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diff --git a/backup/Mass_-_Transfer_Operations_version_backup/Chapter6.ipynb b/backup/Mass_-_Transfer_Operations_version_backup/Chapter6.ipynb new file mode 100755 index 00000000..330c2a7b --- /dev/null +++ b/backup/Mass_-_Transfer_Operations_version_backup/Chapter6.ipynb @@ -0,0 +1,1050 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:154e89b2f76588eed1121bf1db9bf4372804b279864337e5f5dc9c9be7d3f365"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 6: Equipment For Gas-Liquid Operations"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6.1: Page 145"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 6.1\n",
+ "# Page: 145\n",
+ "\n",
+ "print'Illustration 6.1 - Page: 145\\n\\n'\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "# solution\n",
+ "\n",
+ "#****Data****#\n",
+ "# w = Gas flow rate per orifice\n",
+ "w = 0.055/50;# [kg/s]\n",
+ "L = 8*10**(-4);# [liquid flow rate, cubic m/s]\n",
+ "d = 0.003;# [diameter of the orifice,m]\n",
+ "viscocity_gas = 1.8*10**(-5);# [kg/m.s]\n",
+ "#******#\n",
+ "\n",
+ "Re = 4*w/(math.pi*d*viscocity_gas);\n",
+ "Dp = 0.0071*Re**(-0.05);# [m]\n",
+ "h = 3.0;# [height of vessel,m]\n",
+ "P_atm = 101.3;# [kN/square m]\n",
+ "Density_water = 1000.0;# [kg/cubic m]\n",
+ "g = 9.81;# [m/s^2]\n",
+ "Temp = 273+25;# [K]\n",
+ "P_orifice = P_atm+(h*Density_water*g/1000);# [kN/square m]\n",
+ "P_avg = P_atm+((h/2.0)*Density_water*g/1000);# [kN/square m]\n",
+ "Density_gas = (29/22.41)*(273.0/Temp)*(P_avg/P_atm);# [kg/cubic m]\n",
+ "D = 1.0;# [dia of vessel,m]\n",
+ "Area = (math.pi*D**2)/4;# [square m]\n",
+ "Vg = 0.055/(Area*Density_gas);# [m/s]\n",
+ "Vl = L/Area;# [m/s]\n",
+ "sigma = 0.072;# [N/m]\n",
+ "# From fig. 6.2 (Pg 143)\n",
+ "abscissa = 0.0516;# [m/s]\n",
+ "Vg_by_Vs = 0.11;\n",
+ "Vs = Vg/Vg_by_Vs;# [m/s]\n",
+ "def f6(shi_g):\n",
+ " return Vs-(Vg/shi_g)+(Vl/(1-shi_g)) \n",
+ "shi_g = fsolve(f6,0.5);\n",
+ "dp = ((Dp**3)*(P_orifice/P_avg))**(1.0/3);# [bubble diameter,m]\n",
+ "# From eqn. 6.9\n",
+ "a = 6.0*shi_g/dp;# [specific interfacial area,square m]\n",
+ "print\"The Specific Interfacial Area is \",round(a,2),\" square m/cubic m\\n\"\n",
+ "\n",
+ "# For diffsion of Cl2 in H20\n",
+ "Dl = 1.44*10**(-9);# [square m/s]\n",
+ "viscocity_water = 8.937*10**(-4);# [kg/m.s]\n",
+ "Reg = dp*Vs*Density_water/viscocity_water;\n",
+ "Scl = viscocity_water/(Density_water*Dl);\n",
+ "# From Eqn.6.11\n",
+ "Shl = 2+(0.0187*(Reg**0.779)*(Scl**0.546)*(dp*(g**(1.0/3))/(Dl**(2.0/3)))**0.116);\n",
+ "# For dilute soln. of Cl2 in H20\n",
+ "c = 1000/18.02;# [kmol/cubic m]\n",
+ "Fl = (c*Dl*Shl)/dp;# [kmol/square m.s]\n",
+ "print\"Mass Transfer coeffecient is \",round(Fl,5),\" kmol/square m.s\\n\",\n",
+ "#the answers are slightly different in textbook due to approximation while here answers are precise"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 6.1 - Page: 145\n",
+ "\n",
+ "\n",
+ "The Specific Interfacial Area is 148.13 square m/cubic m\n",
+ "\n",
+ "Mass Transfer coeffecient is 0.01335 kmol/square m.s\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6.2: Page 157"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 6.2\n",
+ "# Page: 157\n",
+ "\n",
+ "print'Illustration 6.2 - Page: 157\\n\\n'\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "# solution\n",
+ "\n",
+ "#****Data****#\n",
+ "# a = N2 b = H2O\n",
+ "L = 9.5*10**(-4);# [cubic m/s]\n",
+ "G = 0.061;# [kg/s]\n",
+ "Temp = 273.0+25;# [K]\n",
+ "#*****#\n",
+ "\n",
+ "print\"Construction Arrangement\\n\"\n",
+ "print\"Use 4 vertical wall baffles, 100 mm wide at 90 degree intervals.\\n\"\n",
+ "print\"Use a 305 mm dameter, a six bladed disk flat blade turbine impeller, arranged axially, 300 mm from the bottom of vessel\\n\"\n",
