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+{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14 The Tanks-in-Series Model"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.1 pageno : 329"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#Original and new length(m)\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "L1 = 32. # diameter pipe\n",
+ "L2 = 50. # pipeline length \n",
+ "sigma1 = 8. # bottles \n",
+ "\n",
+ "# Calculations\n",
+ "# For small deviaqtion from plug flow,sigma_sqr is directly proportional to L\n",
+ "sigma2 = sigma1*math.sqrt(L2/L1);\n",
+ "\n",
+ "# Results\n",
+ "print \" No of bottles of rose expected is %.f\"%(sigma2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " No of bottles of rose expected is 10\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.2 pageno : 330"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "sigma1 = 14. # hours\n",
+ "sigma2 = 10.5; # hours\n",
+ "L1 = 119. # ohio miles apart\n",
+ "\n",
+ "# Calculations\n",
+ "#spread of curve is directly proportional to sqrt of distance from origin\n",
+ "L = sigma1**2*L1/(sigma1**2-sigma2**2);\n",
+ "\n",
+ "# Results\n",
+ "print \" The dumping of toxic phenol must have occured within %.f miles upstream of cincinnati\"%(L)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " The dumping of toxic phenol must have occured within 272 miles upstream of cincinnati\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.3 pageno : 332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "# from figure\n",
+ "vo = 1.; \n",
+ "t1 = 1./6;\n",
+ "t2 = 1.;\n",
+ "t3 = 11./6;\n",
+ "w = 1./10;\n",
+ "\n",
+ "# Calculations\n",
+ "A2_by_A1 = 0.5;\n",
+ "R = A2_by_A1/(1-A2_by_A1);\n",
+ "#From the location of 1st peak\n",
+ "V1 = (R+1)*vo*t1;\n",
+ "#From the time between peaks\n",
+ "V2 = (R*vo)*((t2-t1)-(t1));\n",
+ "#From fig 14.3\n",
+ "N = 1+(2*(t1/w))**2;\n",
+ "\n",
+ "# Results\n",
+ "print \" The reflux ratio is %.f\"%(R)\n",
+ "print \" The volume of 1st tank is %.3f\"%( V1)\n",
+ "print \" The volume of 2nd tank is %.3f\"%(V2)\n",
+ "print \" The number of tanks are %.f \"%(N)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " The reflux ratio is 1\n",
+ " The volume of 1st tank is 0.333\n",
+ " The volume of 2nd tank is 0.667\n",
+ " The number of tanks are 12 \n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.4 page no :333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from matplotlib.pyplot import *\n",
+ "import math \n",
+ "from numpy import *\n",
+ "\n",
+ "# Variables\n",
+ "# from figure E14.4a\n",
+ "t2 = 280.\n",
+ "t1 = 220.\n",
+ "sigma1_sqr = 100.\n",
+ "sigma2_sqr = 1000.\n",
+ "\n",
+ "# Calculations\n",
+ "dt = t2-t1;\n",
+ "dsigma_sqr = sigma2_sqr-sigma1_sqr;\n",
+ "N = dt**2/dsigma_sqr;\n",
+ "\n",
+ "E = zeros(200)\n",
+ "\n",
+ "for t in range(200):\n",
+ " E[t] = ((t**(N-1))*(N**N)*math.exp(-t*N/dt))/((math.factorial(N-1))*(dt**N));\n",
+ "\n",
+ "t = zeros(200) \n",
+ "for i in range(200):\n",
+ " t[i] = i;\n",
+ "\n",
+ "# Results\n",
+ "plot(t,E)\n",
+ "xlabel(\"t, s\")\n",
+ "ylabel(\"E, s**-1\")\n",
+ "show()\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Populating the interactive namespace from numpy and matplotlib\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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BBx8EnnlG7UqIqDUME5Xt2CEXw6K2PfYYsH498N13aldCRC1RLExMJhNiY2Oh0+mQm5vb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\njhwBrrySQRKItFr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+ "text": [
+ "<matplotlib.figure.Figure at 0x2625a50>"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file