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-{
- "metadata": {
- "name": "",
- "signature": "sha256:846eb301f0ca3fa07d598406cf96d8fa3abf5c03a27e59bd7b72da3b6c324d13"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 5 : Transport with a net convective flux"
- ]
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example 5.9 - Page No :166\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "v = 1.; \t\t\t #[cm/sec] - volume velocity or bulk velocity\n",
- "vol = 1.; \t\t\t #[cm**3] - volume\n",
- "na = 2.; \t\t\t # moles of a\n",
- "nb = 3.; \t\t\t # moles of b\n",
- "nc = 4.; \t\t\t # moles of c\n",
- "mma = 2.; \t\t\t #molecular weight of a\n",
- "mmb = 3.; \t\t\t #molecular weight of b\n",
- "mmc = 4.; \t\t\t #molecular weight of c\n",
- "ma = na*mma; \t\t\t #[g] weight of a\n",
- "mb = nb*mmb; \t\t\t #[g] weight of b\n",
- "mc = nc*mmc; \t\t\t #[g] weight of c\n",
- "NabyA = 2.+2; \t\t\t #[mol/cm**2*s] - molar flux = diffusing flux +convected flux\n",
- "NbbyA = -1.+3; \t\t\t #[mol/cm**2*s] - molar flux = diffusing flux +convected flux\n",
- "NcbyA = 0.+4; \t\t\t #[mol/cm**2*s] - molar flux = diffusing flux +convected flux\n",
- "NtbyA = NabyA+NbbyA+NcbyA; \t\t\t #[mol/cm**2*s] - total molar flux\n",
- "\n",
- "# Calculations\n",
- "# on a mass basis,these corresponds to\n",
- "nabyA = 4.+4; \t\t\t #[g/cm**2*s]; - mass flux = diffusing flux +convected flux\n",
- "nbbyA = -3.+9; \t\t\t #[g/cm**2*s]; - mass flux = diffusing flux +convected flux\n",
- "ncbyA = 0.+16; \t\t\t #[g/cm**2*s]; - mass flux = diffusing flux +convected flux\n",
- "ntbyA = nabyA+nbbyA+ncbyA; \t\t\t #[g/cm**2*s] - total mass flux\n",
- "\n",
- "# concentrations are expressed in molar basis\n",
- "CA = na/vol; \t\t\t #[mol/cm**3]\n",
- "CB = nb/vol; \t\t\t #[mol/cm**3]\n",
- "CC = nc/vol; \t\t\t #[mol/cm**3]\n",
- "CT = CA+CB+CC; \t\t\t #[mol/cm**3] - total concentration\n",
- "\n",
- "# densities are on a mass basis\n",
- "pa = ma/vol; \t\t\t #[g/cm**3]\n",
- "pb = mb/vol; \t\t\t #[g/cm**3]\n",
- "pc = mc/vol; \t\t\t #[g/cm**3]\n",
- "pt = pa+pb+pc; \t\t\t #[g/cm**3]\n",
- "Ua = NabyA/CA; \t\t\t #[cm/sec];\n",
- "Ub = NbbyA/CB; \t\t\t #[cm/sec];\n",
- "Uc = NcbyA/CC; \t\t\t #[cm/sec];\n",
- "# the same result will be obtained from dividing mass flux by density\n",
- "Uz = (pa*Ua+pb*Ub+pc*Uc)/(pa+pb+pc);\n",
- "\n",
- "# Results\n",
- "print \" Uz = %.3f cm/sec\"%(Uz);\n",
- "Uzstar = (NtbyA/CT);\n",
- "print \" Uz* = %.2f cm/sec\"%(Uzstar);\n",
- "print \" For this Example both Uz and Uz* are slightly greater than the volume \\\n",
- " velocity of 1cm/sec, because there is a net molar and \\n mass diffusion in the positive direction.\"\n",
- " "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- " Uz = 1.034 cm/sec\n",
- " Uz* = 1.11 cm/sec\n",
- " For this Example both Uz and Uz* are slightly greater than the volume velocity of 1cm/sec, because there is a net molar and \n",