+ "print\"The sparger underneath the impeller will be in the form of a 240 mm dameter ring made of 12.7 mm tubing drilled in the top with 3.18 mm dia holes\\n\"\n",
+ "Di = 0.305;# [m]\n",
+ "Do = 0.00316;# [m]\n",
+ "viscocity_a = 1.8*10**(-5);# [kg/m.s]\n",
+ "Re_g = 35000;\n",
+ "Ma = 28.02;# [kg/kmol]\n",
+ "Mb = 18.02;# [kg/kmol]\n",
+ "# w = Gas flow rate per orifice\n",
+ "w = Re_g*math.pi*Do*viscocity_a/4.0;# [kg/s]\n",
+ "N_holes = G/w;\n",
+ "Interval = math.pi*240/round(N_holes);\n",
+ "print\"The number of holes is \",round(N_holes),\" at approx \",round(Interval),\" mm interval around the sparger ring\\n\"\n",
+ "\n",
+ "viscocity_b = 8.9*10**(-4);# [kg/m.s]\n",
+ "Sigma = 0.072;# [N/m]\n",
+ "Density_b = 1000.0;# [kg/cubic m]\n",
+ "D = 1.0;# [dia of vessel,m]\n",
+ "g = 9.81;# [m/s**2]\n",
+ "# From Eqn. 6.18\n",
+ "def f7(N):\n",
+ " return (N*Di/(Sigma*g/Density_b)**0.25)-1.22-(1.25*D/Di)\n",
+ "N_min = fsolve(f7,2);# [r/s]\n",
+ "N = 5.0;# [r/s]\n",
+ "Re_l = ((Di**2)*N*Density_b/viscocity_b);\n",
+ "# From fig 6.5 (Pg 152)\n",
+ "Po = 5.0;\n",
+ "P = Po*Density_b*(N**3)*(Di**5);\n",
+ "h = 0.7;# [m]\n",
+ "P_atm = 101.33;# [kN/square m]\n",
+ "P_gas = P_atm+(h*Density_b*g/1000.0);# [kN/square m]\n",
+ "Qg = (G/Ma)*22.41*(Temp/273.0)*(P_atm/P_gas);# [cubic m/s]\n",
+ "# From Fig.6.7 (Pg 155)\n",
+ "abcissa = Qg/(N*(Di**3));\n",
+ "# abcissa is off scale\n",
+ "Pg_by_P = 0.43;\n",
+ "Pg = 0.43*P;# [W]\n",
+ "Vg = Qg/(math.pi*(D**2)/4);# [superficial gas velocity,m/s]\n",
+ "check_value = (Re_l**0.7)*((N*Di/Vg)**0.3);\n",
+ "vl = math.pi*(D**2)/4;# [cubic m]\n",
+ "# Since value<30000\n",
+ "# From Eqn. 6.21, Eqn.6.23 & Eqn. 6.24\n",
+ "K = 2.25;\n",
+ "m = 0.4;\n",
+ "Vt = 0.250;# [m/s]\n",
+ "shi = 1.0;\n",
+ "err = 1.0;\n",
+ "while (err>10**(-3)):\n",
+ " a = 1.44*((Pg/vl)**0.4)*((Density_b/(Sigma**3))**0.2)*((Vg/Vt)**0.5);# [square m/cubic m]\n",
+ " shin = (0.24*K*((viscocity_a/viscocity_b)**0.25)*((Vg/Vt)**0.5))**(1.0/(1-m));\n",
+ " Dp = K*((vl/Pg)**0.4)*((Sigma**3/Density_b)**0.2)*(shin**m)*((viscocity_a/viscocity_b)**0.25);# [m]\n",
+ " err = abs(shi-shin);\n",
+ " Vt = Vt-0.002;# [m/s]\n",
+ " shi = shin;\n",
+ "\n",
+ "\n",
+ "# For N2 in H2\n",
+ "Dl = 1.9*10**(-9);# [square m/s]\n",
+ "Ra = 1.514*10**(6);\n",
+ "# By Eqn. 6.25\n",
+ "Shl = 2.0+(0.31*(Ra**(1.0/3)));\n",
+ "# For dilute soln.\n",
+ "c = 1000.0/Mb;# [kmol/cubic m]\n",
+ "Fl = Shl*c*Dl*1.0/Dp;# [kmol/square m.s]\n",
+ "print\"The average gas-bubble diameter is \",(\"{:.2e}\".format(Dp)),\" m\\n\",\n",
+ "print\"Gas Holdup:\\n\",round(shi,5)\n",
+ "print\"Interfacial area:\",round(a,4),\" square m/cubic m \\n\"\n",
+ "print\"Mass transfer coffecient:\",(\"{:.2e}\".format(Fl)),\"kmol/square m.s\\n\"\n",
+ "#the answers are slightly different in textbook due to approximation while here answers are precise"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 6.2 - Page: 157\n",
+ "\n",
+ "\n",
+ "Construction Arrangement\n",
+ "\n",
+ "Use 4 vertical wall baffles, 100 mm wide at 90 degree intervals.\n",
+ "\n",
+ "Use a 305 mm dameter, a six bladed disk flat blade turbine impeller, arranged axially, 300 mm from the bottom of vessel\n",
+ "\n",
+ "The sparger underneath the impeller will be in the form of a 240 mm dameter ring made of 12.7 mm tubing drilled in the top with 3.18 mm dia holes\n",
+ "\n",
+ "The number of holes is 39.0 at approx 19.0 mm interval around the sparger ring\n",
+ "\n",
+ "The average gas-bubble diameter is 6.35e-04 m\n",
+ "Gas Holdup:\n",
+ "0.02265\n",
+ "Interfacial area: 214.0106 square m/cubic m \n",
+ "\n",
+ "Mass transfer coffecient: 6.24e-03 kmol/square m.s\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6.3: Page 174"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 6.3\n",
+ "# Page: 174\n",
+ "\n",
+ "print'Illustration 6.3 - Page: 174\\n\\n'\n",
