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diff --git a/Problems_In_Fluid_Flow/ch8.ipynb b/Problems_In_Fluid_Flow/ch8.ipynb new file mode 100644 index 00000000..97b6a74a --- /dev/null +++ b/Problems_In_Fluid_Flow/ch8.ipynb @@ -0,0 +1,467 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 8 : Filtration" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 8.1 page no : 145" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "pressure drop at t = 30 min\n", + "the thickness of filtercake formed\n", + "thickness of cake required\n", + "average particle diameter\n", + "'''\n", + "\n", + "import math \n", + "from numpy import *\n", + "\n", + "# Initialization of Variable\n", + "\n", + "a = 78./1000 #dV/dt\n", + "rho = 998. #density of water\n", + "rhoc = 2230. #density of china clay\n", + "rhod = 1324. #density of cowdung cake\n", + "mu = 1.003/1000\n", + "P2 = 3.23*1000 #pressure after 2 min.\n", + "P5 = 6.53*1000 #pressure after 5 min.\n", + "t = 30*60.\n", + "b = array([[P2],[P5]])\n", + "A = array([[(a**2)*120., a],[(a**2)*300., a]])\n", + "x = linalg.solve(A, b)\n", + "P = x[0]*a**2*t+x[1]*a\n", + "print \"pressure drop at t = 30min in (kN/m**2):\",P/1000\n", + "\n", + "#part2\n", + "J = 0.0278 #mass fraction\n", + "l = 1.25\n", + "b1 = 0.7\n", + "A1 = l*b1*17*2 #area of filtering\n", + "V = a*30*60. #volume of filterate\n", + "e = 1-rhod/rhoc\n", + "nu = J*rho/((1-J)*(1-e)*rhoc-J*e*rho)\n", + "l1 = nu*V/A1\n", + "print \"the thickness of filtercake formed after 30 min in (m): %.4f\"%l1\n", + "\n", + "#part3\n", + "r = x[0][0]/mu/nu*A1**2\n", + "L = x[1][0]*A1/r/mu\n", + "print \"thickness of cake required in (m): %.4f\"%L\n", + "\n", + "#part 4\n", + "S = math.sqrt(r*e**3./5/(1-e)**2)\n", + "d = 6./S\n", + "print \"average particle diameter in(10**-6m): %.4f\"%(d*10**6)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "pressure drop at t = 30min in (kN/m**2): [ 34.03]\n", + "the thickness of filtercake formed after 30 min in (m): 0.1026\n", + "thickness of cake required in (m): 0.0032\n", + "average particle diameter in(10**-6m): 87.9625\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 8.2 pageno :148" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "time at which the required pressure drop have taken place\n", + "volume of filterate \n", + "the time required to collect 750dm**3\n", + "time required to pass 10dm**3 volume \n", + "'''\n", + "\n", + "import math \n", + "from numpy import *\n", + "\n", + "\n", + "# Initialization of Variable\n", + "P1 = 5.34*1000 #pressure after 3 min.\n", + "P2 = 9.31*1000 #pressure after 8 min.\n", + "a = 240./1000000 #dV/dt\n", + "P3 = 15.*10**3 #final pressure\n", + "\n", + "#calculation\n", + "b = array([[P1],[P2]])\n", + "A = array([[a**2*180, a],[a**2*480, a]])\n", + "x = linalg.solve(A,b)\n", + "\n", + "#part1\n", + "t = (P3-x[1][0]*a)/x[0][0]/a**2\n", + "\n", + "print \"time at which the required pressure drop have taken place in (s): %.4f\"%t\n", + "\n", + "#part 2\n", + "V1 = a*t\n", + "print \"volume of filterate in (m**3): %.4f\"%V1\n", + "\n", + "#part 3\n", + "V2 = 0.75\n", + "t2 = t+x[0][0]/2/P3*(V2**2-V1**2)+x[1][0]/P3*(V2-V1)\n", + "print \"the time required to collect 750dm**3 of filterate in (s): %.4f\"%t2\n", + "\n", + "#part 4\n", + "P4 = 12.