path: root/Fundamentals_of_Fluid_Mechanics/ch_11.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 11:Compressible flow"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.1 page no 617."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=4.0                     #in\n",
      "T1=540.0                #degree R\n",
      "p1=100.0                #psia\n",
      "T2=453.0               #degree R\n",
      "p2=18.4                 #psia\n",
      "k=1.4\n",
      "R=1716/32.174        #ft*lb/(lbm*(degree R))\n",
      "cv=R/(k-1)              #ft*lb/(lbm*(degree R))\n",
      "udiff=cv*(T2-T1)    #ft*lb/lbm change in internal energy\n",
      "\n",
      "#Result\n",
      "print \"a)The change in internal energy between (1) and (2)=\",round(udiff,2),\"ft*lb/lbm\"\n",
      "cp=k*round(cv,0)                  #ft*lb/(lbm*(degree R))\n",
      "hdiff=cp*(T2-T1)    #ft*lb/lbm change in enthalpy\n",
      "print \"b)The  change in enthalpy between (1) and (2)=\",round(hdiff,0),\"ft*lb/lbm\"\n",
      "ddiff=(1/R)*((p2*144/T2)-(p1*144/T1))  #lbm/(ft**3) change in density\n",
      "\n",
      "#Result\n",
      "print \"The change in density betwenn (1) and (2)=\",round(ddiff,3),\"ft*lb/lbm\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a)The change in internal energy between (1) and (2)= -11600.36 ft*lb/lbm\n",
        "b)The  change in enthalpl energy between (1) and (2)= -16199.0 ft*lb/lbm\n",
        "The change in density betwenn (1) and (2)= -0.39 ft*lb/lbm\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.2 page no.619"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=4.0              #in\n",
      "T1=540.0         #degree R\n",
      "p1=100.0          #psia\n",
      "T2=453.0         #degree R\n",
      "p2=18.4           #psia\n",
      "\n",
      "#Calculation\n",
      "import math\n",
      "dratio=(p1/T1)*(T2/p2)\n",
      "sdif=(cv*(math.log(T2/T1)))+(R*(math.log(dratio)))#ft*lb/lbm*(degree R) change in entropy\n",
      "\n",
      "#Result\n",
      "print \"The change in entropy between (1) and (2)=\",round(sdif,1),\"ft*lb/lbm*(degree R)\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The change in entropy between (1) and (2)= 57.49 ft*lb/lbm*(degree R)\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.3 page no.623"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "T=0                #degree C\n",
      "R=286.9         #J/(kg*K)\n",
      "k=1.401\n",
      "c=(R*(T+273.15)*k)**0.5        #m/s\n",
      "\n",
      "#Result\n",
      "print \"The speed of sound for air at 0 degree C =\",round(c,1),\"m/s\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The speed of sound for air at 0 degree C = 331.35 m/s\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.4 page no.628"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "z=1000                        #m\n",
      "Ma=1.5\n",
      "T=20                        #degree C\n",
      "#alpha=atan(z/x), x=V*t,and Ma=(1/sin(alpha)) where alpha is the angle of the Mach cone\n",
      "#V=Ma*c\n",
      "#calculation\n",
      "import math\n",
      "c=343.3                  #m/s found from the value of temperature\n",
      "V=Ma*c                #m/sec\n",
      "t=z/(Ma*c*math.tan(math.asin(1/Ma)))       #sec\n",
      "print\"The number of seconds to wait after the plane passes over-head before it is heard=\",round(t,2),\"s\"\n",