+ "\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "# solution\n",
+ "\n",
+ "#****Data****#\n",
+ "# a = methanol b = water\n",
+ "G = 0.100;# [kmol/s]\n",
+ "L = 0.25;# [kmol/s]\n",
+ "Temp = 273+95;# [K]\n",
+ "XaG = 0.18;# [mol % in gas phase]\n",
+ "MaL = 0.15;# [mass % in liquid phase]\n",
+ "#*****#\n",
+ "\n",
+ "Ma = 32;# [kg/kmol]\n",
+ "Mb = 18;# [kg/kmol]\n",
+ "Mavg_G = XaG*Ma+((1-XaG)*Mb);# [kg/kmol]\n",
+ "Density_G = (Mavg_G/22.41)*(273.0/Temp);# [kg/cubic cm]\n",
+ "Q = G*22.41*(Temp/273.0);# [cubic cm/s]\n",
+ "Density_L = 961.0;# [kg/cubic cm]\n",
+ "Mavg_L = 1.0/((MaL/Ma)+(1-MaL)/Mb);# [kg/kmol]\n",
+ "q = L*Mavg_L/Density_L;\n",
+ "\n",
+ "# Perforations\n",
+ "print\"Perforations\\n\"\n",
+ "print\"Do = 4.5mm on an equilateral triangle pitch 12 mm between the hole centres, punched in sheet metal 2 mm thick\\n\"\n",
+ "Do = 0.0045;# [m]\n",
+ "pitch = 0.012;# [m]\n",
+ "# By Eqn.6.31\n",
+ "Ao_by_Aa = 0.907*(Do/pitch)**2;\n",
+ "print\"The ratio of Hole Area By Active Area is:\",round(Ao_by_Aa,4),\"\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Tower Diameter\n",
+ "print\"Tower Diameter\\n\"\n",
+ "t = 0.50;# [tray spacing,m]\n",
+ "print\"Tower Spacing:\",t,\" m\\n\"\n",
+ "# abcissa = (L/G)*(Density_G/Density_L)^0.5 = (q/Q)*(Density_L/Density_G)**0.5\n",
+ "abcissa = (q/Q)*(Density_L/Density_G)**0.5;\n",
+ "# From Table 6.2 (Pg 169)\n",
+ "alpha = (0.0744*t)+0.01173;\n",
+ "beeta = (0.0304*t)+0.015;\n",
+ "if (abcissa<0.1):\n",
+ " abcissa = 0.1;\n",
+ "\n",
+ "sigma = 0.040;# [N/m]\n",
+ "# From Eqn.6.30\n",
+ "Cf = ((alpha*math.log10(1.0/abcissa))+beeta)*(sigma/0.02)**0.2;\n",
+ "# From Eqn. 6.29\n",
+ "Vf = Cf*((Density_L-Density_G)/Density_G)**(1/2);# [m/s]\n",
+ "# Using 80% of flooding velocity\n",
+ "V = 0.8*Vf;# [m/s]\n",
+ "An = Q/V;# [square m]\n",
+ "# The tray area used by one downspout = 8.8%\n",
+ "At = An/(1-0.088);# [square m]\n",
+ "D = (4*At/math.pi)**(1.0/2);# [m]\n",
+ "# Take D = 1.25 m\n",
+ "D = 1.25; #[m]\n",
+ "At = math.pi*(D**2)/4;# [corrected At, square m]\n",
+ "W = 0.7*D;# [weir length,m]\n",
+ "Ad = 0.088*At;# [square m]\n",
+ "# For a design similar to Fig 6.14 (Pg 168)\n",
+ "# A 40 mm wide supporting ring, beams between downspouts and a 50 mm wide disengaging & distributing zones these areas total 0.222 square m\n",
+ "Aa = At-(2.0*Ad)-0.222;\n",
+ "print\"Weir Length:\",round(W,4),\"\\n\"\n",
+ "print\"Area for perforated sheet: \",round(Aa,4),\" square m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Weir crest h1 & Weir height hw\n",
+ "print\"Weir crest h1 & Weir height hw\\n\"\n",
+ "h1 = 0.025;# [m]\n",
+ "h1_by_D = h1/D;\n",
+ "D_by_W = D/W;\n",
+ "# From Eqn. 6.34\n",
+ "Weff_by_W = math.sqrt(((D_by_W)**2)-((((D_by_W)**2-1)**0.5)+(2*h1_by_D*D_by_W))**2);\n",
+ "# Set hw to 50 mm\n",
+ "hw = 0.05;# [m]\n",
+ "print\"Weir crest: \",h1,\" m\\n\"\n",
+ "print\"Weir height: \",hw,\" m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Dry Pressure Drop\n",
+ "print\"Dry Pressure Drop\\n\"\n",
+ "l = 0.002;# [m]\n",
+ "# From Eqn. 6.37\n",
+ "Co = 1.09*(Do/l)**0.25;\n",
+ "Ao = 0.1275*Aa;# [square m]\n",
+ "Vo = Q/Ao;# [m/sec]\n",
+ "viscocity_G = 1.25*10**(-5);# [kg/m.s]\n",
+ "Re = Do*Vo*Density_G/viscocity_G;\n",
+ "# From \"The Chemical Engineers Handbook,\" 5th Edition fig 5.26\n",
+ "fr = 0.008;\n",
+ "g = 9.81;# [m/s**2]\n",
+ "# From Eqn. 6.36\n",
+ "def f(hd):\n",
+ " return (2*hd*g*Density_L/(Vo**2*Density_G))-(Co*(0.40*(1.25-(Ao/An))+(4*l*fr/Do)+(1-(Ao/An))**2))\n",
+ "hd = fsolve(f,1);\n",
+ "print\"Dry Pressure Drop:\",round(hd,4),\" m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Hydraulic head hl\n",
+ "print\"Hydraulic head hl\"\n",
+ "Va = Q/Aa;# [m/s]\n",
+ "z = (D+W)/2.0;# [m]\n",
+ "# From Eqn. 6.38\n",
+ "hl = 6.10*10**(-3)+(0.725*hw)-(0.238*hw*Va*(Density_G)**0.5)+(1.225*q/z);# [m]\n",
