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+{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13 : Centrifugal Separation Operations\n"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "example 13.1 page no : 259"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "find\n",
+ "ratio of cetrifugal force & gravitational force\n",
+ "equivalent to gravity settling tank of crossectional area\n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Initialization of Variable\n",
+ "rho = 998.\n",
+ "g = 9.81\n",
+ "pi = 3.1428\n",
+ "omega = 2*pi*1055./60 #angular rotation\n",
+ "r = 2.55/100 #radius outer\n",
+ "ld = 1.55/100. #liq. depth\n",
+ "l = 10.25/100.\n",
+ "\n",
+ "#calculation\n",
+ "#part1\n",
+ "a = r*omega**2/g\n",
+ "print \"ratio of cetrifugal force & gravitational force is: %.4f\"%a\n",
+ "\n",
+ "#part2\n",
+ "ri = r-ld #radius internal\n",
+ "V = pi*(r**2-ri**2)*l\n",
+ "sigma = (omega**2*V)/(g*math.log(r/ri))\n",
+ "print \"equivalent to gravity settling tank of crossectional area of in (m**2): %.4f\"%sigma\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ratio of cetrifugal force & gravitational force is: 31.7517\n",
+ "equivalent to gravity settling tank of crossectional area of in (m**2): 0.2358\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "example 13.2 page no : 261"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "find\n",
+ "The maximum safe speed allowed in rpm\n",
+ "the power in N/m**2\n",
+ "pressure gradient in radial direction \n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Initialization of Variable\n",
+ "sigma = 55.*10**6 #maximum stress\n",
+ "d = 35.2/100\n",
+ "rhos = 8890. #density of bronze\n",
+ "rho = 1105. #density of solution\n",
+ "t = 80./1000 #thickness\n",
+ "tau = 4.325/1000.\n",
+ "pi = 3.1428\n",
+ "\n",
+ "#calculation\n",
+ "#part1\n",
+ "ri = d/2.-t #radius internal\n",
+ "def fround(x,n):\n",
+ " # fround(x,n)\n",
+ " # Round the floating point numbers x to n decimal places\n",
+ " # x may be a vector or matrix# n is the integer number of places to round to\n",
+ " y = round(x*10**n)/10**n\n",
+ " return y\n",
+ "\n",
+ "omega = math.sqrt((sigma*tau*2/d)/(.5*rho*(d**2/4-ri**2)+rhos*tau*d/2))\n",
+ "N = 60*omega/2/pi\n",
+ "print \"The maximum safe speed allowed in rpm: %.4f\"%N\n",
+ "\n",
+ "#part2\n",
+ "P = .5*rho*(d**2./4-ri**2)*omega**2\n",
+ "P = fround(P/10**4,1)*10.**4\n",
+ "#print (P,\"the power in N/m**2:\")\n",
+ "print 'the power in N/m**2: %3.2e'%( P)\n",
+ "a = rho*omega**2*d/2\n",
+ "a = fround(a/10**6,1)*10**6\n",
+ "#print (a,\"pressure gradient in radial direction in N/m**3:\")\n",
+ "print 'pressure gradient in radial direction in N/m**3: %3.2e'%( a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum safe speed allowed in rpm: 2560.1495\n",
+ "the power in N/m**2: 8.65e+05\n",
+ "pressure gradient in radial direction in N/m**3: 1.40e+07\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "example 13.3 page no : 262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# find minimum diameter in organic pigment\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Initialization of Variable\n",
+ "rhos = 1425. #density of organic pigment\n",
+ "rho = 998. #density of water\n",
+ "pi = 3.1428\n",
+ "omega = 360*2*pi/60.\n",
+ "mu = 1.25/1000.\n",
+ "t = 360.\n",
+ "r = 0.165+0.01\n",
+ "ro = 0.165\n",
+ "\n",
+ "#calculation\n",
+ "d = math.sqrt(18*mu*math.log(r/ro)/t/(rhos-rho)/omega**2)\n",
+ "print 'the minimum diameter in organic pigment in m: %3.1e'%( d)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the minimum diameter in organic pigment in m: 2.5e-06\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "example 13.4 page no : 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# find maximum volumetric flow rate\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Initialization of Variable\n",
+ "rhos = 1455. #density of crystals\n",
+ "rho = 998. #density of wliquid\n",
+ "g = 9.81\n",
+ "pi = 3.1428\n",
+ "mu = 1.013/1000\n",
+ "omega = 2*pi*60000/60.\n",
+ "l = 0.5\n",
+ "d = 2*10.**-6. #dia of particles\n",
+ "r = 50.5/1000. #radius\n",
+ "t = 38.5/1000 #thickness of liquid\n",
+ "\n",
+ "#calculation\n",
+ "ri = r-t\n",
+ "V = pi*l*(r**2-ri**2)\n",
+ "Q = d**2*(rhos-rho)/18/mu*omega**2*V/math.log(r/ri)\n",
+ "print \"the maximum volumetric flow rate in (m**3/s): %.4f\"%Q\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the maximum volumetric flow rate in (m**3/s): 0.0104\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "example 13.5 pageno : 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# find distance of xis of rotation of cream milk interface\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Initialization of Variable\n",
+ "rhoc = 867. #density of cream\n",
+ "rhom = 1034. #density of skimmem milk\n",
+ "rm = 78.2/1000. #radius of skimmed milk\n",
+ "rc = 65.5/1000. #radius of cream\n",
+ "\n",
+ "#calculation\n",
+ "r = math.sqrt((rhom*rm**2-rhoc*rc**2)/(rhom-rhoc))\n",
+ "\n",
+ "# results\n",
+ "print \"distance of xis of rotation of cream milk interface in (m): %.4f\"%r\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "distance of xis of rotation of cream milk interface in (m): 0.1249\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "example 13.6 page no : 266"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# find volumetric flow rate\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Initialization of Variable\n",
+ "rho = 1.210 #density of air\n",
+ "mu = 1.78/10**5\n",
+ "g = 9.81\n",
+ "rhos = 2655. #density of ore\n",
+ "pi = 3.1428\n",
+ "d = 0.095\n",
+ "dp = 2.*10**-6 #particle diameter\n",
+ "dt = 0.333 #dia of cyclone separator\n",
+ "h = 1.28\n",
+ "\n",
+ "#calculation\n",
+ "U = dp**2*g*(rhos-rho)/18/mu\n",
+ "Q = 0.2*(pi*d**2/4)**2*d*g/U/pi/h/dt\n",
+ "print \"volumetric flow rate in(m**3/s): %.4f\"%Q\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "volumetric flow rate in(m**3/s): 0.0215\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "example 13.7 page no : 268"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# find overall efficiency of cyclone separator\n",
+ "\n",
+ "import math \n",
+ "from numpy import linspace\n",
+ "# Initialization of Variable\n",
+ "b = 4.46*10**4\n",
+ "c = 1.98*10**4\n",
+ "s = 0.\n",
+ "def intregrate():\n",
+ " s = 0.\n",
+ " for i in range(10889):\n",
+ " d = linspace(0,10000,10889)\n",
+ " y = (1-math.exp(-b*d[i])*c*(1-math.exp(-c*d[i])))*0.69\n",
+ " s = s+y\n",
+ " a = y\n",
+ " return a\n",
+ "\n",
+ "a = intregrate()\n",
+ "\n",
+ "print \"overall efficiency of cyclone separator in %\",a*100\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "overall efficiency of cyclone separator in % 69.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-07 17:56:55 +0000