*10**3\n", + "a = P4/(x[0][0]*V2+x[1][0])\n", + "t = 10./1000/a\n", + "print \"time required to pass 10dm**3 volume in (s): %.4f\"%t\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time at which the required pressure drop have taken place in (s): 909.9748\n", + "volume of filterate in (m**3): 0.2184\n", + "the time required to collect 750dm**3 of filterate in (s): 5289.2396\n", + "time required to pass 10dm**3 volume in (s): 153.8617\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 8.3 pageno : 150" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# find the thickness of filter \n", + "\n", + "import math \n", + "from numpy import *\n", + "\n", + "# Initialization of Variable\n", + "a = 16./1000 #dV/dt\n", + "J = 0.0876 #mass fraction\n", + "rho = 999. #density of water\n", + "rhoc = 3470. #density of slurry\n", + "mu = 1.12/1000\n", + "rhos = 1922. #density of dry filter cake\n", + "t1 = 3*60.\n", + "t2 = 8*60.\n", + "V1 = 33.8/1000 #volume at t1\n", + "V2 = 33.8/1000+23.25/1000 #volume at t2\n", + "P = 12*1000. #pressure difference\n", + "Ap = 70.**2./10000*2*9\n", + "As = 650/10000.\n", + "\n", + "#calculation\n", + "\n", + "b = array([t1,t2])\n", + "A = array([[V1**2/2/P, V1/P],[V2**2/2/P, V2/P]])\n", + "x = linalg.solve(A, b)\n", + "K1p = x[0]*As**2/Ap**2\n", + "K2p = x[1]*As/Ap\n", + "P2 = 15*1000. #final pressure drop\n", + "t = (P2-K2p*a)/K1p/a**2 #time for filterate\n", + "V = a*t #volume of filterate\n", + "e = 1-rhos/rhoc\n", + "nu = J*rho/((1-J)*(1-e)*rhoc-J*e*rho)\n", + "l = (11.-1)/200.\n", + "Vf = Ap*l/nu\n", + "tf = t+K1p/2/P2*(Vf**2-V**2)+K2p/P2*(Vf-V)\n", + "r = K1p/mu/nu*Ap**2\n", + "L = K2p*Ap/r/mu\n", + "print \"the thickness of filter which has resistance equal to resistance of filter medium in (m):%.5f\"%L\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "the thickness of filter which has resistance equal to resistance of filter medium in (m):0.00247\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 8.4 page no : 154" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "Volume at P = 90kPa \n", + "Volume at p = 45kPa \n", + "'''\n", + "\n", + "import math \n", + "from numpy import *\n", + "\n", + "# Initialization of Variable\n", + "\n", + "t1 = 3*60. #time 3min\n", + "t2 = 12*60. #time 12min\n", + "t3 = 5*60. #time 5min\n", + "P = 45*1000. #pressure at t1&t2\n", + "P2 = 85*1000. #pres. at t3\n", + "a = 1.86 #area\n", + "mu = 1.29/1000.\n", + "c = 11.8\n", + "V1 = 5.21/1000 #volume at t1\n", + "V2 = 17.84/1000 #volume at t2\n", + "V3 = 10.57/1000 #volume at t3\n", + "\n", + "#calculation\n", + "b = array([t1,t2])\n", + "A = array([[mu*c/2/a**2/P*V1**2, V1/P],[mu*c/2/a**2/P*V2**2, V2/P]])\n", + "x = linalg.solve(A,b)\n", + "r45 = x[0]\n", + "r85 = (t3-x[1]*V3/P2)*2*a**2*P2/V3**2/mu/c\n", + "n = math.log(r45/r85)/math.log(45./85)\n", + "rbar = r45/(1-n)/(45.*1000)**n\n", + "r78 = rbar*(1-n)*(78.*1000)**n\n", + "\n", + "#part1\n", + "#polynomial in V as a1x**2+bx+c1 = 0\n", + "c1 = 90.*60 #time at 90 \n", + "Pt = 78*1000. #Pt = pressure at time t = 90\n", + "r78 = round(r78/10.**12)*10.**12\n", + "a1 = r78*mu/a**2/Pt*c/2.\n", + "b = x[1]/Pt\n", + "y = poly1d([a1,b,-c1],False)\n", + "V1 = roots(y)\n", + "print \"Volume at P = 90kPa in (m**3): %.4f\"%V1[1]\n", + "\n", + "#part2\n", + "Pt = 45.*1000\n", + "c1 = 90.