+ "print\"Hydraulic head: \",round(hl,4),\" m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "#Residual Pressure drop hr\n",
+ "print\"Residual Pressure drop hr\\n\"\n",
+ "# From Eqn. 6.42\n",
+ "hr = 6*sigma/(Density_L*Do*g);# m\n",
+ "print\"Residual Pressure Drop:\",round(hr,4),\"m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Total Gas pressure Drop hg\n",
+ "print\"Total Gas pressure Drop hg\\n\"\n",
+ "# From Eqn. 6.35\n",
+ "hg = hd+hl+hr;# [m]\n",
+ "print\"Total gas pressure Drop: \",round(hg,4),\" m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Pressure loss at liquid entrance h2\n",
+ "print\"Pressure loss at liquid entrance h2\\n\"\n",
+ "# Al: Area for the liquid flow under the apron\n",
+ "Al = 0.025*W;# [square m]\n",
+ "Ada = min(Al,Ad);\n",
+ "# From Eqn. 6.43\n",
+ "h2 = (3.0/(2*g))*(q/Ada)**2;\n",
+ "print\"Pressure loss at liquid entrance:\",round(h2,4),\"m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Backup in Downspout h3\n",
+ "print\"Backup in Downspout h3\\n\"\n",
+ "# From Eqn.6.44\n",
+ "h3 = hg+h2;\n",
+ "print\"Backup in Downspout:\",round(h3,4),\" m\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Check on Flooding\n",
+ "print\"Check on Flooding\\n\"\n",
+ "if((hw+h1+h3)<(t/2.0)):\n",
+ " print\"Choosen Tower spacing is satisfactory\\n\"\n",
+ "else:\n",
+ " print\"Choosen Tower spacing is not satisfactory\\n\"\n",
+ "\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Weeping Velocity\n",
+ "print\"Weeping Velocity\\n\"\n",
+ "print\"For W/D ratio \",W/D,\" weir is set at \",0.3296*D,\" m from the center from the tower\\n\",\n",
+ "Z = 2*(0.3296*D);# [m]\n",
+ "# From Eqn.6.46\n",
+ "def f8(Vow):\n",
+ " return (Vow*viscocity_G/(sigma))-(0.0229*((viscocity_G**2/(sigma*Density_G*Do))*(Density_L/Density_G))**0.379)*((l/Do)**0.293)*(2*Aa*Do/(math.sqrt(3.0)*(pitch**3)))**(2.8/((Z/Do)**0.724))\n",
+ "Vow = fsolve(f8,0.1);# [m/s]\n",
+ "print\"The minimum gas velocity through the holes below which excessive weeping is likely:\",round(Vow,3),\" m/s\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# Entrainment\n",
+ "print\"Entrainment\\n\"\n",
+ "V_by_Vf = V/Vf;\n",
+ "# From Fig.6.17 (Pg 173), V/Vf = 0.8 & abcissa = 0.0622\n",
+ "E = 0.05;\n",
+ "print\"Entrainment:\\n\",E\n",
+ "#the answers are slightly different in textbook due to approximation while here answers are precise"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 6.3 - Page: 174\n",
+ "\n",
+ "\n",
+ "Perforations\n",
+ "\n",
+ "Do = 4.5mm on an equilateral triangle pitch 12 mm between the hole centres, punched in sheet metal 2 mm thick\n",
+ "\n",
+ "The ratio of Hole Area By Active Area is: 0.1275 \n",
+ "\n",
+ "\n",
+ "\n",
+ "Tower Diameter\n",
+ "\n",
+ "Tower Spacing: 0.5 m\n",
+ "\n",
+ "Weir Length: 0.875 \n",
+ "\n",
+ "Area for perforated sheet: 0.7892 square m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Weir crest h1 & Weir height hw\n",
+ "\n",
+ "Weir crest: 0.025 m\n",
+ "\n",
+ "Weir height: 0.05 m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Dry Pressure Drop\n",
+ "\n",
+ "Dry Pressure Drop: 0.0654 m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Hydraulic head hl\n",
+ "Hydraulic head: 0.0106 m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Residual Pressure drop hr\n",
+ "\n",
+ "Residual Pressure Drop: 0.0057 m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Total Gas pressure Drop hg\n",
+ "\n",
+ "Total gas pressure Drop: 0.0816 m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Pressure loss at liquid entrance h2\n",
+ "\n",
+ "Pressure loss at liquid entrance: 0.008 m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Backup in Downspout h3\n",
+ "\n",
+ "Backup in Downspout: 0.0897 m\n",
+ "\n",
+ "\n",
+ "\n",