- " mass diffusion in the positive direction.\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example 5.10 - Page No :171\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "na = 2.; \t\t\t # moles of a\n",
- "nb = 3.; \t\t\t # moles of b\n",
- "nc = 4.; \t\t\t # moles of c\n",
- "mma = 2.; \t\t\t #molecular weight of a\n",
- "mmb = 3.; \t\t\t #molecular weight of b\n",
- "mmc = 4.; \t\t\t #molecular weight of c\n",
- "ma = na*mma; \t\t\t #[g] weight of a\n",
- "mb = nb*mmb; \t\t\t #[g] weight of b\n",
- "mc = nc*mmc; \t\t\t #[g] weight of c\n",
- "NabyA = 2.+2; \t\t\t #[mol/cm**2*s] - molar flux = diffumath.sing flux +convected flux\n",
- "NbbyA = -1.+3; \t\t\t #[mol/cm**2*s] - molar flux = diffusing flux +convected flux\n",
- "NcbyA = 0.+4; \t\t\t #[mol/cm**2*s] - molar flux = diffusing flux +convected flux\n",
- "NtbyA = NabyA+NbbyA+NcbyA; \t\t\t #[mol/cm**2*s] - total molar flux\n",
- "vol= 1.\n",
- "# Calculations\n",
- "# on a mass basis,these corresponds to\n",
- "nabyA = 4+4; \t\t\t #[g/cm**2*s]; - mass flux = diffusing flux +convected flux\n",
- "nbbyA = -3+9; \t\t\t #[g/cm**2*s]; - mass flux = diffusing flux +convected flux\n",
- "ncbyA = 0+16; \t\t\t #[g/cm**2*s]; - mass flux = diffusing flux +convected flux\n",
- "\n",
- "# concentrations are expressed in molar basis\n",
- "CA = na/vol; \t\t\t #[mol/cm**3]\n",
- "CB = nb/vol; \t\t\t #[mol/cm**3]\n",
- "CC = nc/vol; \t\t\t #[mol/cm**3]\n",
- "CT = CA+CB+CC; \t\t #[mol/cm**3] - total concentration\n",
- "\n",
- "# densities are on a mass basis\n",
- "pa = ma/vol; \t\t\t #[g/cm**3]\n",
- "pb = mb/vol; \t\t\t #[g/cm**3]\n",
- "pc = mc/vol; \t\t\t #[g/cm**3]\n",
- "Ua = NabyA/CA; \t\t\t #[cm/sec];\n",
- "Ub = NbbyA/CB; \t\t\t #[cm/sec];\n",
- "Uc = NcbyA/CC; \t\t\t #[cm/sec];\n",
- "U = (pa*Ua+pb*Ub+pc*Uc)/(pa+pb+pc);\n",
- "Ustar = (NtbyA/CT);\n",
- "\n",
- "# the fluxes relative to mass average velocities are found as follows\n",
- "JabyA = CA*(Ua-U); \t\t\t #[mol/cm**2*sec]\n",
- "JbbyA = CB*(Ub-U); \t\t\t #[mol/cm**2*sec]\n",
- "JcbyA = CC*(Uc-U); \t\t\t #[mol/cm**2*sec]\n",
- "\n",
- "# Results\n",
- "print \" fluxes relative to mass average velocities are-\";\n",
- "print \" Ja/A = %.4f mol/cm**2*sec\"%(JabyA);\n",
- "print \" Jb/A = %.4f mol/cm**2*sec\"%(JbbyA);\n",
- "print \" Jc/A = %.4f mol/cm**2*sec\"%(JcbyA);\n",
- "jabyA = pa*(Ua-U); \t\t\t #[g/cm**2*sec]\n",
- "jbbyA = pb*(Ub-U); \t\t\t #[g/cm**2*sec]\n",
- "jcbyA = pc*(Uc-U); \t\t\t #[g/cm**2*sec]\n",
- "print \" ja/A = %.4f g/cm**2*sec\"%(jabyA);\n",
- "print \" jb/A = %.4f g/cm**2*sec\"%(jbbyA);\n",
- "print \" jc/A = %.4f g/cm**2*sec\"%(jcbyA);\n",
- "\n",
- "# the fluxes relative to molar average velocity are found as follows\n",
- "JastarbyA = CA*(Ua-Ustar); \t\t\t #[mol/cm**2*sec]\n",
- "JbstarbyA = CB*(Ub-Ustar); \t\t\t #[mol/cm**2*sec]\n",
- "JcstarbyA = CC*(Uc-Ustar); \t\t\t #[mol/cm**2*sec]\n",
- "print \" fluxes relative to molar average velocities are-\";\n",
- "print \" Ja*/A = %.4f mol/cm**2*sec\"%(JastarbyA);\n",
- "print \" Jb*/A = %.4f mol/cm**2*sec\"%(JbstarbyA);\n",