      "\n",
      "#Plot\n",
      "import matplotlib.pyplot as plt\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "Ma=[1,1.1,1.3,1.5,2,4]\n",
      "t=[0,1.5,2,2.17,2.3,2.75]\n",
      "xlabel(\"Ma\") \n",
      "ylabel(\"t  (s)\") \n",
      "plt.xlim((0,4))\n",
      "plt.ylim((0,3))\n",
      "ax.plot([1.5], [2.17], 'o')\n",
      "ax.annotate('(1.5,2.17s)', xy=(1.7,2.1))\n",
      "a=plot(Ma,t)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The number of seconds to wait after the plane passes over-head before it is heard= 2.17 s\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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LMosy4ePlg0lDJ8ldChF1AwYDddmN0QJvjEd0a2AwUJcUlheiqLoIj416TO5SiKibMBio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\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.5 page no.635"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " \n",
      "A=1*(10**(-4))                    #m**2\n",
      "p1=80.0                             #kPa(abs)\n",
      "p2=40.0                             #kPa(abs)\n",
      "p0=101.0                            #kPa(abs)\n",
      "pcritical=0.528*p0                  #kPa(abs)\n",
      "k=1.4\n",
      "#for (a) pth=p1>pcritical\n",
      "Math1=((((p0/p1)**((k-1)/k))-1)/((k-1)/2))**(0.5)           #Math=Mach number at throat\n",
      "#dth/d0=p1/p0 dth=density at throat\n",
      "dth1=(1.23)*(1/(1+(((k-1)/2)*(Math1**2))))**(1/(k-1))     #kg/(m**3) density at throat\n",
      "Tth1=(288)*(1/(1+(((k-1)/2)*(Math1**2))))                  #K temperature at throat\n",
      "Vth1=Math1*(286.9*269*k)**(0.5)             #m/sec\n",
      "m1=dth1*A*Vth1             #kg/sec\n",
      "\n",
      "#Result\n",
      "print \"a) The mass flowrate through the duct=\",round(m1,4),\"kg/s\"\n",
      "#for (b) pth=p2<pcritical, hence\n",
      "Math2=1\n",
      "dth2=1.23*(1/(1+(((k-1)/2)*(Math2**2))))**(1/(k-1))    #kg/(m**3) density at throat\n",
      "Tth2=(288)*(1/(1+(((k-1)/2)*(Math2**2))))                 #K temperature at throat\n",
      "Vth2=Math2*(286.9*Tth2*k)**0.5                             #m/sec\n",
      "m2=dth2*A*Vth2             #kg/sec\n",
      "print \"b) The mass flowrate through the duct=\",round(m2,3),\"kg/s\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a) The mass flowrate through the duct= 0.0201 kg/s\n",
        "b) The mass flowrate through the duct= 0.024 kg/s\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.6 page no.637"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "A=1*(10**(-4))               #m**2\n",
      "p1=80                        #kPa(abs)\n",
      "p2=40                        #kPa(abs)\n",
      "\n",
      "p0=101                       #kPa(abs)\n",
      "k=1.4\n",
      "#for (a)\n",
      "pratio1=p1/p0\n",
      "#for this value of p1/p0, \n",
      "Math1=0.59\n",
      "Tratio1=0.94                 #=Tth/T0\n",
      "dratio1=0.85                 #=dth/d0\n",
      "Tth1=Tratio1*(288)     #K\n",
      "dth1=dratio1*(1.23)    #kg/(m**3)\n",
      "Vth1=Math1*(286.9*Tth1*k)**0.5        #m/sec\n",
      "m1=(dth1*A*Vth1)                             #kg/sec\n",
      "print \"a)The mass flowrate=\",round(m1,3),\"kg/s\"\n",
      "#for (b)\n",
      "Math2=1\n",
      "Tratio2=0.83              #=Tth/T0\n",