+ "Check on Flooding\n",
+ "\n",
+ "Choosen Tower spacing is satisfactory\n",
+ "\n",
+ "\n",
+ "\n",
+ "Weeping Velocity\n",
+ "\n",
+ "For W/D ratio 0.7 weir is set at 0.412 m from the center from the tower\n",
+ "The minimum gas velocity through the holes below which excessive weeping is likely: 8.703 m/s\n",
+ "\n",
+ "\n",
+ "\n",
+ "Entrainment\n",
+ "\n",
+ "Entrainment:\n",
+ "0.05\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6.4: Page 183"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 6.4\n",
+ "# Page: 183\n",
+ "\n",
+ "print'Illustration 6.4 - Page: 183\\n\\n'\n",
+ "\n",
+ "# solution\n",
+ "import math\n",
+ "#****Data****#\n",
+ "#From Illustrtion 6.3:\n",
+ "G = 0.100;# [kmol/s]\n",
+ "Density_G = 0.679;# [kg/cubic m]\n",
+ "q = 5*10**(-3);# [cubic m/s]\n",
+ "Va = 3.827;# [m/s]\n",
+ "z = 1.063;# [m]\n",
+ "L = 0.25;# [kmol/s]\n",
+ "hL = 0.0106;# [m]\n",
+ "hW = 0.05;# [m]\n",
+ "Z = 0.824;# [m]\n",
+ "E = 0.05;\n",
+ "ya = 0.18;# [mole fraction methanol]\n",
+ "\n",
+ "# a:CH3OH b:H2O\n",
+ "Ma = 32;# [kg/kmol]\n",
+ "Mb = 18;# [kg/kmol]\n",
+ "# From Chapter 2:\n",
+ "ScG = 0.865;\n",
+ "Dl = 5.94*10**(-9);# [square m/s]\n",
+ "# From Eqn. 6.61:\n",
+ "NtG = (0.776+(4.57*hW)-(0.238*Va*Density_G**0.5)+(104.6*q/Z))/ScG**0.5;\n",
+ "DE = ((3.93*10**(-3))+(0.0171*Va)+(3.67*q/Z)+(0.1800*hW))**2;# [square m/s]\n",
+ "thethaL = hL*z*Z/q;# [s]\n",
+ "NtL = 40000*Dl**0.5*((0.213*Va*Density_G**0.5)+0.15)*thethaL;\n",
+ "# For 15 mass% methanol:\n",
+ "xa = (15.0/Ma)/((15.0/Ma)+(85.0/Mb));\n",
+ "# From Fig 6.23 (Pg 184)\n",
+ "mAC = -(NtL*L)/(NtG*G);# [Slope of AC line]\n",
+ "meqb = 2.50;# [slope of equilibrium line]\n",
+ "# From Eqn. 6.52:\n",
+ "NtoG = 1.0/((1/NtG)+(meqb*G/L)*(1.0/NtL));\n",
+ "# From Eqn. 6.51:\n",
+ "EOG = 1-math.exp(-NtoG);\n",
+ "# From Eqn. 6.59:\n",
+ "Pe = Z**2/(DE*thethaL);\n",
+ "# From Eqn. 6.58:\n",
+ "eta = (Pe/2.0)*((1+(4*meqb*G*EOG/(L*Pe)))**0.5-1);\n",
+ "# From Eqn. 6.57:\n",
+ "EMG = EOG*(((1-math.exp(-(eta+Pe)))/((eta+Pe)*(1+(eta+Pe)/eta)))+(math.exp(eta)-1)/(eta*(1+eta/(eta+Pe))));\n",
+ "# From Eqn. 6.60:\n",
+ "EMGE = EMG/(1+(EMG*E/(1-E)));\n",
+ "print\"Efficiency of Sieve trays: \",round(EMGE,1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 6.4 - Page: 183\n",
+ "\n",
+ "\n",
+ "Effeciency of Sieve trays: 0.7\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6.5: Page 200"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 6.5\n",
+ "# Page: 200\n",
+ "\n",
+ "print'Illustration 6.5 - Page: 200\\n\\n'\n",
+ "\n",
+ "# solution\n",
+ "\n",
+ "import math\n",
+ "# ****Data****#\n",
+ "G = 0.80;# [cubic m/s]\n",
+ "P = 10**2;# [kN/square m]\n",
+ "XaG = 0.07;\n",
+ "Temp = 273+30.0;# [K]\n",
+ "L = 3.8;# [kg/s]\n",
+ "Density_L = 1235.0;# [kg/cubic m]\n",
+ "viscocity_L = 2.5*10**(-3);# [kg/m.s]\n",
+ "#******#\n",
+ "\n",
+ "# a = SO2 b = air\n",
+ "\n",
+ "# Solution (a) \n",
+ "\n",
+ "# Since the larger flow quantities are at the bottom for an absorber, the diameter will be choosen to accomodate the bottom condition\n",
+ "Mavg_G = XaG*64+((1-XaG)*29);# [kg/kmol]\n",
+ "G1 = G*(273/Temp)*(P/101.33)*(1/22.41);# [kmol/s]\n",
+ "G2 = G1*Mavg_G;# [kg/s]\n",
+ "Density_G = G2/G;# [kg/cubic m]\n",
+ "# Assuming Complete absorption of SO2\n",
+ "sulphur_removed = G1*XaG*64;# [kg/s]\n",
+ "abcissa = (L/G)*((Density_G/Density_L)**0.5);\n",
+ "#From Fig. 6.24, using gas pressure drop of 400 (N/square m)/m\n",
+ "ordinate = 0.061;\n",
+ "# For 25 mm ceramic Intalox Saddle:\n",
+ "Cf = 98.0;# [Table 6.3 Pg 196]\n",
+ "J = 1;\n",
+ "G_prime = (ordinate*Density_G*(Density_L-Density_G)/(Cf*viscocity_L**0.1*J))**0.5;# [kg/square m.s]\n",
+ "A = G2/G_prime;# [square m]\n",
+ "D = (4*A/math.pi)**0.5;# [m]\n",
+ "print\"The Tower Diameter is \",round(D,4),\" m\\n\"\n",
+ "\n",
+ "# Solution (b)\n",
