3)\n",
    "p_quartz=2650#\n",
    "#density of galena (kg/m**3)\n",
    "p_galena=7500#\n",
    "#minimum density of the particle which will give this seperation\n",
    "#When stoke's law is applied the required density is as given below\n",
    "def stoke_required_density():\n",
    "    p=symbols('p')\n",
    "    d=solve((p-7500)-(p-2650)*(d_max/d_min)**2)[0]\n",
    "    return d\n",
    "d=stoke_required_density()#\n",
    "print\"\\n required density is = %d kg/m**3\"%(d)\n",
    "#When Newton's law is applied then the required density is as given below\n",
    "def newton_required_density():\n",
    "    r=symbols('r')\n",
    "    e=solve((r-7500)-(r-2650)*(d_max/d_min))[0]\n",
    "    return e\n",
    "e=newton_required_density()#\n",
    "print\"\\nrequired density is by newton law =%d kg/m**3\"%(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 71 Example 1.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " the overall efficiency is = 65.7\n"
     ]
    }
   ],
   "source": [
    "#efficiency of the collector for different size ranges\n",
    "efficiency_1=45##in percentage for the size range of 0-5um\n",
    "efficiency_2=80##in percentage for the size range of 5-10um\n",
    "efficiency_3=96##in percentage for the size range greater than 10um\n",
    "\n",
    "#mass percent of the ndust for various size range\n",
    "mass_1=50# #in percentage for the size range of 0-5um\n",
    "mass_2=30# #in percetage for the size range of 5-10um\n",
    "mass_3=20# #in percentage for the size range greater than 10um\n",
    "# on the basis of 100kg dust\n",
    "mass_retained_1=0.45*50##mass retained(kg) in the size range of 0-5um\n",
    "mass_retained_2=0.80*30##mass retained(kg) in the size range of 5-10um\n",
    "mass_retained_3=0.96*20##mass retained(kg) in the size range greater than10um\n",
    "overall_efficiency=0.45*50+0.80*30+0.96*20#\n",
    "print\"\\n the overall efficiency is = %.1f\"%(overall_efficiency)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 71 Example 1.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "total mass retained = 13.230000 g\n",
      "\n",
      "total efficiency is = 73.500000\n",
      "total mass emitted is:4.770000 g\n",
      "\n",
      "total mass emitted less than 20 um is 4.320000g\n",
      "\n",
      "The efficiency of particles emitted is 90.566038\n",
      "\n",
      "mass flow rate is:1.431000 kg/sec\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "#To calculate mass flow of the dust emitted\n",
    "mass_1=10##in percentage in the size range of 0-5um\n",
    "mass_2=15##in percentage in the size range of 5-10um\n",
    "mass_3=35##in percentage in the size range of 10-20um\n",
    "mass_4=20##in percentage in the size range of 20-40um\n",
    "mass_5=10##in percentage in the size range of 40-80um\n",
    "mass_6=10##in percentage in the size range of 80-160um\n",
    "efficiecny_1=20##in percentage in the size range of 0-5um\n",
    "efficiency_2=40##in percentage in the size range of 5-10um\n",
    "efficiency_3=80##in percentage in the size range of 10-20um\n",
    "efficiency_4=90##in percentage in the size range of 20-40um\n",
    "efficiency_5=95##in percentage in the size range of 40-80um\n",
    "efficiency_6=100##in percentage in the size range of 80-160um\n",
    "dust_burden=18##in g/m**3 at the entrance\n",
    "#taking 1m**3 as the basis of calculation\n",
    "total_mass_retained=18*(0.1*0.20+0.15*0.40+0.35*0.80+0.2*0.9+0.1*0.95+0.1*1)#\n",
    "print\"\\ntotal mass retained = %f g\"%(total_mass_retained)#\n",
    "total_efficiency=(total_mass_retained/18)*100#\n",
    "print\"\\ntotal efficiency is = %f\"%(total_efficiency)#\n",
    "total_mass_emitted=18-total_mass_retained#\n",
    "print\"total mass emitted is:%f g\"%(total_mass_emitted)#\n",
    "t=18*(0.1*0.80+0.15*0.60+0.35*0.20)#\n",
    "print\"\\ntotal mass emitted less than 20 um is %fg\"%(t)\n",
    "e=t*100/total_mass_emitted#\n",
    "print\"\\nThe efficiency of particles emitted is %f\"%(e)#\n",
    "#gas flow is 0.3m**3/sec\n",
    "f=0.3*total_mass_emitted#\n",
    "print\"\\nmass flow rate is:%f kg/sec\"%(f)#\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 79 Example 1.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " cross sectional area at the gas inlet is 0.004418 m**2\n",
      "\n",
      "gas outlet diameter is 0.075000 m\n",
      "\n",
      "gas density is 1.300000 kg/m**3\n",
      "\n",
      "height of the seperator is 1.200000 m\n",
      "\n",
      "seperator diameter is0.300000 m\n",
      "\n",
      "mass flow rate of the gas is 0.008615 kg/sec\n",
      "\n",
      "the terminal velocity of the smallest particle retained by the seperator =0.000383m/sec\n",
      "\n",
      " particle diameter by the stoke law is 2.165585um\n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "from __future__ import division\n",
    "Ai=(pi/4)*(0.075)**2##cross sectional area at the gas inlet in m**2\n",
    "do=0.075##gas outlet diameter in m\n",
    "p=1.3##gas density in kg/m**3\n",
    "Z=1.2##height of the seperator in m\n",
    "dt=0.3##seperator diameter in m\n",
    "v=1.5##gas entry velocity in m/sec\n",
    "G=(Ai*v*p)##mass flow rate of the gas in kg/sec\n",
    "print\"\\n cross sectional area at the gas inlet is %f m**2\"%(Ai)#\n",
    "print\"\\ngas outlet diameter is %f m\"%(do)#\n",
    "print\"\\ngas density is %f kg/m**3\"%(p)#\n",
    "print\"\\nheight of the seperator is %f m\"%(Z)#\n",
    "print\"\\nseperator diameter is%f m\"%(dt)#\n",
    "print\"\\nmass flow rate of the gas is %f kg/sec\"%(G)\n",
    "def terminal_vel():\n",
    "    u=0.2*(Ai)**2*(do)*p*9.8/(pi*Z*(dt)*G)##velocity is in m/sec\n",
    "    return u\n",
    "\n",
    "u=terminal_vel()#\n",
    "print\"\\nthe terminal velocity of the smallest particle retained by the seperator =%fm/sec\"%(u)#\n",
    "def particle_diameter(u):\n",
    "    u=terminal_vel()#\n",
    "    n=0.018*10**(-3)##viscosity in mNs/m**2\n",
    "    ps=2700##density of the particle in kg/m**3\n",
    "    d=((u*18*n)/(9.8*(ps-p)))**(0.5)##particle size in um\n",
    "    return d\n",
    "u=terminal_vel()#\n",
    "d=particle_diameter(u)#\n",
    "do=d*10**6#\n",
    "print\"\\n particle diameter by the stoke law is %fum\"%(do)"
   ]
  }
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