      "dratio2=0.64              #=dth/d0\n",
      "Tth2=Tratio2*(288)        #K\n",
      "dth2=dratio2*(1.23)       #kg/(m**3)\n",
      "Vth2=Math2*(286.9*Tth2*k)**0.5        #m/sec\n",
      "m2=(dth2*A*Vth2)                             #kg/sec\n",
      "\n",
      "#Result\n",
      "print \"b)The mass flowrate=\",round(m2,3),\"kg/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a)The mass flowrate= 0.02 kg/s\n",
        "b)The mass flowrate= 0.024 kg/s\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.7 page no.638"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Given\n",
      "pratio=0.82                 #ratio of static to stagnation pressure\n",
      "T=68                        #degree F\n",
      "#for (a)\n",
      "#for the value of pratio given Ma is calculated as\n",
      "Ma1=0.54\n",
      "k1=1.4\n",
      "Tratio1=0.94               #T/T0\n",
      "T1=Tratio1*(T+460)         # degree R\n",
      "V1=(Ma1*(53.3*T1*k1)**0.5)*(32.2**0.5)    #ft/sec\n",
      "#for (b)\n",
      "k2=1.66\n",
      "Ma2=((((1/pratio)**((k2-1)/k2))-1)/((k2-1)/2))**0.5\n",
      "Tratio2=1/(1+(((k2-1)/2)*(Ma2**2)))       #T/T0\n",
      "T2=Tratio2*(T+460)                        #degree R\n",
      "V2=(Ma2*(386*T2*k2)**0.5)*(32.2**0.5)      #ft/sec\n",
      "\n",
      "#Result\n",
      "print \"The flow velocity if fluid is air=\",round(V1,0),\"ft/s\"\n",
      "print \"The flow velocity if fluid is helium=\",round(V2,0),\"ft/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The flow velocity if fluid is air= 590.0 ft/s\n",
        "The flow velocity if fluid is helium= 1583.0 ft/s\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.11 page no.648"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#Given\n",
      "k=1.4   \n",
      "T0=518.67                #degree R\n",
      "T1=514.55                #degree R\n",
      "p1=14.3                    #psia\n",
      "R=53.3                    #(ft*lb)/(lbm* degree R)\n",
      "\n",
      "#calculation\n",
      "from scipy.optimize import fsolve\n",
      "import math\n",
      "cp=R*k/(k-1)            #(ft*lb/(lbm* degree R))\n",
      "Tratio=T1/T0\n",
      "Ma=(((1/Tratio)-1)/((k-1)/2))**0.5\n",
      "x=(R*T1*k*32.2)**0.5          #ft/sec where x=(R*T1*k)**0.5\n",
      "y=p1*144/(R*T1)*(Ma*x)      # lbm/((ft**2)*sec) where y=d*V\n",
      "#for p=7 psia \n",
      "p=7                         #psia\n",
      "\n",
      "def f(T):\n",
      "    return(6.5*10**-5*T**2+T-518.67)\n",
      "T=fsolve(f,500)\n",
      "sdif=(cp*math.log(T/T1))-(R*math.log(p/p1))      #(ft*lb)/(lbm* degree R)\n",
      "\n",
      "#Result\n",
      "print \"The corrosponding value of temperature for Fanno for downstream pressure of 7psia=\",round(T,1),\"K\"\n",
      "print \"The corrosponding value of entropy change for Fanno for downstream pressure of 7psia=\",round(sdif,1),\"(ft*lb)/(lbm* degree R)\"\n",
      "#Plot\n",
      "s=[33.6,39.8,46.3,52.6,57.3,57.9,55.5,53.0,47.0,44.2]\n",
      "T=[502.3,496.8,488.3,474.0,447.7,432.1,394.7,378.1,347.6,335.6]\n",
      "a=plot(s,T)\n",
      "xlabel(\"s-s1  (ft lb/lbm R)\") \n",
      "ylabel(\"T (R)\") \n",
      "plt.xlim((30, 65))\n",
      "plt.ylim((300,550))\n",
      "show(a)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The corrosponding value of temperature for Fanno for downstream pressure of 7psia= 502.3 K\n",