+ "\n",
+ "# Let\n",
+ "D = 1.0;# [m]\n",
+ "A = math.pi*D**2.0/4;# [square m]\n",
+ "# The pressure drop for 8 m of irrigated packing\n",
+ "delta_p = 400*8.0;# [N/square m]\n",
+ "# For dry packing\n",
+ "G_prime = (G2-sulphur_removed)/A;# [kg/square m.s]\n",
+ "P = P-(delta_p/1000.0);# [kN/square m]\n",
+ "Density_G = (29/22.41)*(273.0/Temp)*(P/101.33);# [kg/cubic m]\n",
+ "# From Table 6.3 (Pg 196)\n",
+ "Cd = 241.5;\n",
+ "# From Eqn. 6.68\n",
+ "delta_p_by_z = Cd*G_prime**2/Density_G;# [N/square m for 1m of packing]\n",
+ "pressure_drop = delta_p+delta_p_by_z;# [N/square m]\n",
+ "V = 7.5;# [m/s]\n",
+ "head_loss = 1.5*V**2.0/2;# [N.m/kg]\n",
+ "head_loss = head_loss*Density_G;# [N/square m]\n",
+ "Power = (pressure_drop+head_loss)*(G2-sulphur_removed)/(Density_G*1000.0);# [kW]\n",
+ "eta = 0.6;\n",
+ "Power = Power/eta;# [kW]\n",
+ "print\"The Power for the fan motor is \",round(Power,2),\" kW\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 6.5 - Page: 200\n",
+ "\n",
+ "\n",
+ "The Tower Diameter is 0.981 m\n",
+ "\n",
+ "The Power for the fan motor is 4.49 kW\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6.6: Page 204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 6.6\n",
+ "# Page: 204\n",
+ "\n",
+ "print'Illustration 6.6 - Page: 204\\n\\n'\n",
+ "\n",
+ "# solution\n",
+ "\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "#****Data****#\n",
+ "# Gas\n",
+ "Mavg_G = 11.0;# [kg/kmol]\n",
+ "viscocity_G = 10**(-5);# [kg/m.s]\n",
+ "Pt = 107.0;# [kN/square m]\n",
+ "Dg = 1.30*10**(-5);# [square m/s]\n",
+ "Temp = 273.0+27;# [K]\n",
+ "G_prime = 0.716;# [kg/square m.s]\n",
+ "\n",
+ "# Liquid:\n",
+ "Mavg_L = 260.0;\n",
+ "viscocity_L = 2*10**(-3);# [kg/m.s]\n",
+ "Density_L = 840.0;# [kg/cubic m]\n",
+ "sigma = 3*10.0**(-2);# [N/m]\n",
+ "Dl = 4.71*10**(-10);# [square m/s]\n",
+ "#******#\n",
+ "\n",
+ "#Gas:\n",
+ "Density_G = (Mavg_G/22.41)*(Pt/101.33)*(273/Temp);# [kg/cubic m]\n",
+ "ScG = viscocity_G/(Density_G*Dg);\n",
+ "G = G_prime/Mavg_G;# [kmol/square m.s]\n",
+ "\n",
+ "# Liquid:\n",
+ "L_prime = 2.71;# [kg/square m.s]\n",
+ "ScL = viscocity_L/(Density_L*Dl);\n",
+ "\n",
+ "# Holdup:\n",
+ "# From Table 6.5 (Pg 206), L_prime = 2.71 kg/square m.s\n",
+ "Ds = 0.0472;# [m]\n",
+ "beeta = 1.508*Ds**0.376;\n",
+ "shiLsW = 5.014*10**(-5)/Ds**1.56;# [square m/cubic m]\n",
+ "shiLtW = (2.32*10**(-6))*(737.5*L_prime)**beeta/(Ds**2);# [square m/cubic m]\n",
+ "shiLoW = shiLtW-shiLsW;# [square m/cubic m]\n",
+ "H = (1404*(L_prime**0.57)*(viscocity_L**0.13)/((Density_L**0.84)*((3.24*L_prime**0.413)-1)))*(sigma/0.073)**(0.2817-0.262*math.log10(L_prime));\n",
+ "shiLo = shiLoW*H;# [square m/cubic m]\n",
+ "shiLs = 4.23*10**(-3)*(viscocity_L**0.04)*(sigma**0.55)/((Ds**1.56)*(Density_L**0.37));# [square m/cubic m]\n",
+ "shiLt = shiLo+shiLs;# [square m/cubic m]\n",
+ "\n",
+ "# Interfacial Area:\n",
+ "# From Table 6.4 (Pg 205)\n",
+ "m = 62.4;\n",
+ "n = (0.0240*L_prime)-0.0996;\n",
+ "p = -0.1355;\n",
+ "aAW = m*((808*G_prime/(Density_G**0.5))**n)*(L_prime**p);# [square m/cubic m]\n",
+ "# From Eqn. 6.73\n",
+ "aA = aAW*shiLo/shiLoW;# [square m/cubic m]\n",
+ "# From Table 6.3 (Pg 196)\n",
+ "e = 0.75;\n",
+ "# From Eqn. 6.71\n",
+ "eLo = e-shiLt;\n",
+ "# From Eqn. 6.70\n",
+ "def f9(Fg):\n",
+ " return ((Fg*ScG**(2.0/3))/G)-1.195*((Ds*G_prime)/(viscocity_G*(1-eLo)))**(-0.36) \n",
+ "Fg = fsolve(f9,1);# [kmol/square m.s]\n",
+ "# From Eqn. 6.72:\n",
+ "def f10(Kl):\n",
+ " return (Kl*Ds/Dl)-(25.1*(Ds*L_prime/viscocity_L)**0.45)*ScL**0.5\n",
+ "Kl = fsolve(f10,1);# [(kmol/square m.s).(kmol/cubic m)]\n",
+ "# Since the value of Kl is taken at low conc., it can be converted into Fl\n",
+ "c = (Density_L/Mavg_L);# [kmol/cubic m]\n",
+ "Fl = Kl*c;# [kmol/cubic m]\n",
+ "print\"The volumetric coeffecients are\\n\"\n",