*60\n", + "a1 = r45*mu/a**2/Pt*c/2\n", + "b = x[1]/Pt\n", + "y = poly1d([a1,b,-c1],False)\n", + "V1 = roots(y)\n", + "print \"Volume at p = 45kPa in (m**3): %.4f\"%V1[1]\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Volume at P = 90kPa in (m**3): 0.0660\n", + "Volume at p = 45kPa in (m**3): 0.0789\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 8.5 page no : 157" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "thickness of filter cake \n", + "rate at which wet cake will be scrapped\n", + "rate of which slurry is treated\n", + "'''\n", + "\n", + "from numpy import *\n", + "import math \n", + "\n", + "\n", + "# Initialization of Variable\n", + "t = 60*0.3/0.5 #time of 1 revollution\n", + "d = 34/1000000.\n", + "S = 6./d\n", + "e = 0.415\n", + "J = 0.154\n", + "P = 34.8*1000\n", + "mu = 1.17/1000\n", + "L = 2.35/1000\n", + "rho = 999. #density of water\n", + "rhos = 4430. #density of barium carbonate\n", + "\n", + "#calculation\n", + "#part1\n", + "nu = J*rho/((1-J)*(1-e)*rhos-J*e*rho)\n", + "r = 5*S**2*(1-e)**2/e**3\n", + "\n", + "#quadratic in l\n", + "#in the form of ax**2+bx+c = 0\n", + "c = -t\n", + "b = r*mu*L/nu/P\n", + "a = r*mu/2/nu/P\n", + "y = poly1d([a,b,c],False)\n", + "l = roots(y)\n", + "print \"thickness of filter cake in (m): %.4f\"%l[1]\n", + "\n", + "#part2\n", + "d = 1.2\n", + "l1 = 2.6\n", + "pi = 3.1428\n", + "u = pi*d*0.5/60\n", + "Q = u*l1*l[1]\n", + "mnet = Q*(1-e)*rhos+Q*e*rho\n", + "print \"rate at which wet cake will be scrapped in (kg/s): %.4f\"%mnet\n", + "\n", + "#part3\n", + "md = Q*(1-e)*rhos #rate at which solid scrapped from the drum\n", + "r = md/0.154\n", + "print \"rate of which slurry is treated is (kg/h): %.4f\"%(r*3600)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness of filter cake in (m): 0.0122\n", + "rate at which wet cake will be scrapped in (kg/s): 3.0088\n", + "rate of which slurry is treated is (kg/h): 60635.4180\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 8.6 page no : 159" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "time taken to collect sucrose crystal\n", + "volume of liquid separated\n", + "'''\n", + "\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "mu = 0.224\n", + "rho = 1328.\n", + "K = 5.\n", + "b = 3*.5 #radius\n", + "h = 2.5\n", + "pi = 3.1428\n", + "x = 2.1*.5\n", + "rhos = 1581. #density of sucrose\n", + "e = 0.435 #void ratio\n", + "J = 0.097 #mass fraction\n", + "m = 3500. #mass flowing\n", + "a = 85/10.**6 #side length\n", + "L = 48./1000 #thickness\n", + "omega = 2*pi*325./60.\n", + "\n", + "#calculation\n", + "bi = b**2-m/pi/h/(1-e)/rhos #inner radius\n", + "bi = math.sqrt(bi)\n", + "bi = round(bi*1000)/1000.\n", + "nu = J*rho/((1-J)*(1-e)*rhos-J*e*rho)\n", + "S = 6./a\n", + "r = 5*S**2*(1-e)**2/e**3\n", + "t = ((b**2-bi**2)*(1+2*L/b)+2*bi**2*math.log(bi/b))/(2*nu*rho*omega**2/r/mu*(b**2-x**2))\n", + "print \"time taken to collect sucrose crystal in (s): %.4f\"%t\n", + "\n", + "#part2\n", + "vl = pi*(b**2-bi**2)*h*e\n", + "vs = pi*(b**2-bi**2)*h/nu-vl\n", + "print \"volume of liquid separated as filterate i (m**3): %.4f\"%vs\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time taken to collect sucrose crystal in (s): 3287.3308\n", + "volume of liquid separated as filterate i (m**3): 21.1677\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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