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diff --git a/Problems_In_Fluid_Flow/ch11.ipynb b/Problems_In_Fluid_Flow/ch11.ipynb new file mode 100644 index 00000000..c36db144 --- /dev/null +++ b/Problems_In_Fluid_Flow/ch11.ipynb @@ -0,0 +1,479 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11 : Fluidisation\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 11.1 page no : 216" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "Bubbling fluidisation \n", + "fluidisation \n", + "'''\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "pi = 3.1428\n", + "d = 0.3/1000\n", + "mu = 2.21/100000\n", + "rho = 106.2 #density under operating condition\n", + "u = 2.1/100\n", + "rhos = 2600. #density of particles\n", + "l = 3.25\n", + "g = 9.81\n", + "dt = 0.95 #fluidising diameter\n", + "\n", + "\n", + "#part 1\n", + "#calculation\n", + "a = u**2./d/g*d*rho*u/mu*(rhos-rho)/rho*l/dt\n", + "if a>100 :\n", + " print \"Bubbling fluidisation will occur as value is %.4f\"%a\n", + "\n", + "#part 2\n", + "Q = 2.04/100000\n", + "rhos = 2510.\n", + "rho = 800.\n", + "mu = 2.85/1000\n", + "l = 4.01\n", + "dt = 0.63\n", + "d = 0.1/1000\n", + "u = Q*4/pi/dt**2\n", + "a = u**2/d/g*d*rho*u/mu*(rhos-rho)/rho*l/dt\n", + "if a<100*10**-4: #compare as value of a is much less than 100\n", + " print \"fluidisation occur in smooth mode as value is: %.4e\"%a\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Bubbling fluidisation will occur as value is 364.4332\n", + "fluidisation occur in smooth mode as value is: 1.0898e-07\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 11.2 page no ;218" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "The superficial linear flow rate\n", + "Terminal Settling Velocity\n", + "Stoke law assumption\n", + "Pressure drop across fluidised bed \n", + "'''\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "d = 50./1000000\n", + "rhos = 1850. #density of particle\n", + "rho = 880. #density of hydrocarbon\n", + "mu = 2.75/1000 #viscosity of hydrocarbon\n", + "e = 0.45 #void fraction coeff.\n", + "g = 9.81\n", + "h = 1.37 #flow depth\n", + "c = 5.5/1000 #c = 1/K\n", + "\n", + "#calculation\n", + "#part 1\n", + "u = c*e**3*d**2*g*(rhos-rho)/mu/(1-e)\n", + "print \"The superficial linear flow rate in (m/s): %.3e\"%u\n", + "\n", + "#part 2\n", + "u = d**2*g*(rhos-rho)/18/mu\n", + "print \"Terminal Settling Velocity in (m/s): %.4f\"%u\n", + "Re = d*u*rho/mu\n", + "if Re<2 :\n", + " print \"Stoke law assumption is sustained with this velocity\"\n", + "\n", + "#part 3\n", + "P = g*(rhos-rho)*h*(1-e)\n", + "print \"Pressure drop across fluidised bed in (N/m**2):\",P\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The superficial linear flow rate in (m/s): 7.883e-06\n", + "Terminal Settling Velocity in (m/s): 0.0005\n", + "Stoke law assumption is sustained with this velocity\n", + "Pressure drop across fluidised bed in (N/m**2): 7170.07995\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 11.3 page no : 221" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "the linear air flow rate\n", + "speed required for smallest particle\n", + "'''\n", + "\n", + "import math \n", + "from numpy import *\n", + "# Initialization of Variable\n", + "g = 9.81\n", + "rhos = 1980. #density of ore\n", + "rho = 1.218 #density of air\n", + "e = 0.4\n", + "mu = 1.73/10**5\n", + "s = 0\n", + "wp = array([0, .08, .20, .40, .60, .80, .90, 1.00]) #weight percent\n", + "d = true_divide([0.4 ,0.5, 0.56, 0.62, 0.68, 0.76, 0.84, 0.94],1000)\n", + "dav = [0,0,0,0,0,0,0]\n", + "mf = [0,0,0,0,0,0,0]\n", + "a = [0,0,0,0,0,0,0]\n", + "#part 1\n", + "for i in range(7):\n", + " dav[i] = d[i+1]/2+d[i]/2. #average dia\n", + " mf[i] = wp[i+1]-wp[i] #mass fraction\n", + " a[i] = mf[i]/dav[i]\n", + " s = s+a[i]\n", + "\n", + "db = 1/s #d bar\n", + "\n", + "#quadratic coeff. ax**2 +bx +c = 0\n", + "c = -(rhos-rho)*g\n", + "b = 150.*(1-e)/e**3/db**2*mu\n", + "a = 1.75*rho/e**3/db\n", + "y = poly1d([a,b,c],False)\n", + "U = roots(y)\n", + "print \"the linear air flow rate in (m/s): %.4f\"%(abs(U[1]))\n", + "\n", + "#part 2\n", + "d = 0.4/1000\n", + "a = 2*d**3/3/mu**2*rho*(rhos-rho)*g\n", + "a = math.log10(a)\n", + "print \"log10(Re**2/rho/U**2*R) = %.4f\"%a\n", + "\n", + "#using chart\n", + "Re = 10**1.853\n", + "u = Re*mu/rho/d\n", + "print \"speed required for smallest particle in (m/s): %.4f\"%u\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "the linear air flow rate in (m/s): 0.2643\n", + "log10(Re**2/rho/U**2*R) = 3.5277\n", + "speed required for smallest particle in (m/s): 2.5313\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 