        "The corrosponding value of entropy change for Fanno for downstream pressure of 7psia= 33.6 (ft*lb)/(lbm* degree R)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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D1WolLi4O8K/2d1W/v7R/VVUVt99+O9dddx0Wi4VPP/3Ur9r+3Pq3bNnS4Lb3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\npeUsIOIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x85c1c18>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.12 page no.655"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#Given\n",
      "T0=288                  #K\n",
      "p0=101                  #kPa(abs)\n",
      "l=2                        #m\n",
      "D=0.1                   #m\n",
      "f=0.02\n",
      "k=1.4\n",
      "x=f*l/D\n",
      "Tratio=2/(k+1)            #where Tratio is Tcritical/T0\n",
      "Tcritical=Tratio*T0     #K = T2\n",
      "Vcritical=(286.9*Tcritical*k)**0.5              #m/sec = V2\n",
      "#from value of x, the following are found\n",
      "Ma=0.63\n",
      "Trat=1.1                    #where Trat=T1/Tcritical\n",
      "Vrat=0.66                  #where Vrat=V1/Vcritical\n",
      "prat=1.7                   #where prat=p1/pcritical\n",
      "pratio=1.16              #where pratio=p0,1/p0critical\n",
      "#from value of Ma, the following are found\n",
      "Tfraction=0.93         #whereTfraction=T1/T0\n",
      "pfraction=0.76          #where pfraction=p1/p0,1\n",
      "dfraction=0.83         #where dfraction=d1/d0,1\n",
      "\n",
      "#hence,\n",
      "#calculation\n",
      "import math\n",
      "V1=Vrat*Vcritical              #m/sec\n",
      "d1=dfraction*(1.23)           #kg/(m**3)\n",
      "m=d1*math.pi*(D**2)*V1/4    #kg/sec\n",
      "T1=Tfraction*T0               #K\n",
      "p1=pfraction*p0                 #kPa(abs)\n",
      "T01=T0                             #K and T01=T02\n",
      "p01=p0                             #kPa(abs)\n",
      "p2=(1/prat)*(pfraction)*p01      #kpa(abs)\n",
      "p02=(1/pratio)*p01           #kPa(abs)\n",
      "\n",
      "#Result\n",
      "print \"Critical temperature=\",round(Tcritical,2),\"K\"\n",
      "print \"Critical velocity=\",round(Vcritical,0),\"m/s\"\n",
      "print \"Velocity at inlet=\",round(V1,0),\"m/s\"\n",
      "print \"Maximum mass flowrate=\",round(m,2),\"Kg/s\"\n",
      "print \"Temperature at inlet=\",round(T1,2),\"K\"\n",
      "print \"Pressure at inlet=\",round(p1,0),\"kPa(abs)\"\n",
      "print \"stagnation temperature at inlet and exit=\",round(T01,2),\"K\"\n",
      "print \"The stagnation pressure at inlet=\",round(p01,2),\"kPa(abs)\"\n",
      "print \"Pressure at exit=\",round(p2,2),\"kPa(abs)\"\n",
      "print \"The stagnation pressure at exit=\",round(p02,2),\"kPa(abs)\"\n",
      "\n",
      "#Plot\n",
      "#import numpy as np\n",
      "#import matplotlib.pyplot as plt\n",
      "#fig = plt.figure()\n",
      "#ax = fig.add_subplot(111)\n",
      "\n",
      "s=[-5,50]\n",
      "T=[288,288]\n",
      "s1=[0,0]\n",
      "T1=[288,268]\n",
      "s2=[40,40]\n",
      "T2=[288,240]\n",
      "s3=[0,10,20,30,40]\n",
      "T3=[268,265,261,252,240]\n",
      "s4=[30,50]\n",
      "T4=[240,240]\n",
      "s5=[-3,50]\n",
      "T5=[288,288]\n",
      "s6=[-2,8]\n",
      "T6=[284,294]\n",
      "s7=[35,45]\n",