+ "print\"Based on Gas Phase \",round(Fg*aA,3),\" kmol/cubic m.s\\n\"\n",
+ "print\"based on Liquid Phase\",round(Fl*aA,3),\" kmol/cubic m.s\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 6.6 - Page: 204\n",
+ "\n",
+ "\n",
+ "The volumetric coeffecients are\n",
+ "\n",
+ "Based on Gas Phase 0.071 kmol/cubic m.s\n",
+ "\n",
+ "based on Liquid Phase 0.014 kmol/cubic m.s\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6.7: Page 207"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 6.7\n",
+ "# Page: 207\n",
+ "\n",
+ "print'Illustration 6.7 - Page: 207\\n\\n'\n",
+ "\n",
+ "# solution\n",
+ "from scipy.optimize import fsolve\n",
+ "\n",
+ "#****Data****#\n",
+ "# Air\n",
+ "G_prime = 1.10;# [kg/square m.s]\n",
+ "viscocity_G = 1.8*10**(-5);# [kg/m.s]\n",
+ "ScG = 0.6;# [for air water mixture]\n",
+ "Temp1 = 273+20.0;# [K]\n",
+ "\n",
+ "# Water\n",
+ "L_prime = 5.5;# [kg/square m.s]\n",
+ "#*****#\n",
+ "\n",
+ "# Air:\n",
+ "Ma = 29.0;# [kg/kmol]\n",
+ "G = G_prime/Ma;# [kmol/square m.s]\n",
+ "Density_G = (Ma/22.41)*(273.0/Temp1);\n",
+ "Cpa = 1005.0;# [N.m/kg.K]\n",
+ "PrG = 0.74;\n",
+ "\n",
+ "# Liquid:\n",
+ "kth = 0.587;# [W/m.K]\n",
+ "Cpb = 4187.0;# [N.m/kg.K]\n",
+ "viscocity_L = 1.14*10**(-3);# [kg/m.s]\n",
+ "\n",
+ "# From Table 6.5 (Pg 206)\n",
+ "Ds = 0.0725;# [m]\n",
+ "beeta = 1.508*(Ds**0.376);\n",
+ "shiLtW = (2.09*10**(-6))*(737.5*L_prime)**beeta/(Ds**2);# [square m/cubic m]\n",
+ "shiLsW = 2.47*10**(-4)/(Ds**1.21);# [square m/cubic m]\n",
+ "shiLoW = shiLtW-shiLsW;# [square m/cubic m]\n",
+ "# From Table 6.4 (Pg 205)\n",
+ "m = 34.03;\n",
+ "n = 0.0;\n",
+ "p = 0.362;\n",
+ "aAW = m*(808.0*G_prime/Density_G**0.5)**(n)*L_prime**p;# [square m/cubic m]\n",
+ "# From Eqn. 6.75\n",
+ "aVW = 0.85*aAW*shiLtW/shiLoW;# [square m/cubic m]\n",
+ "# From Table 6.3\n",
+ "e = 0.74;\n",
+ "eLo = e-shiLtW;\n",
+ "# From Eqn. 6.70\n",
+ "def f11(Fg):\n",
+ " return ((Fg*ScG**(2.0/3))/G)-1.195*((Ds*G_prime)/(viscocity_G*(1-eLo)))**(-0.36)\n",
+ "Fg = fsolve(f11,1);# [kmol/square m.s]\n",
+ "# Since the liquid is pure water. It has no mass trnsfer coeffecient.\n",
+ "# For such process we need convective heat transfer coeffecient for both liquid & gas.\n",
+ "# Asuming Jd = Jh\n",
+ "# From Eqn. 6.70\n",
+ "Jh = 1.195*((Ds*G_prime)/(viscocity_G*(1-eLo)))**(-0.36);\n",
+ "Hg = Jh*Cpa*G_prime/(PrG**(2.0/3));# [W/square m.K]\n",
+ "PrL = Cpb*viscocity_L/kth;\n",
+ "# Heat transfer analog of Eqn. 6.72\n",
+ "Hl = 25.1*(kth/Ds)*(Ds*L_prime/viscocity_L)**0.45*PrL**0.5;# [W/square m.K]\n",
+ "print\"The volumetric coeffecients are\\n\"\n",
+ "print\"Based on Gas Phase \",round(Hg*aVW), \"W/cubic m.K\\n\"\n",
+ "print\"based on Liquid Phase\",round(Hl*aVW,2),\" W/cubic m.K\\n\"\n",
+ "#the answers are slightly different in textbook due to approximation while here answers are precise"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 6.7 - Page: 207\n",
+ "\n",
+ "\n",
+ "The volumetric coeffecients are\n",
+ "\n",
+ "Based on Gas Phase 3183.0 W/cubic m.K\n",
+ "\n",
+ "based on Liquid Phase 503701.46 W/cubic m.K\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 45
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "# Illustration 10.1\n",
+ "# Page: 494\n",
+ "\n",
+ "print'Illustration 10.1 - Page: 494\\n\\n'\n",
+ "\n",
+ "# solution\n",
+ "import matplotlib.pyplot as plt\n",
+ "import pylab\n",
+ "#****Data****#\n",
+ "# a:water b:isopropyl ether c:acetic acid\n",
+ "xF = 0.30;# [mol fraction]\n",
+ "yS = 0;# [mol fraction]\n",
+ "S1 = 40.0;# [kg]\n",
+ "B1 = 40.0;# [kg]\n",
+ "#*******#\n",
+ "\n",
+ "# Equilibrium data at 20 OC:\n",
+ "# Wa: Wt. percent of a\n",
+ "# Wb: Wt. percent of b\n",
+ "# Wc: Wt. percent of c\n",
+ "# Data1 = [Wc Wa Wb]\n",
+ "# Data1: water layer\n",