11.4 page no : 224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "the diameter of vessel\n", + "depth of bed \n", + "depth of fluidised bed under operating condition\n", + "'''\n", + "\n", + "import math \n", + "from numpy import *\n", + "\n", + "# Initialization of Variable\n", + "U = 2.032/10**4\n", + "pi = 3.1428\n", + "rho = 852\n", + "g = 9.81\n", + "mu = 1.92/1000\n", + "mf = 125/3600. #mass flow rate\n", + "\n", + "#calculation\n", + "#part 1\n", + "G = U*rho\n", + "A = mf/G\n", + "d = math.sqrt(4*A/pi)\n", + "print \"the diameter of vessel will be in(m): %.4f\"%d\n", + "\n", + "#part 2\n", + "A = 0.201\n", + "e = 0.43\n", + "ms = 102. #mass of solids\n", + "rhos = 1500. #density of solid\n", + "L = ms/rhos/A\n", + "Lmf = L/(1-e)\n", + "print \"depth of bed in (m): %.4f\"%Lmf \n", + "\n", + "#part 3\n", + "d1 = 0.2/1000\n", + "U = 2.*5.5/10**3*e**3*d1**2*(rhos-rho)*g/mu/(1-e)\n", + "\n", + "#now euating for e\n", + "#a = e**3/(1-e)\n", + "a = U/5.5*10**3/(d1**2*(rhos-rho)*g/mu)\n", + "y = poly1d([1,0,a,-a],False)\n", + "e2 = roots(y)\n", + "L = Lmf*(1-e)/(1-e2[2])\n", + "print \"depth of fluidised bed under operating condition in (m): %.4f\"%L\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "the diameter of vessel will be in(m): 0.5052\n", + "depth of bed in (m): 0.5935\n", + "depth of fluidised bed under operating condition in (m): 0.6958\n" + ] + }, + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "-c:45: ComplexWarning: Casting complex values to real discards the imaginary part\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 11.5 page no : 227" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# find power supplies to the blower\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "g = 9.81\n", + "pi = 3.1428\n", + "r = 0.51\n", + "e = 0.48 #void ratio\n", + "rhos = 2280. #density of glass\n", + "rho = 1.204 #density of air\n", + "U = 0.015 #velocity of water entering bed\n", + "L = 7.32\n", + "gam = 1.4 #gamma\n", + "neta = 0.7 #efficiency\n", + "P4 = 1.013*10**5\n", + "P1 = P4\n", + "v1 = 1/1.204 #volume 1\n", + "\n", + "#calculation\n", + "P3 = P4+g*(rhos-rho)*(1-e)*L\n", + "P2 = P3+0.1*85090\n", + "v2 = (P1*v1**gam/P2)**(1/gam) #vlume 2\n", + "W = 1/neta*gam/(gam-1)*(P2*v2-P1*v1) #work done\n", + "v3 = P2*v2/P3 #volume 3\n", + "M = U*pi*r**2/v3 #mass flow rate\n", + "P = M*W\n", + "\n", + "# Results\n", + "print \"The power supplies to the blower in (W): %.4f\"%P\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The power supplies to the blower in (W): 1948.7509\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 11.6 page no : 230" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "minimum fluidising velocity\n", + "fluidising velocity\n", + "'''\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "dt = 12.7/1000\n", + "d = 1.8/1000\n", + "Q = 2.306/10**6\n", + "pi = 3.1428\n", + "\n", + "#calculation\n", + "#part 1\n", + "Sc = 4./dt\n", + "S = 6./d\n", + "f = (1+0.5*Sc/S)**2\n", + "U = Q*4/pi/dt**2 #velocity\n", + "Ua = f*U #actual velocity\n", + "print \"minimum fluidising velocity found using smaller glass column in (m/s): %.4f\"%Ua\n", + "\n", + "#part 2\n", + "dt = 1.5\n", + "Sc = 4./dt\n", + "f = (1+0.5*Sc/S)**2\n", + "Ua = f*U #actual velocity\n", + "print \"fluidising velocity found using larger glass column in (m/s): %.4f\"%Ua\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "minimum fluidising velocity found using smaller glass column in (m/s): 0.0200\n", + "fluidising velocity found using larger glass column in (m/s): 0.0182\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 11.7 page no : 232" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# find ratio of terminal velocity\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "e = 0.4 #incipent to fluidisation\n", + "\n", + "#calculation\n", + "#part 1\n", + "print \"for Re<500\"\n", + "print \"the ratio of terminal velocity & minimmum fluidising velocity is\"\n", + "\n", + "a = 3.1*1.75/e**3\n", + "\n", + "print math.sqrt(a)\n", + "\n", + "#part 2\n", + "print \"for Re>500\"\n", + "print \"the ratio of terminal velocity & minimmum fluidising velocity is\"\n", + "a = 150.*(1-e)/18./e**3\n", + "print a\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "for Re<500\n", + "the ratio of terminal velocity & minimmum fluidising velocity is\n", + "9.20682491416\n", + "for Re>500\n", + "the ratio of terminal velocity & minimmum fluidising velocity is\n", + "78.125\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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