      "T7=[281,295]\n",
      "s8=[-2,8]\n",
      "T8=[265,275]\n",
      "s9=[35,45]\n",
      "T9=[235,245]\n",
      "\n",
      "a=plot(s,T)\n",
      "a1=plot(s1,T1)\n",
      "a2=plot(s2,T2)\n",
      "a3=plot(s3,T3,linestyle='--')\n",
      "a4=plot(s4,T4)\n",
      "a5=plot(s5,T5)\n",
      "a6=plot(s6,T6)\n",
      "a7=plot(s7,T7)\n",
      "a8=plot(s8,T8)\n",
      "a9=plot(s9,T9)\n",
      "\n",
      "xlabel(\"s-s1  (J/kg K)\") \n",
      "ylabel(\"T (K)\") \n",
      "plt.xlim((-5, 70))\n",
      "plt.ylim((230,300))\n",
      "plt.text(50,240,'T2=240K')\n",
      "plt.text(50,288,'T0=288K')\n",
      "plt.text(15,255,'fanno line')\n",
      "plt.text(10,280,'p1=70kpa(abs)')\n",
      "plt.text(15,268,'T1=268K')\n",
      "plt.text(10,295,'p01=101kpa(abs)')\n",
      "plt.text(50,295,'p02=84kpa(abs)')\n",
      "plt.text(45,245,'p2=45kpa(abs)')\n",
      "\n",
      "show(a)\n",
      "show(a1)\n",
      "show(a2)\n",
      "show(a3)\n",
      "show(a4)\n",
      "show(a5)\n",
      "show(a6)\n",
      "show(a7)\n",
      "show(a8)\n",
      "show(a9)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Critical temperature= 240.0 K\n",
        "Critical velocity= 310.0 m/s\n",
        "Velocity at inlet= 205.0 m/s\n",
        "Maximum mass flowrate= 1.64 Kg/s\n",
        "Temperature at inlet= 267.84 K\n",
        "Pressure at inlet= 77.0 kPa(abs)\n",
        "stagnation temperature at inlet and exit= 288.0 K\n",
        "The stagnation pressure at inlet= 101.0 kPa(abs)\n",
        "Pressure at exit= 45.15 kPa(abs)\n",
        "The stagnation pressure at exit= 87.07 kPa(abs)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SEdwbdO7g2IHIgZGSGIQQJkdaDqVIBp2FEGWFtBxKiQw6CyHKEmk5GJgMOgsh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\nRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.13 page no.657"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Given\n",
      "T0=288                #K  Temprature\n",
      "p0=101                #kPa(abs)  pressure\n",
      "l=2                   #m  length of duct\n",
      "D=0.1                 #m  diameter\n",
      "f=0.02\n",
      "pd=45                 #kPa(abs)\n",
      "f=0.02\n",
      "k=1.4\n",
      "lnew=(50/100)*l       #m new length of duct\n",
      "x=lnew*f/D\n",
      "\n",
      "#Calculation\n",
      "#from this value of x, following are found\n",
      "Ma=0.7\n",
      "prat=1.5               #where prat=p1/pcritical\n",
      "#from this value of Ma, following are found\n",
      "pratio=0.72            #where pratio=p1/p0\n",
      "dratio=0.79            #where dratio=d1/d0,1\n",
      "Vratio=0.73            #where Vratio=V1/Vcritical\n",
      "#hence,\n",
      "p2=(1/prat)*pratio*p0   #kPa(abs)\n",
      "pcritical=p2 \n",
      "#we find that pd<pcritical\n",
      "d1=dratio*(1.23)                         #kg/(m**3)\n",
      "Vcritical=310                            #m/sec = V2, from example 11.12\n",
      "V1=Vratio*Vcritical                      #m/sec\n",
      "m=d1*math.pi*(D**2)*V1/4                 #kg/sec\n",
      "\n",
      "#Result\n",
      "print \"The flowrate for the smaller tube is =\",round(m,2),\"kg/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The flowrate for the smaller tube is = 1.73 kg/s\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.14 page no.658"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#given\n",