+ "Data1 = numpy.array([(0.69 ,98.1, 1.2),(1.41, 97.1 ,1.5),(2.89 ,95.5 ,1.6),(6.42 ,91.7 ,1.9),(13.30, 84.4, 2.3),(25.50 ,71.1 ,3.4),(36.70 ,58.9 ,4.4),(44.30 ,45.1 ,10.6),(46.40 ,37.1 ,16.5)])\n",
+ "# Data2: isopropyl ether layer\n",
+ "Data2 = numpy.array([(0.18 ,0.5 ,99.3),(0.37, 0.7 ,98.9),(0.79, 0.8, 98.4),(1.93 ,1, 97.1),(4.82, 1.9, 93.3),(11.40, 3.9, 84.7),(21.60, 6.9, 71.5),(31.10, 10.8, 58.1),(36.20 ,15.1 ,48.7)])\n",
+ "\n",
+ "plt.plot((Data1[:,2])/100,(Data1[:,0])/100,label=\"x Vs fraction ether\")\n",
+ "plt.plot((Data2[:,2])/100,(Data2[:,0])/100,label=\"y Vs fraction ether\")\n",
+ "plt.grid('on');\n",
+ "plt.legend(loc='lower center');\n",
+ "ax=pylab.gca()\n",
+ "ax.set_xlabel(\"Wt fraction of isopropyl ether\");\n",
+ "ax.set_ylabel(\"Wt fraction of acetic acid\");\n",
+ "plt.ylim((0,0.3))\n",
+ "plt.xlim((0,1))\n",
+ "plt.show();\n",
+ "# x: Wt fraction of acetic acid in water layer.\n",
+ "# y: Wt fraction of acetic acid in isopropyl layer.\n",
+ "\n",
+ "# The rectangular coordinates of Fig 10.9(a) will be used but only upto x = 0.30\n",
+ "\n",
+ "# Stage 1:\n",
+ "F = 100;# [kg]\n",
+ "# From Eqn. 10.4:\n",
+ "M1 = F+S1;# [kg]\n",
+ "# From Eqn. 10.5:\n",
+ "xM1 = ((F*xF)+(S1*yS))/M1;\n",
+ "# From Fig. 10.15 (Pg 495):\n",
+ "# Point M1 is located on the line FB and with the help of tie line passing through M1:\n",
+ "x1 = 0.258;# [mol fraction]\n",
+ "y1 = 0.117;# [mol fraction]\n",
+ "# From Eqn. 10.8:\n",
+ "E1 = (M1*(xM1-x1)/(y1-x1));# [kg]\n",
+ "# From Eqn. 10.4:\n",
+ "R1 = M1-E1;# [kg]\n",
+ "\n",
+ "# Stage 2:\n",
+ "S2 = 40;# [kg]\n",
+ "B2 = 40;# [kg]\n",
+ "# From Eqn. 10.15:\n",
+ "M2 = R1+B2;# [kg]\n",
+ "# From Eqn. 10.16:\n",
+ "xM2 = ((R1*x1)+(S2*yS))/M2;\n",
+ "# Point M2 is located on the line R1B and the tie line passing through R2E2 through M2:\n",
+ "x2 = 0.227;\n",
+ "y2 = 0.095;\n",
+ "# From Eqn. 10.8:\n",
+ "E2 = (M2*(xM2-x2)/(y2-x2));# [kg]\n",
+ "# From Eqn. 10.4:\n",
+ "R2 = M2-E2;# [kg]\n",
+ "\n",
+ "# Stage 3:\n",
+ "S3 = 40;# [kg]\n",
+ "B3 = 40;# [kg]\n",
+ "# From Eqn. 10.15:\n",
+ "M3 = R2+B3;# [kg]\n",
+ "# From Eqn. 10.16:\n",
+ "xM3 = ((R2*x2)+(S3*yS))/M3;\n",
+ "# Point M3 is located on the line R2B and the tie line passing through R3E3 through M3:\n",
+ "x3 = 0.20;# [mol fraction]\n",
+ "y3 = 0.078;# [mol fraction]\n",
+ "# From Eqn. 10.8:\n",
+ "E3 = (M3*(xM3-x3)/(y3-x3));# [kg]\n",
+ "# From Eqn. 10.4:\n",
+ "R3 = M3-E3;# [kg]\n",
+ "Ac = x3*R3;\n",
+ "print\"The composited extract is\",round((E1+E2+E3),2),\" kg\\n\"\n",
+ "print\"The acid content is \",round(((E1*y1)+(E2*y2)+(E3*y3)),2),\" kg\\n\"\n",
+ "print\"\\n\"\n",
+ "\n",
+ "# If an extraction to give the same final raffinate concentration were to be done in single stage, the point M would be at the intersection of tie line R3E3 and the line BF.\n",
+ "x = 0.20;# [mol fraction]\n",
+ "xM = 0.12;# [mol fraction]\n",
+ "# From Eqn. 10.6:\n",
+ "S = F*(xF-xM)/(xM-yS);# [kg]\n",
+ "print round(S,2),\"kg of solvent would be recquired if the same final raffinate concentration were to be obtained with one stage.\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Illustration 10.1 - Page: 494\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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F6AM8U4J9C5SIVVLGmMhIrpzM4+c+Tp+P+3BAY2J4oDLjdTyM0cB+4BxgHDDB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\niRUYxhhjPPl/ptoLDFmMWJUAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x917b748>"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The composited extract is 135.05 kg\n",
+ "\n",
+ "The acid content is 13.01 kg\n",
+ "\n",
+ "\n",
+ "\n",
+ "150.0 kg of solvent would be recquired if the same final raffinate concentration were to be obtained with one stage.\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 82
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |