path: root/Gas_Dynamics_and_Jet_Propulsion_by_P._Murugaperumal/ch1.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 1 : Compressible Flow-Fundamentals"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1 page : 18"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import linspace\n",
      "from matplotlib.pyplot import plot,legend,suptitle,xlabel,ylabel\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "m = 0.75 \t\t\t\t#Mass of air in kg \n",
      "T1 = 800. \t\t\t\t#Intial Temperature in K\n",
      "P1 = 400. \t\t\t\t#Initial Pressure in kPa\n",
      "P2 = 150. \t\t\t\t#Final Pressure in kPa\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 0.287 \t\t\t\t#Specific Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p1 = P2/P1 \t\t\t\t#pressure ratio of process\n",
      "T2 = T1*p1**((k-1)/k) \t\t\t\t#Final temperature in K\n",
      "W = ((m*R*(T1-T2))/(k-1)) \t\t\t\t#Workdone in kJ\n",
      "\n",
      "\t\t\t\t\n",
      "#P-V Diagram\n",
      "\n",
      "V1 = (((m*R*T1)/P1)**(1/k))*10**3 \t\t\t\t#Inlet volume in cc\n",
      "V2 = (((m*R*T2)/P2)**(1/k))*10**3 \t\t\t\t#Final volume in cc\n",
      "V = linspace(V1,V2,101)   \t\t\t\t#Representing volume on graph, adiabatic expansion\n",
      "P  =  P1*V1**k/V**k \t\t\t\t#Representing pressure on graph\n",
      "plot(V, P) \t\t\t\t\t\t\t#Plotting  \n",
      "legend('P*V**k = C') \t\t\t\t#Defining curve\n",
      "suptitle(\"PV Diagram\")\n",
      "xlabel(\"V (cc)\")\n",
      "ylabel(\"P (kPa)\") \t\t\t\t#Titles of axes\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Workdone is %3.2f kJ'%(W)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Workdone is 105.21 kJ\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g/mIEMS7FVDSKqeiCGFcQYyotV3+5DwY+BCYDtbxz9bHuqZBsoEGM4xIRkQhc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\nERERERGREvp/sG5+0yvB71cAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105fc1750>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.2 page : 18"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import linspace\n",
      "from matplotlib.pyplot import plot,legend,suptitle,xlabel,ylabel\n",
      "\n",
      "\n",
      "#Input data\n",
      "V1 = 0.35 \t\t\t\t#Volume of gas in m**3\n",
      "P1 = 110. \t\t\t\t#Initial Pressure in kPa\n",
      "T1 = 300. \t\t\t\t#Intial Temperature in K\n",
      "P2 = 600. \t\t\t\t#Final Pressure in kPa,mismath.sing data\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "Cv = 718. \t\t\t\t#Specific heat at consmath.tant volume in J/kg-K\n",
      "R = 287. \t\t\t\t#Specific Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "dQ = 0 \t\t\t\t#Heat transfer in J, Since Adiabatic process\n",
      "m = (P1*10**3*V1)/(R*T1) \t\t\t\t#Mass of air in kg \n",
      "p1 = P2/P1 \t\t\t\t#Pressure ratio\n",
      "T2 = T1*p1**((k-1)/k) \t\t\t\t#Final temperature in K\n",
      "dU = (m*Cv*(T2-T1))*10**-3 \t\t\t\t#Change in internal energy in kJ\n",
      "dW = -dU \t\t\t\t#Workdone in kJ, Since dQ = 0\n",
      "\n",
      "\t\t\t\t\n",
      "#P-V Diagram\n",
      "\n",
      "V1cc = V1*10**3 \t\t\t\t#Inlet volume in cc\n",
      "V2cc = V1cc*(T2/T1)**(1/(k-1)) \t\t\t\t#Final volume in cc\n",
      "V = linspace(V1cc,V2cc,101)   \t\t\t\t#Representing volume on graph, adiabatic expansion\n",
      "P  =  P2*V1cc**k/V**k \t\t\t\t#Representing pressure on graph\n",
      "plot(V, P) \t\t\t\t#Plotting  \n",
      "legend('P*V**k = C') \t\t\t\t#Defining curve\n",
      "suptitle(\"PV Diagram\")\n",
      "xlabel(\"V (cc)\")\n",
      "ylabel(\"P (kPa)\") \t\t\t\t#Titles of axes\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Heat transfer is %3i J \\nB)Change in internal energy is %3.3f kJ \\nC)Workdone is %3.3f kJ'%(dQ,dU,dW)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Heat transfer is   0 J \n",
        "B)Change in internal energy is 60.072 kJ \n",
        "C)Workdone is -60.072 kJ\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9ViIJb6tW2cqGHTvmbx06wBlnxE/VlpKGiIiPPvvMEsjq1fnb/v3Qvj2ce65t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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105f799d0>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.3 page : 21"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P1 = 3.2 \t\t\t\t#Initial Pressure in bar\n",
      "P2 = 1. \t\t\t\t#Final Pressure in bar\n",
      "T1 = 475. \t\t\t\t#Initial temperature in K\n",
      "Mol = 44. \t\t\t\t#Molecular weight of carbondioxide in kg/mol\n",
      "Ri = 8314. \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "k = 1.3 \t\t\t\t#Adiabatic consmath.tant\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R = Ri/Mol \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "Cp = (k*R)/(k-1) \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "Cv = Cp/k \t\t\t\t#Specific heat capacity at consmath.tant volume in J/kg-K\n",
      "p1 = P2/P1 \t\t\t\t#Pressure ratio\n",
      "T2 = T1*p1**((k-1)/k) \t\t\t\t#Final Temperature\n",
      "dh = Cp*(T1-T2)*10**-3 \t\t\t\t#Enthalpy drop in kJ/kg\n",
      "dU = Cv*(T2-T1)*10**-3 \t\t\t\t#Change in internal energy in kJ/kg, -ve sign indicates loss\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Temperature is %3.3f K \\nB)Enthalpy drop is %3.3f kJ/kg \\\n",
      "\\nC)Change in internal energy is %3.2f kJ/kg i.e. %3.2f kJ/kgloss'%(T2,dh,dU,abs(dU))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Temperature is 363.179 K \n",
        "B)Enthalpy drop is 91.560 kJ/kg \n",
        "C)Change in internal energy is -70.43 kJ/kg i.e. 70.43 kJ/kgloss\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.4 page : 25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P1 = 0.5 \t\t\t\t#Initial Pressure in bar\n",
      "T1 = 50.+273 \t\t\t\t#Intial Temperature in K\n",
      "C1 = 240. \t\t\t\t#Inlet velocity in m/s\n",
      "C2 = 120. \t\t\t\t#Outlet velocity in m/s, mismath.sing data\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "T2 = T1+((C1**2-C2**2)/(2*Cp)) \t\t\t\t#Final Temperature in K\n",
      "t1 = T2/T1 \t\t\t\t#Temperature ratio\n",
      "P2 = P1*t1**(k/(k-1)) \t\t\t\t#Final Pressure in bar\n",
      "ar = (P1*T2*C1)/(P2*T1*C2) \t\t\t\t#Ratio of outlet to inlet area\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)At outlet:    Temperature is %3.2f K    \\\n",
      "\\nPressure is %3.4f bar \\\n",
      "\\nB)Ratio of outlet to inlet area is %3.4f'%(T2,P2,ar)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)At outlet:    Temperature is 344.49 K    \n",
        "Pressure is 0.6265 bar \n",
        "B)Ratio of outlet to inlet area is 1.7025\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.5 page : 26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "m = 25. \t\t\t\t#Mass flow rate of air in kg/s\n",
      "C2 = 115. \t\t\t\t#Outlet velocity in m/s\n",
      "P1 = 100. \t\t\t\t#\t\t\t\t#Initial Pressure in kPa\n",
      "T1 = 300. \t\t\t\t#Intial Temperature in K\n",
      "C1 = 40. \t\t\t\t#Inlet velocity in m/s\n",
      "R = 0.287 \t\t\t\t#Specific gas consmath.tant in kJ/kg-K\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "T2 = T1+((C1**2-C2**2)/(2*Cp)) \t\t\t\t#Final Temperature in K\n",
      "t1 = T2/T1 \t\t\t\t#Temperature ratio\n",
      "P2 = P1*t1**(k/(k-1)) \t\t\t\t#Final Pressure in bar\n",
      "A1 = (m*R*T1)/(P1*C1) \t\t\t\t#Area at inlet in m**2\n",
      "A2 = (m*R*T2)/(P2*C2) \t\t\t\t#Area at outlet in m**2\n",
      "F = ((P1*A1)-(P2*A2))+(m*(C1-C2))*10**-3 \t\t\t\t#Axial force on mouthpiece resulting from acceleration of air in kN\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Static pressure at intake face is %3.3f kPa \\\n",
      "\\nB)Magnitude of axial force on mouthpiece resulting from acceleration of air is %3.3f kN'%(P2,F)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Static pressure at intake face is 93.414 kPa \n",
        "B)Magnitude of axial force on mouthpiece resulting from acceleration of air is 33.581 kN\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.6 page : 27"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P = 200. \t\t\t\t#Pressure in kPa\n",
      "C = 50. \t\t\t\t#Velocity of air in m/s\n",
      "d = 2.9 \t\t\t\t#Density in kg/m**3\n",
      "Mol = 32. \t\t\t\t#Molecular weight of oxygen in kg/mol\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "Ri = 8314 \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "\n",
      "#Calculation\n",
      "R = Ri/Mol \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "T = P*10**3/(R*d) \t\t\t\t#Temperature in K\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Velocity of sound in m/s \n",
      "M = C/a \t\t\t\t#Mach number \n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Mach number is %3.2f'%(M)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mach number is 0.16\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.7 page : 32"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "Pa = 1.3 \t\t\t\t#Pressure at section-A in bar\n",
      "Ta = 50.+273 \t\t\t\t#Temperature at section-A in K\n",
      "Pb = 1. \t\t\t\t#Pressure at section-B in bar\n",
      "Tb = 13.+273 \t\t\t\t#Temperature at section-B in K\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "ds = ((Cp*math.log(Tb/Ta))-(R*math.log(Pb/Pa)))*10**-3 \t\t\t\t#The change in the entropy is kJ/kg\n",
      "#+ve sign indicates A to B\n",
      "#-ve sign indicates B to A\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'The change in the entropy is %3.4f kJ/kg Since value is -ve, process must takes place from B to A'%(ds)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The change in the entropy is -0.0470 kJ/kg Since value is -ve, process must takes place from B to A\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.8 page : 34"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "V1 = 8. \t\t\t\t#Intial volume in litre\n",
      "V2 = 7.8 \t\t\t\t#Final volume in litre\n",
      "P1 = 0.7 \t\t\t\t#Intial Pressure in MPa\n",
      "P2 = 2.7 \t\t\t\t#Final Pressure in MPa\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculations\n",
      "K = (P2-P1)/(math.log(V1/V2)) \t\t\t\t#Bulk modulus of liquid in kPa\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Bulk modulus of liquid is %3.3f kPa'%(K)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Bulk modulus of liquid is 78.996 kPa\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.9 page : 35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "V1 = 0.5 \t\t\t\t#Voume of Water required to fill pressure vessel in m**3\n",
      "P = 3000. \t\t\t\t#Test pressure in bar\n",
      "dv = 0.6 \t\t\t\t#Change of empty volume of container due to pressurisation in percentage \n",
      "K = 20000. \t\t\t\t#Bulk modulus of water in MPa\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "m1 = V1*10**3 \t\t\t\t#Mass of water required to fill pressure vessel in kg\n",
      "Vr = (P*V1)/K \t\t\t\t#Reduced volume of water due to compression in m**3\n",
      "Vi = dv*V1/100 \t\t\t\t#Increased volume of container in m**3\n",
      "V = Vr+Vi \t\t\t\t#Volume of additional water required in m**3\n",
      "m = V*10**3 \t\t\t\t#Mass of additional water required in kg\n",
      "mt = m1+m \t\t\t\t#Total mass of water required in litre, Since 1kg = 1Lit\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Mass of water to be pumped into the vesel to obtain the desired pressure is %3i lit'%(mt)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mass of water to be pumped into the vesel to obtain the desired pressure is 578 lit\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.10 page : 35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "SG_oil = 0.8 \t\t\t\t#Specific gravity of crude oil \n",
      "K_oil = 153036.*10**4 \t\t\t\t#Bulk modulus of Oil in N/m**2\n",
      "K_hg = 2648700.*10**4 \t\t\t\t#Bulk modulus of Mercury in N/m**2\n",
      "d_steel = 7860. \t\t\t\t#Density of steel in kg/m**3\n",
      "E_steel = 200.*10**9 \t\t\t\t#Modulus of elasticity in Pa\n",
      "d_hg = 13600. \t\t\t\t#Density of mercury in kg/m**3\n",
      "d_water = 1000. \t\t\t\t#Density of water in kg/m**3\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "d_oil = SG_oil*d_water \t\t\t\t#Density of oil in kg/m**3\n",
      "a_oil = math.sqrt(K_oil/d_oil) \t\t\t\t#Sonic velocity of crude oil in m/s\n",
      "a_hg = math.sqrt(K_hg/d_hg) \t\t\t\t#Sonic velocity of mercury in m/s\n",
      "a_steel = math.sqrt(E_steel/d_steel) \t\t\t\t#Sonic velocity of steel in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Sonic velocity of crude oil is %3.2f m/s \\\n",
      "\\nB)Sonic velocity of mercury is %3.2f m/s \\\n",
      "\\nA)Sonic velocity of steel is %3.1f m/s'%(a_oil,a_hg,a_steel)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Sonic velocity of crude oil is 1383.09 m/s \n",
        "B)Sonic velocity of mercury is 1395.55 m/s \n",
        "A)Sonic velocity of steel is 5044.3 m/s\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.11 page : 36"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "T = 20.+273 \t\t\t\t#Temperarture of medium in K\n",
      "Cp_fr = 678. \t\t\t\t#Specific heat capacity at consmath.tant pressure of freon in J/kg-K\n",
      "Cv_fr = 543. \t\t\t\t#Specific heat capacity at consmath.tant volime of freon in J/kg-K\n",
      "T_air = 0.+273 \t\t\t\t#Temperature of air in K\n",
      "Ri = 8314. \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "mol_h = 2. \t\t\t\t#Molecular weight of Hydrogen in kg/mol\n",
      "mol_water = 18. \t\t\t\t#Molecular weight of water in kg/mol\n",
      "R_air = 287. \t\t\t\t#Specific gas consmath.tant of air in J/kg-K\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant of hydrogen\n",
      "k_water = 1.3 \t\t\t\t#Adiabatic consmath.tant of water\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R_h = Ri/mol_h \t\t\t\t#Specific gas consmath.tant of hydrogen in J/kg-K\n",
      "a_h = math.sqrt(k*R_h*T) \t\t\t\t#Velocity of sound in hydrogen in m/s\n",
      "R_water = Ri/mol_water \t\t\t\t#Specific gas consmath.tant of water in J/kg-K\n",
      "a_water = math.sqrt(k_water*R_water*T) \t\t\t\t#Velocity of sound in water vapour in m/s\n",
      "k_fr = Cp_fr/Cv_fr \t\t\t\t#Adiabatic consmath.tant of feoan\n",
      "R_fr = Cp_fr-Cv_fr \t\t\t\t#Specific gas consmath.tant of freon in J/kg-K\n",
      "a_fr = math.sqrt(k_fr*R_fr*T) \t\t\t\t#Velocity of sound in freon in m/s\n",
      "a_air = math.sqrt(k*R_air*T_air) \t\t\t\t#Sonic Velocity of air at in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Velocity of sound in hydrogen is %3.2f m/s \\\n",
      "\\nB)Velocity of sound in water vapour is %3.2f m/s \\\n",
      "\\nC)Velocity of sound in freon is %3.2f m/s \\\n",
      "\\nD)Sonic Velocity of air at %3i K is %3.4f m/s'%(a_h,a_water,a_fr,T_air,a_air)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Velocity of sound in hydrogen is 1305.83 m/s \n",
        "B)Velocity of sound in water vapour is 419.44 m/s \n",
        "C)Velocity of sound in freon is 222.24 m/s \n",
        "D)Sonic Velocity of air at 273 K is 331.1969 m/s\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.12 page : 41"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M = 0.85 \t\t\t\t#Mach number\n",
      "P = 80. \t\t\t\t#Pressure in kPa\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "Po = P*(1+(((k-1)/2)*M**2))**(k/(k-1)) \t\t\t\t#Pressure acting on the surface of the body in kPa\n",
      "\n",
      "\t\t\t\t\n",
      "#Output \n",
      "print 'The highest pressure acting on the surface of the body is %3.1f kPa'%(Po)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The highest pressure acting on the surface of the body is 128.3 kPa\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.13 page : 41"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P = 96. \t\t\t\t#Pressure in kPa\n",
      "T = 27.+273 \t\t\t\t#Temperature in K\n",
      "dP = 32. \t\t\t\t#Difference between pivot and static pressure\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "R = 287. \t\t\t\t#Specific Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "d = (P*10**3)/(R*T) \t\t\t\t#Density in kg/m**3\n",
      "Ci = math.sqrt((2*(dP*10**3))/d) \t\t\t\t#Velocity of incompressible flow in m/s\n",
      "pr = (dP)/P \t\t\t\t#Pressure ratio\n",
      "p1 = pr+1 \t\t\t\t#Stagnation to static pressure ratio\n",