      "T0=288                       #K\n",
      "p0=101                       #kPa(abs)\n",
      "l=2                             #m\n",
      "D=0.1                        #m\n",
      "f=0.02\n",
      "pd=45                     #kPa(abs)\n",
      "f=0.02\n",
      "m=1.65                   #kg/sec\n",
      "lnew=l/2                  #m\n",
      "\n",
      "x=f*l/D\n",
      "#from this value of x, Ma at exit is found as\n",
      "Ma=0.7\n",
      "#and p2/pcritical is found as\n",
      "pratio=1.5\n",
      "#and, from example 11.12,\n",
      "prat=1.7                     #where prat=p1/pcritical\n",
      "pfraction=0.76             #where pfraction=p1/p0,1\n",
      "#Hence,\n",
      "p2=pratio*(1/prat)*pfraction*p0         #kPa(abs)\n",
      "\n",
      "#Result\n",
      "print \"The Mach number at the exit=\",round(Ma,3)\n",
      "print \"The back pressure required=\",round(p2,0),\"kPa(abs)\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Mach number at the exit= 0.7\n",
        "The back pressure required= 68.0 kPa(abs)\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.15 page no.659"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "k=1.4   \n",
      "T0=518.67                         #degree R\n",
      "T1=514.55                        #degree R\n",
      "p1=14.3                            #psia\n",
      "\n",
      "R=53.3                            #(ft*lb)/(lbm*degree R)\n",
      "cp=R*k/(k-1)                  #(ft*lb/(lbm* degree R))\n",
      "Tratio=T1/T0\n",
      "Ma=(((1/Tratio)-1)/((k-1)/2))**0.5\n",
      "x=(R*T1*k*32.2)**0.5        #ft/sec where x=(R*T1*k)**0.5\n",
      "y=p1*144/(R*T1)*(Ma*x)   #lbm/((ft**2)*sec) where y=d*V\n",
      "z=R*T1/(p1*144)                 #(ft**3)/lbm\n",
      "c=(p1)+(y*y*z/(32.2*144))   #psia =constant\n",
      "#when downstream pressure p=13.5 psia\n",
      "p=13.5                                       #psia \n",
      "a=(y**2)*R/(p*144*32.2*144)                  #(lb/(in**2))/degree R\n",
      "                                 \n",
      "T=(c-p)/a\n",
      "sdif=(cp*math.log(T/T1))-(R*math.log(p/p1))  #ft*lb/(lbm*degree R)\n",
      "\n",
      "#Result\n",
      "print \"The corrosponding value of temperature for the downstream pressure of 13.5 psia=\",round(T,0),\"degree R\"\n",
      "print \"The corrosponding value of change in entropy for the downstream pressure of 13.5 psia=\",round(sdif,0), \"ft*lb/(lbm*degree R)\"\n",
      "\n",
      "s=[93.2,202,251,285,317,330,333,334,336,338,338,336,333,328,321,259,181]\n",
      "T=[969,1459,1859,2168,2464,2549,2558,2558,2544,2488,2450,2369,2260,2140,1992,1175,633]\n",
      "a=plot(s,T)\n",
      "xlabel(\"s-s1  (ft lb/lbm R)\") \n",
      "ylabel(\"T (R)\") \n",
      "plt.xlim((90,350))\n",
      "plt.ylim((500,3000))\n",
      "show(a)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The corrosponding value of temperature for the downstream pressure of 13.5 psia= 971.0 degree R\n",
        "The corrosponding value of change in entropy for the downstream pressure of 13.5 psia= 121.0 ft*lb/(lbm*degree R)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9++w0zLQ0eP99uPhimzQWLYKoKH2zlOr997+2iOK//mWvFwkcaokI27fbUhRp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\niIjXlERERMRrSiIiIuK1/w8VnHZxfGG+nwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.18 page no.670"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#Given\n",
      "p=60                               #psia total pressure\n",
      "T=1000                             #degree R  Temprature\n",
      "px=12                              #psia\n",
      "k=1.4                              \n",
      "R=53.3                             #ft*lb/(lbm*degree R)\n",
      "pratio=p/px\n",
      "#for this value of pratio, Max is calculated as(from fig D.4)\n",
      "Max=1.9\n",
      "#using this value of Max,  Tx/T0,x is found as\n",
      "Tratio=0.59\n",
      "#T=T0,x=T0,y\n",
      "\n",
      "#Calculation\n",
      "Tx=Tratio*T                      #degree R\n",
      "cx=(R*Tx*k)**0.5                 #ft/sec\n",
      "Vx=1.87*cx*(32.2**0.5)           #ft/sec\n",
      "\n",
      "#Result\n",
      "print \"The Mach number for the flow=\",round(Max,1)\n",
      "print \"The velocity of the flow=\",round(Vx,0),\"ft/sec\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Mach number for the flow= 1.9\n",
        "The velocity of the flow= 2227.0 ft/sec\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.19 page no.671"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "x1=0.5                             #m  exit of duct\n",
      "x2=0.3                             #m  entring of duct\n",
      "Acritical=0.1                      #m**2 area\n",
      "#at x1, Max1 is found as\n",
      "Max1=2.8\n",
      "#and px/p0,x is found as\n",
      "pratio1=0.04\n",
      "#For this value of Max, py/px is found as\n",
      "prat1=9\n",
      "pfraction1=prat1*pratio1           #where pfraction=py/p0,x = pIII/p0,x\n",
      "#at x2, Max2 is found as\n",
      "Max2=2.14\n",
      "#for this value of Max2, the following are found\n",
      "prat2=5.2\n",
      "prat22=0.66                       #where prat22=p0,y/p0,x\n",
      "May=0.56\n",
      "#for this valur of May, Ay/Acritical is found as\n",
      "Aratio=1.24\n",
      "Arat=(Acritical+(x1**2))/(Acritical+(x2**2))       #where Aratio=A2/Ay\n",
      "Afraction=Aratio*Arat           #where Afraction=A2/Acritical\n",
      "A2=Acritical+(x1**2)           #m**2\n",
      "Acritical1=A2/Afraction       #where Acritical1 critical area for the isentropic flow downstream of the shock\n",
      "#with the value of Afraction, the following are found\n",
      "Ma2=0.26\n",
      "pfraction=0.95                      #where pfraction=p2/p0,y\n",
      "#hence,\n",
      "pfrac=pfraction*prat22         #where pfrac=p2/p0,x\n",
      "\n",
      "#Result\n",
      "print \"The ratio of back pressure to inlet stagnation pressure \\n that will result in a normal shock at the exit of the duct=\",round(pfraction1,2)\n",
      "print \"The value of back pressure to inlet stagnation pressure required to position the shock at (x=0.3 m)=\",round(pfrac,2)\n",
      "\n",
      "#Plot\n",
      "s=[0,0]\n",
      "T=[288,112]\n",
      "s1=[0,360]\n",
      "T1=[288,288]\n",
      "s2=[0,280]\n",
      "T2=[112,275]\n",
      "s3=[240,320]\n",
      "T3=[275,275]\n",
      "s4=[-10,80]\n",
      "T4=[112,112]\n",
      "s5=[280,280]\n",
      "T5=[288,275]\n",
      "\n",
      "\n",
      "a=plot(s,T)\n",
      "a1=plot(s1,T1)\n",
      "a2=plot(s2,T2,linestyle='--')\n",
      "a3=plot(s3,T3)\n",
      "a4=plot(s4,T4)\n",
      "a5=plot(s5,T5)\n",
      "xlabel(\"s-s1  (J/Kg K)\") \n",
      "ylabel(\"T (K)\") \n",
      "plt.xlim((-40,500))\n",
      "plt.ylim((60,340))\n",
      "plt.text(82,112,'Tx=112K')\n",
      "plt.text(60,310,'p0x=101kpa(abs)')\n",
      "plt.text(300,315,'p0y=38kpa(abs)')\n",
      "plt.text(340,270,'py=36kpa(abs)')\n",
      "plt.text(10,275,'0,x')\n",
      "plt.text(10,110,'x')\n",
      "plt.text(300,290,'0,y')\n",
      "plt.text(280,270,'y')\n",
      "plt.text(280,375,'Ty=275K')\n",
      "plt.text(350,285,'Tox=Toy=288K')\n",
      "plt.text(40,125,'px=4kpa(abs)')\n",
      "plt.text(80,90,'shock at nozzle exit plane x=(0.5m)')\n",
      "\n",
      "show(a)\n",
      "show(a1)\n",
      "show(a2)\n",
      "show(a3)\n",
      "show(a4)\n",
      "show(a5)\n",
      "\n",
      "# For 2nd flow\n",
      "s=[0,0]\n",
      "T=[288,150]\n",
      "s1=[0,360]\n",
      "T1=[288,288]\n",
      "s2=[80,200]\n",
      "T2=[284,284]\n",
      "s3=[80,160]\n",
      "T3=[271,271]\n",
      "s4=[0,120]\n",
      "T4=(150,271)\n",
      "s5=[-10,80]\n",
      "T5=[150,150]\n",
      "s6=[120,120]\n",
      "T6=[271,284]\n",
      "s7=[120,250]\n",
      "T7=[288,320]\n",
      "s8=[120,250]\n",
      "T8=[284,300]\n",
      "\n",
      "a=plot(s,T)\n",
      "a1=plot(s1,T1)\n",
      "a2=plot(s2,T2)\n",
      "a3=plot(s3,T3)\n",
      "a4=plot(s4,T4,linestyle='--')\n",
      "a5=plot(s5,T5)\n",
      "a6=plot(s6,T6)\n",
      "a7=plot(s7,T7)\n",
      "a8=plot(s8,T8)\n",
      "\n",
      "plt.text(100,140,'Tx=150K')\n",
      "plt.text(40,310,'p0x=101 kpa(abs)')\n",
      "plt.text(250,320,'p0y=67kpa(abs)')\n",
      "plt.text(120,250,'py=52kpa(abs)')\n",
      "plt.text(10,275,'0,x')\n",
      "plt.text(10,140,'x')\n",
      "plt.text(120,290,'0,y')\n",
      "plt.text(80,270,'y')\n",
      "plt.text(160,265,'Ty=271K')\n",
      "plt.text(200,280,'T2=284K')\n",
      "plt.text(380,288,'Tox=Toy=288K')\n",
      "plt.text(40,160,'px=10kpa(abs)')\n",
      "plt.text(240,300,'p2=64kpa(abs)')\n",
      "plt.text(80,100,'shock with nozzle x=(0.3m)')\n",
      "plt.text(20,200,'normal shock')\n",
      "\n",
      "xlabel(\"s-s1  (J/Kg K)\") \n",
      "ylabel(\"T (K)\") \n",
      "plt.xlim((-40,500))\n",
      "plt.ylim((60,340))\n",
      "show(a)\n",
      "show(a1)\n",
      "show(a2)\n",
      "show(a3)\n",
      "show(a4)\n",
      "show(a5)\n",
      "show(a6)\n",
      "show(a7)\n",
      "show(a8)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The ratio of back pressure to inlet stagnation pressure \n",
        " that will result in a normal shock at the exit of the duct= 0.36\n",
        "The value of back pressure to inlet stagnation pressure required to position the shock at (x=0.3 m)= 0.63\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qKgCUWq6oqEiIMTAwEE5OTiAiPHz4EAqFAn5+fkhPT0dWVhaAOjbO/AaxWIwbN26UufzX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\ng4aGBgwPD2PTpk1LxhQWFqKzsxNXrlyB3+/Hxo0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      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NAfQFkPX3oyOAPAA7AEwCoFGFehIAtP778QrAQQCLABQC8AXwBYAWAC4CUAQg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\nphUXCsYYY1r9F/d10F9PEo61AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}