- "print \" Jc*/A = %.4f mol/cm**2*sec\"%(JcstarbyA);\n",
- "jastarbyA = pa*(Ua-Ustar); \t\t\t #[g/cm**2*sec]\n",
- "jbstarbyA = pb*(Ub-Ustar); \t\t\t #[g/cm**2*sec]\n",
- "jcstarbyA = pc*(Uc-Ustar); \t\t\t #[g/cm**2*sec]\n",
- "print \" ja*/A = %.4f g/cm**2*sec\"%(jastarbyA);\n",
- "print \" jb*/A = %.4f g/cm**2*sec\"%(jbstarbyA);\n",
- "print \" jc*/A = %.4f g/cm**2*sec\"%(jcstarbyA);\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- " fluxes relative to mass average velocities are-\n",
- " Ja/A = 1.9310 mol/cm**2*sec\n",
- " Jb/A = -1.1034 mol/cm**2*sec\n",
- " Jc/A = -0.1379 mol/cm**2*sec\n",
- " ja/A = 3.8621 g/cm**2*sec\n",
- " jb/A = -3.3103 g/cm**2*sec\n",
- " jc/A = -0.5517 g/cm**2*sec\n",
- " fluxes relative to molar average velocities are-\n",
- " Ja*/A = 1.7778 mol/cm**2*sec\n",
- " Jb*/A = -1.3333 mol/cm**2*sec\n",
- " Jc*/A = -0.4444 mol/cm**2*sec\n",
- " ja*/A = 3.5556 g/cm**2*sec\n",
- " jb*/A = -4.0000 g/cm**2*sec\n",
- " jc*/A = -1.7778 g/cm**2*sec\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example 5.11 - Page No :176\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "import math\n",
- "# Variables\n",
- "# given\n",
- "T = 0+273.15; \t\t\t #[K] - temperature in Kelvins\n",
- "pa2 = 1.5; \t\t\t #[atm] - partial presuure of a at point2\n",
- "pa1 = 0.5; \t\t\t #[atm] - partial pressure of a at point 1\n",
- "z2 = 20.; \t\t\t #[cm] - position of point 2 from reference point\n",
- "z1 = 0.; \t\t\t #[cm] - position of point1 from reference point\n",
- "p = 2.; \t\t\t #[atm] - total pressure\n",
- "d = 1.; \t\t\t #[cm] - diameter\n",
- "D = 0.275; \t\t #[cm**2/sec] - diffusion coefficient\n",
- "A = (math.pi*((d)**2))/4.;\n",
- "R = 0.082057; \t\t\t #[atm*m**3*kmol**-1*K**-1] - gas constant\n",
- "\n",
- "# Calculations\n",
- "# (a) using the formula Na/A = -(D/(R*T))*((pa2-pa1)/(z2-z1))\n",
- "Na = (-(D/(R*T))*((pa2-pa1)/(z2-z1)))*(A)/(10.**6);\n",
- "print \" Na = %.2e kmol/sec \\n The negative sign indicates diffusion from point 2 to point 1\"%(Na);\n",
- "pb2 = p-pa2;\n",
- "pb1 = p-pa1;\n",
- "\n",
- "# (b) using the formula Na/A = ((D*p)/(R*T*(z2-z1)))*ln(pb2/pb1)\n",
- "Na = (((D*p)/(R*T*(z2-z1)))*math.log(pb2/pb1))*(A)/(10**6);\n",
- "\n",
- "# Results\n",
- "print \" Na = %.2e kmol/sec\"%(Na);\n",
- "print \" The induced velocity increases the net transport of A by the ratio of 10.6*10**-10 \\\n",
- "to 4.82*10**-10 or 2.2 times.This increse is equivalent to 120 percent\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- " Na = -4.82e-10 kmol/sec \n",
- " The negative sign indicates diffusion from point 2 to point 1\n",
- " Na = -1.06e-09 kmol/sec\n",
- " The induced velocity increases the net transport of A by the ratio of 10.6*10**-10 to 4.82*10**-10 or 2.2 times.This increse is equivalent to 120 percent\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example 5.12 - Page No :178\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "\n",
- "# Variables\n",
- "# given\n",
- "T = 0+273.15; \t\t\t #[K] - temperature in Kelvins\n",
- "pa2 = 1.5; \t\t\t #[atm] - partial presuure of a at point2\n",
- "pa1 = 0.5; \t\t\t #[atm] - partial pressure of a at point 1\n",
- "z2 = 20.; \t\t\t #[cm] - position of point 2 from reference point\n",
- "z1 = 0.; \t\t\t #[cm] - position of point1 from reference point\n",
- "p = 2.; \t\t\t #[atm] - total pressure\n",
- "d = 1.; \t\t\t #[cm] - diameter\n",
- "D = 0.275; \t\t\t #[cm**2/sec] - diffusion coefficient\n",
- "\n",
- "# Calculations\n",
- "A = (math.pi*((d)**2.))/4;\n",
- "R = 0.082057; \t\t\t #[atm*m**3*kmol**-1*K**-1] - gas consmath.tant\n",
- "k = 0.75;\n",
- "\n",
- "# umath.sing the formula (Na/A) = -(D/(R*T*(z2-z1)))*ln((1-(pa2/p)*(1-k))/(1-(pa1/p)*(1-k)))\n",
- "NabyA = -(D/(R*T*(z2-z1)))*(2*0.7854)*math.log((1-(pa2/p)*(1-k))/(1-(pa1/p)*(1-k)))/(10**6);\n",
- "\n",
- "# Results\n",
- "print \" Na/A = %.2e kmol/sec\"%(NabyA);\n",
- "print \" Note that this answer is larger than the rate for equimolar counter diffusion \\\n",
- "but smaller tahn the rate for diffusion through a stagnant film. \\nSometimes the\\\n",
- " rate for diffusin through a stagnant film can be considered as an upper bound\\\n",
- " if k ties between zero and one\"\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- " Na/A = 1.38e-10 kmol/sec\n",
- " Note that this answer is larger than the rate for equimolar counter diffusion but smaller tahn the rate for diffusion through a stagnant film. \n",
- "Sometimes the rate for diffusin through a stagnant film can be considered as an upper bound if k ties between zero and one\n"
- ]
- }
- ],
- "prompt_number": 10
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example 5.13 - Page No :184\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "\n",
- "# Variables\n",
- "# given\n",
- "l = 4.; \t\t\t #[m] - length of the tube\n",
- "id_ = 1.6*10**-3; \t\t\t #[m] - insid_e diameter\n",
- "Nkn = 10.; \t\t \t # - knudsen no.\n",
- "Ma = 92.; \t\t\t # - molecular weight of gas\n",
- "mu = 6.5*10**-4; \t\t\t #[kg/m*sec] - vismath.cosity\n",
- "T = 300.; \t \t\t #[K] - temperature\n",
- "R = 8314.; \t \t\t #[kPa*m**3*kmol**-1*K**-1] - gas consmath.tant\n",
- "lambdaA = Nkn*id_; \t\t\t #[m] mean free path\n",
- "\n",
- "# Calculations\n",
- "# for calculating pressure umath.sing the formula lamdaA = 32*(mu/p)*((R*T)/(2*pi*Ma))**(1/2)\n",
- "p = 32*(mu/lambdaA)*((R*T)/(2*math.pi*Ma))**(1/2.);\n",
- "patm = p/(1.01325*10**5);\n",
- "\n",
- "# Results\n",
- "print \" p = %.2f kg/m*sec**2 = %.2f Pa = %.2e atm\"%(p,p,patm);\n",
- "print \" The value of 10 for the knudsen number is on the border \\\n",
- " between Knudsen diffusion and transition flow\";\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- " p = 85.39 kg/m*sec**2 = 85.39 Pa = 8.43e-04 atm\n",
- " The value of 10 for the knudsen number is on the border between Knudsen diffusion and transition flow\n"
- ]
- }
- ],
- "prompt_number": 11
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-03-12 09:40:14 +0000