      "M = math.sqrt(((p1**((k-1)/k)-1)*2)/(k-1)) \t\t\t\t#Mach number\n",
      "Cc = M*math.sqrt(k*R*T) \t\t\t\t#Velocity of compressible flow in m/s\n",
      "\n",
      "#Output\n",
      "print 'A)Air velocity in incompressible flow is %3.1f m/s \\\n",
      "\\nB)Air velocity if flow is compressible is %3.3f m/s'%(Ci,Cc)\n",
      "\n",
      "# note : rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Air velocity in incompressible flow is 239.6 m/s \n",
        "B)Air velocity if flow is compressible is 227.226 m/s\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.14 page : 42"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "T1 = 200.+273 \t\t\t\t#Intial Temperature in K\n",
      "P1 = 1.7 \t\t\t\t#Initial Pressure in bar\n",
      "P2 = 1. \t\t\t\t#Final Pressure in bar\n",
      "C1 = 30. \t\t\t\t#Inlet velocity in m/s\n",
      "m = 1. \t\t\t\t#Mass flow rate in kg/s\n",
      "D = 0.025 \t\t\t\t#Nozzle diameter in m\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "R = 287. \t\t\t\t#Specific Gas consmath.tant in J/kg-K\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p1 = P2/P1 \t\t\t\t#Pressure ratio\n",
      "T2 = T1*p1**((k-1)/k) \t\t\t\t#Final temperature in K\n",
      "E1 = T1+(C1**2/(2*Cp)) \t\t\t\t#LHS of Steady flow energy equation\n",
      "C2 = math.sqrt((E1-T2)*2*Cp) \t\t\t\t#Exit velocity of the air in m/s\n",
      "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at outlet in kg/m**3\n",
      "A2 = math.pi*D**2/4 \t\t\t\t#Area at outlet in m**2\n",
      "n = ceil(m/(d2*A2*C2)) \t\t\t\t#Number of nozzles to be used\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Exit velocity of the air is %3.2f m/s \\\n",
      "\\nB)Number of nozzles to be used are %1.0f'%(C2,n)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Exit velocity of the air is 366.94 m/s \n",
        "B)Number of nozzles to be used are 7\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.15 page : 44"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\t\n",
      "#Input data\n",
      "Po = 300. \t\t\t\t#Pressure in the vessel in kPa\n",
      "To = 50.+273 \t\t\t\t#Temperature in vessel in K\n",
      "M = 1. \t\t\t\t#Mach number \n",
      "k = 1.667 \t\t\t\t#Adiabatic consmath.tant\n",
      "Ri = 8314. \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "Mol = 4. \t\t\t\t#Molecular weight of helium in kg/mol\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R = Ri/Mol \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "Cp = (k*R)/(k-1) \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "p1 = (2/(k+1))**(k/(k-1)) \t\t\t\t#Pressure ratio\n",
      "Pt = Po*p1 \t\t\t\t#Pressure at test condition in kPa\n",
      "t1 = (2/(k+1)) \t\t\t\t#Temperature ratio \n",
      "Tt = To*t1 \t\t\t\t#Temperature at test condition in K\n",
      "at = math.sqrt(k*R*Tt) \t\t\t\t#Velocity of sound in m/s\n",
      "Ct = at \t\t\t\t#Velocity of gas at test condition in m/s\n",
      "Cmax = math.sqrt(2*Cp*To) \t\t\t\t#Maximum velocity due to expanding of gases through nozzle system in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)At test point:    \\\n",
      "\\nPressure is %3.2f kPa    \\\n",
      "\\nTemperature is %3.2f K    \\\n",
      "\\nVelocity is %3.1f m/s \\\n",
      "\\nB)Maximum velocity due to expanding of gases through nozzle system is %3.2f m/s'%(Pt,Tt,Ct,Cmax)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)At test point:    \n",
        "Pressure is 146.13 kPa    \n",
        "Temperature is 242.22 K    \n",
        "Velocity is 916.1 m/s \n",
        "B)Maximum velocity due to expanding of gases through nozzle system is 1831.88 m/s\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.16 page  :43"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "T = 40+273 \t\t\t\t#Temperature in K\n",
      "p1 = 0.5 \t\t\t\t#Static to Stagnation pressure ratio\n",
      "k = 1.67 \t\t\t\t#Adiabatic consmath.tant\n",
      "Ri = 8314 \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "Mol = 39.94 \t\t\t\t#Molecular weight of argon in kg/mol\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R = Ri/Mol \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "p2 = 1/p1 \t\t\t\t#Pressure ratio\n",
      "M = math.sqrt(((p2**((k-1)/k)-1)*2)/(k-1)) \t\t\t\t#Mach number \n",
      "C = M*math.sqrt(k*R*T) \t\t\t\t#Velocity in the flow in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output \n",
      "print 'A)Mach number is %3.3f \\\n",
      "\\nB)Velocity in the flow is %3.1f m/s'%(M,C)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Mach number is 0.978 \n",
        "B)Velocity in the flow is 322.7 m/s\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.17 page  : 46"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M = 2.5 \t\t\t\t#Mach number \n",
      "h = 10 \t\t\t\t#Height in km\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "alp = math.asin((1/M)) \t\t\t\t#Mach cone angle in degree\n",
      "d = 10/math.tan((alp)) \t\t\t\t#Distance the jet would cover before a sonic boom is heard on ground in km\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Distance the jet would cover before a sonic boom is heard on ground is %3.2f km'%(d)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Distance the jet would cover before a sonic boom is heard on ground is 22.91 km\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.18 page : 46"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "h = 1100 \t\t\t\t#Height in m\n",
      "M1 = 2.5 \t\t\t\t#Mach number of aircraft @h\n",
      "T = 280 \t\t\t\t#Temperature @h\n",
      "M2 = 0.5 \t\t\t\t#Mach number of observer\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "alp = math.sin((1/M1)) \t\t\t\t#Mach cone angle in degree\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Velocity of sound in m/s\n",
      "C1 = M1*a \t\t\t\t#Velocity of aircraft when the observer is stationary in m/s\n",
      "t1 = h/(C1*(math.tan(alp))) \t\t\t\t#Time elapsed when the observer is stationary in sec\n",
      "C2 = (M1-M2)*a \t\t\t\t#Velocity of aircraft when the observer is moving in the direction of aircraft in m/s\n",
      "t2 = h/(C2*(math.tan(alp))) \t\t\t\t#Time elapsed when the observer is moving in the direction of aircraft in sec\n",
      "C3 = (M1+M2)*a \t\t\t\t#Velocity of aircraft when the observer is moving in the opposite direction in m/s\n",
      "t3 = h/(C3*(math.tan(alp))) \t\t\t\t#Time elapsed when the observer is moving in the opposite direction in sec\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Time elapsed when the observer is stationary is %3.3f sec \\\n",
      "\\nB)Time elapsed when the observer is moving in the direction of aircraft with M = %3.1f is %3.2f sec \\\n",
      "\\nC)Time elapsed when the observer is moving in the opposite direction is %3.2f sec'%(t1,M2,t2,t3)\n",
      "\n",
      "# note : rounding off error ."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Time elapsed when the observer is stationary is 3.197 sec \n",
        "B)Time elapsed when the observer is moving in the direction of aircraft with M = 0.5 is 4.00 sec \n",
        "C)Time elapsed when the observer is moving in the opposite direction is 2.66 sec\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.19 page : 55"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P = 200. \t\t\t\t#Pressure in kPa\n",
      "d = 2.9 \t\t\t\t#Density in kg/m**3\n",
      "C = 50. \t\t\t\t#Velocity in m/s\n",
      "mol = 32. \t\t\t\t#Molecular weight of oxygen in kg/mol\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "Ri = 8314. \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R = Ri/mol \t\t\t\t#Specific gas Consmath.tant in J/kg-k\n",
      "T = (P*10**3)/(R*d) \t\t\t\t#Temperature in K\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Velocity of sound in m/s \n",
      "M = C/a \t\t\t\t#Mach number\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Mach number is %3.4f'%(M)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mach number is 0.1609\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.20 page : 55"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "C = 200 \t\t\t\t#Velocity of object in m/s\n",
      "mol = 4 \t\t\t\t#Molecular weight of helium in kg/mol\n",
      "k = 1.67 \t\t\t\t#Adiabatic consmath.tant\n",
      "Ri = 8314 \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "T = 288 \t\t\t\t#Temperature in K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R = Ri/mol \t\t\t\t#Specific gas Consmath.tant in J/kg-k\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Velocity of sound in m/s\n",
      "M = C/a \t\t\t\t#Mach number \n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Mach number is %3.1f'%(M)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mach number is 0.2\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.21 page : 56"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "Z1 = 0. \t\t\t\t#Height from sea level in m\n",
      "Z2 = 11. \t\t\t\t#Height from sea level in m\n",
      "T1 = 288. \t\t\t\t#Temperature @Z1 in K, from gas tables\n",
      "T2 = 216.5 \t\t\t\t#Temperature @Z2 in K, from gas tables\n",
      "C = 1000.*(5./18) \t\t\t\t#Velocity in m/s\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity @Z1 in m/s\n",
      "M1 = C/a1 \t\t\t\t#Mach number @Z1\n",
      "a2 = math.sqrt(k*R*T2) \t\t\t\t#Sound velocity @Z2 in m/s\n",
      "M2 = C/a2 \t\t\t\t#Mach number @Z2\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Speed of sound at:    \\\n",
      "\\nsea level is %3.2f    and altitude of %3i km is %3.2f m/s \\\n",
      "\\nB)Mach numbeer at:    sea level is %3.2f    an altitude of %3i km is %3.2f'%(a1,Z2,a2,M1,Z2,M2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Speed of sound at:    \n",
        "sea level is 340.17    and altitude of  11 km is 294.94 m/s \n",
        "B)Mach numbeer at:    sea level is 0.82    an altitude of  11 km is 0.94\n"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.22 page : 56"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "T = 300+273 \t\t\t\t#Static Temperature in K\n",
      "C = 200 \t\t\t\t#Velocity in m/s\n",
      "Cp = 1005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "To = T+(C**2/(2*Cp)) \t\t\t\t#Stagnation Temperature in K\n",
      "C_max = math.sqrt(2*Cp*To) \t\t\t\t#Maximum possible velocity obtained by air in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Maximum possible velocity obtained by air is %3.f m/s'%(C_max)\n",
      "\n",
      "# rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum possible velocity obtained by air is 1091 m/s\n"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.23 page : 57"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "dT = 37 \t\t\t\t#Temperature difference between air inside the tyre and nozzle exit\n",
      "Cp = 1005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "C = math.sqrt(2*Cp*dT) \t\t\t\t#Exit velocity of air in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Exit velocity of air is %3.1f m/s'%(C)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exit velocity of air is 272.7 m/s\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.24 page : 57"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "C = 800*(5./18) \t\t\t\t#Velocity in m/s\n",
      "Po = 105. \t\t\t\t#Stagnation pressure in kPa\n",
      "To = 35.+273 \t\t\t\t#Stagnation temperature in K\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "T = To-(C**2/(2*Cp)) \t\t\t\t#Static temperature in K\n",
      "P = Po*(T/To)**(k/(k-1)) \t\t\t\t#Static pressure in kPa\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Sound Velocity in m/s \n",
      "M = C/a \t\t\t\t#Mach number\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Static conditions:    \\\n",
      "\\nPressure is %3.2f kPa    \\\n",
      "\\nTemperature is %3.2f K    \\\n",
      "\\nSound Velocity is %3.2f m/s \\\n",
      "\\nB)Mach number is %3.2f'%(P,T,a,M)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Static conditions:    \n",
        "Pressure is 78.49 kPa    \n",
        "Temperature is 283.43 K    \n",
        "Sound Velocity is 337.47 m/s \n",
        "B)Mach number is 0.66\n"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.25 page : 57"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "C = 215 \t\t\t\t#Velocity in m/s\n",
      "T = 30+273 \t\t\t\t#Static temperature in K\n",
      "P = 5 \t\t\t\t#Static pressure in bar\n",
      "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculations\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Sound Velocity in m/s \n",
      "M = C/a \t\t\t\t#Mach number\n",
      "To = T*(1+(((k-1)/2)*M**2)) \t\t\t\t#Stagnation temperature in K\n",
      "Po = P*(To/T)**(k/(k-1)) \t\t\t\t#Stagnation pressure in kPa\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Stagnation Pressure is %3.4f bar \\\n",
      "\\nB)Mach number is %3.3f'%(Po,M)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Stagnation Pressure is 6.4599 bar \n",
        "B)Mach number is 0.616\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.26 page : 58"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "T = 400. \t\t\t\t#Static temperature in K\n",
      "k = 1.4 \t\t\t\t#Adiabatic Consmath.tant\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Sound velocity in m/s\n",
      "C = a \t\t\t\t#Velocity of jet in m/s, Since jet has sonic velocity\n",
      "To = T+(C**2/(2*Cp)) \t\t\t\t#Stagnation temperature in K\n",
      "ao = math.sqrt(k*R*To) \t\t\t\t#Sound velocity at Stagnation condition in m/s \n",
      "ho = (Cp*To)*10**-3 \t\t\t\t#Stagnation enthalpy in kJ/kg\n",
      "C_max = math.sqrt(2*Cp*To) \t\t\t\t#Maximum velocity of jet in m/s\n",
      "cr = C/C_max \t\t\t\t#Crocco number\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Velocity of sound at %3i K is %3.3f m/s \\\n",
      "\\nB)Velocity of sound at stagnation condition is %3.3f m/s \\\n",
      "\\nC)Maximum velocity of jet is %3.3f m/s \\\n",
      "\\nD)Stagnation enthalpy is %3.3f kJ/kg \\\n",
      "\\nE)Crocco number is %3.4f'%(T,C,ao,C_max,ho,cr)\n",
      "\n",
      "# rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Velocity of sound at 400 K is 400.899 m/s \n",
        "B)Velocity of sound at stagnation condition is 439.145 m/s \n",
        "C)Maximum velocity of jet is 982.202 m/s \n",
        "D)Stagnation enthalpy is 482.360 kJ/kg \n",
        "E)Crocco number is 0.4082\n"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.27 page : 59"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "C = 250. \t\t\t\t#Velocity of air in m/s \n",
      "D = 10. \t\t\t\t#Diameter in duct in cm\n",
      "T = 5.+273 \t\t\t\t#Static temperature in K\n",
      "P = 40. \t\t\t\t#Static pressure in kPa\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "To = T+(C**2/(2*Cp)) \t\t\t\t#Stagnation temperature in K\n",
      "Po = P*(To/T)**(k/(k-1)) \t\t\t\t#Stagnation pressure in kPa\n",
      "d = (P*10**3)/(R*T) \t\t\t\t#Density in kg/m**3\n",
      "A = (math.pi*D**2/4)*10**-4 \t\t\t\t#Area in m**2\n",
      "m = d*A*C \t\t\t\t#Mass flow rate in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Stagnation pressure is %3.2f kPa \\\n",
      "\\nB)Stagnation temperature is %3.2f K \\\n",
      "\\nC)Mass flow rate is %3.4f kg/s'%(Po,To,m)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Stagnation pressure is 57.97 kPa \n",
        "B)Stagnation temperature is 309.09 K \n",
        "C)Mass flow rate is 0.9844 kg/s\n"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.28 page : 59"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "C = 300. \t\t\t\t#Velocity of air in m/s \n",
      "P = 1. \t\t\t\t#Static pressure in kPa\n",
      "T = 290. \t\t\t\t#Static temperature in K\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "To = T+(C**2/(2*Cp)) \t\t\t\t#Stagnation temperature in K\n",
      "Po = P*(To/T)**(k/(k-1)) \t\t\t\t#Stagnation pressure in kPa\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Sound velocity in m/s\n",
      "Co = math.sqrt(k*R*To) \t\t\t\t#Sound velocity at Stagnation condition in m/s \n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Stagnation pressure and temperature are %3.4f bar and %3.2f K \\\n",
      "\\nB)Velocity of sound in the dynamic and stagnation conditions are %3.2f m/s and %3.2f m/s'%(Po,To,a,Co)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Stagnation pressure and temperature are 1.6529 bar and 334.78 K \n",
        "B)Velocity of sound in the dynamic and stagnation conditions are 341.35 m/s and 366.76 m/s\n"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.29 page : 60"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data \n",
      "dP = 490*(1.01325/760) \t\t\t\t#Pressure in pivot tube in bar\n",
      "P = 0.3546+1.01325 \t\t\t\t#Static pressure(absolute) in bar \n",
      "To = 25.+273 \t\t\t\t#Stagnation temperature in K\n",
      "k = 1.4 \t\t\t\t#Adiabaatic consmath.tant\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "Po = dP+P \t\t\t\t#Stagnation pressure in bar\n",
      "T = To*(P/Po)**((k-1)/k) \t\t\t\t#Static temperature\n",
      "C1 = math.sqrt(2*Cp*(To-T)) \t\t\t\t#Flow velocity for Compressible flow in m/s\n",
      "di = Po/(R*To) \t\t\t\t#Density in kg/m**3\n",
      "C2 = math.sqrt((2*dP)/di) \t\t\t\t#Flow velocity for incompressible flow in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Flow velocity for: A)Compressible flow is %3.2f m/s \\\n",
      "\\nB)Incompressible flow is %3.2f m/s'%(C1,C2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Flow velocity for: A)Compressible flow is 251.44 m/s \n",
        "B)Incompressible flow is 235.13 m/s\n"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.30 page : 61"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "To = 27.+273 \t\t\t\t#Stagnation temperature in K\n",
      "Po = 8. \t\t\t\t#Stagnation Pressure in bar\n",
      "P = 5.6 \t\t\t\t#Static pressure in bar, taken from diagram given\n",
      "m = 2. \t\t\t\t#Mass flow rate in kg/s\n",
      "k = 1.4 \t\t\t\t#Adiabaatic consmath.tant\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "T = To*(P/Po)**((k-1)/k) \t\t\t\t#Static temperature in K\n",
      "a = math.sqrt(k*R*T) \t\t\t\t#Sound velocity in m/s\n",
      "C = math.sqrt(2*Cp*(To-T)) \t\t\t\t#Velocity in m/s\n",
      "M = C/a \t\t\t\t#Mach number\n",
      "A = ((m*R*T)/(P*10**5*C))*10**4 \t\t\t\t#Area at a point in the channal in cm**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Mach number is %3.4f \\\n",
      "\\nB)Velocity is %3.1f m/s \\\n",
      "\\nC)Area at a point in the channal is %3.3f cm**2'%(M,C,A)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Mach number is 0.7326 \n",
        "B)Velocity is 241.7 m/s \n",
        "C)Area at a point in the channal is 11.489 cm**2\n"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.31 page  : 61"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "Po = 1.8 \t\t\t\t#Stagnation pressure in atm\n",
      "To = 20+273 \t\t\t\t#Stagnation temperature in K\n",
      "P = 1 \t\t\t\t#Surrounding pressure in atm\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p1 = 0.528 \t\t\t\t#Static to Stagnation pressure ratio @Mach number = 1, from gas tables\n",
      "Pt = p1*Po \t\t\t\t#Critical pressure in atm, Since Pt<P the flow is not chocked \n",
      "di = (Po*10**5)/(R*To) \t\t\t\t#Density in kg/m**3 \n",
      "ao = math.sqrt(k*R*To) \t\t\t\t#Sound velocity at Stagnation condition in m/s\n",
      "Cp = (k*R)/(k-1) \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "C = math.sqrt(2*Cp*To*(1-(P/Po)**((k-1)/k))) \t\t\t\t#Velocity of air flow which will take place from chamber to the outside through a unit area hole in m/s\n",
      "G = di*ao*math.sqrt(2/(k-1))*(P/Po)**(1/k)*math.sqrt((1-(P/Po)**((k-1)/k))) \t\t\t\t#Mass flow rate per unit area in kg/s-m**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Velocity of air flow which will take place from chamber to the outside through a unit area hole is %3.3f m/s \\\n",
      "\\nB)Mass flow rate per unit area is %3.3f kg/s-m**2'%(C,G)\n",
      "\n",
      "# note : rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Velocity of air flow which will take place from chamber to the outside through a unit area hole is 301.662 m/s \n",
        "B)Mass flow rate per unit area is 424.333 kg/s-m**2\n"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.32 page: 62"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "A1 = 465.125 \t\t\t\t#Cross sectional area at entry in cm**2\n",
      "T1 = 26.66+273 \t\t\t\t#Static temperature at section-1 in K\n",
      "P1 = 3.4473 \t\t\t\t#Static Pressure at section-1 in bar\n",
      "C1 = 152.5 \t\t\t\t#Velocity at section-1 in m/s\n",
      "P2 = 2.06838 \t\t\t\t#Static Pressure at section-2 in bar\n",
      "T2 = 277.44 \t\t\t\t#Static temperature at section-2 in K\n",
      "C2 = 260.775 \t\t\t\t#Velocity at section-2 in m/s\n",
      "Cp = 1005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287 \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculations\n",
      "To1 = T1+(C1**2/(2*Cp)) \t\t\t\t#Stagnation temperature at entry in K\n",
      "To2 = T2+(C2**2/(2*Cp)) \t\t\t\t#Stagnation temperature at exit in K\n",
      "#here To1 = To2 from answers\n",
      "d1 = (P1*10**5)/(R*T1) \t\t\t\t#Density at section-1\n",
      "d2 = (P2*10**5)/(R*T2) \t\t\t\t#Density at section-2\n",
      "ar = (d2*C2)/(d1*C1) \t\t\t\t#Ratio of inlet to outlet area\n",
      "A2 = A1/ar \t\t\t\t#Cross sectional area at exit in cm**2\n",
      "C_max = math.sqrt(2*Cp*To1) \t\t\t\t#Maximum velocity at exit in m/s\n",
      "m = d1*A1*C1*10**-4 \t\t\t\t#Mass flow rate in kg/s \n",
      "F = ((P1*10**5*A1*10**-4)-(P2*10**5*A2*10**-4))+(m*(C1-C2)) \t\t\t\t#Force acting on the duct wall between two sections in N\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Maximum velocity and stagnation temperature at exit are %3.2f m/s and %3.2f K \\\n",
      "\\nB)Since Stagnation temperature %3i K at entry and %3i K at exit are equal, the flow is adiabatic \\\n",
      "\\nC)Cross sectional area at exit is %3.2f cm**2 \\\n",
      "\\nD)Force acting on the duct wall between two sections is %3.2f N'%(C_max,To2,To1,To2,A2,F)\n",
      "\n",
      "# rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Maximum velocity and stagnation temperature at exit are 790.93 m/s and 311.27 K \n",
        "B)Since Stagnation temperature 311 K at entry and 311 K at exit are equal, the flow is adiabatic \n",
        "C)Cross sectional area at exit is 419.72 cm**2 \n",
        "D)Force acting on the duct wall between two sections is 4274.31 N\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.33 page : 63"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P1 = 250. \t\t\t\t#Static Pressure at section-1 in kPa\n",
      "T1 = 26.+273 \t\t\t\t#Static temperature at section-1 in K\n",
      "M1 = 1.4 \t\t\t\t#Mach number at entry\n",
      "M2 = 2.5 \t\t\t\t#Mach number at exit\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "C1 = math.sqrt(k*R*T1)*M1 \t\t\t\t#Air velocity at entry in m/s \n",
      "To = T1*(1+(((k-1)/2)*M1**2)) \t\t\t\t#Stagnation temperature in K\n",
      "t1 = (1+(((k-1)/2)*M2**2)) \t\t\t\t#Stagnation to exit Temperature ratio\n",
      "T2 = To/t1 \t\t\t\t#Exit temperature in K\n",
      "C2 = math.sqrt(k*R*T2)*M2 \t\t\t\t#Air velocity at exit in m/s \n",
      "P2 = P1*(T2/T1)**(k/(k-1)) \t\t\t\t#Exit static pressure in kPa\n",
      "d2 = (P2*10**3)/(R*T2) \t\t\t\t#Density at section-2 in kg/m**3\n",
      "G = d2*C2 \t\t\t\t#)Mass flow rate through the duct per square metre in kg/s-m**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)At second section:    \\\n",
      "\\nTemperature is %3.2f K    \\\n",
      "\\nPressure is %3.2f kPa    \\\n",
      "\\nVelocity is %3.4f m/s \\\n",
      "\\nB)Mass flow rate through the duct per square metre is %3.1f kg/s-m**2'%(T2,P2,C2,G)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)At second section:    \n",
        "Temperature is 184.98 K    \n",
        "Pressure is 46.56 kPa    \n",
        "Velocity is 681.5676 m/s \n",
        "B)Mass flow rate through the duct per square metre is 597.8 kg/s-m**2\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.34 page : 64"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M = 2. \t\t\t\t#Mach number\n",
      "h = 20. \t\t\t\t#Altitude in km\n",
      "Tc = -56. \t\t\t\t#Ambient temperature in degree Centigrade\n",
      "Ta = -56.+273 \t\t\t\t#Ambient temperature in K\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-k\n",
      "Cp = 1005. \t\t\t\t#Specific heat capacity at consmath.tant pressure in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "a = math.sqrt(k*R*Ta) \t\t\t\t#Sound velocity in m/s\n",
      "C = M*a \t\t\t\t#Velocity of flight in m/s\n",
      "To = Tc+(C**2/(2*Cp)) \t\t\t\t#The maximum temperature encountered is %3.1f degree Centigrade\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'The maximum temperature encountered is %3.1f degree Centigrade'%(To)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The maximum temperature encountered is 117.5 degree Centigrade\n"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.35 page : 65"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "#Input data\n",
      "W = 20000. \t\t\t\t#Power developed in kW\n",
      "m = 12. \t\t\t\t#Mass flow rate in kg/s\n",
      "C1 = 50. \t\t\t\t#Velocity of air entering in m/s\n",
      "T1 = 700.+273 \t\t\t\t#Temperature of air entering in K\n",
      "T2 = 298. \t\t\t\t#Temperature of air leaving in K\n",
      "C2 = 125. \t\t\t\t#Velocity of air leaving in m/s\n",
      "Cp = 1.005 \t\t\t\t#Specific heat capacity at consmath.tant pressure in kJ/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "dh = Cp*(T2-T1) \t\t\t\t#Change in enthalpy in kJ/kg\n",
      "Q = ((m*dh)+W-(m*(1./2000)*(C2**2-C1**2))) \t\t\t\t#The rate of heat transfer in kJ/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'The rate of heat transfer is %3.2f kJ/s'%(Q)\n",
      "\n",
      "# rounding off error. kindly check."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The rate of heat transfer is 11780.75 kJ/s\n"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.36 page : 65"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\t\n",
      "#Input data\n",
      "mol = 39.9 \t\t\t\t#Molecular weight of gas in kg/mol\n",
      "k = 1.67 \t\t\t\t#Adiabatic consmath.tant\n",
      "Po = 500. \t\t\t\t#Pressure in chamber in kPa\n",
      "To = 30.+273 \t\t\t\t#Temperature in chamber in K\n",
      "P1 = 80. \t\t\t\t#Pressure of nozzle at given section in kPa\n",
      "D = 0.012 \t\t\t\t#Cross section diameter of nozzle in m\n",
      "Ri = 8314. \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R = Ri/mol \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "p1 = Po/P1 \t\t\t\t#Stagnation to static pressure ratio\n",
      "M1 = math.sqrt((((p1**((k-1)/k))-1)*2)/(k-1)) \t\t\t\t#Mach number at section\n",
      "T1 = To*((1+(((k-1)/2)*M1**2))**(-1)) \t\t\t\t#Temperature at section in K\n",
      "a = math.sqrt(k*R*T1) \t\t\t\t#Sound Velocity in m/s\n",
      "C1 = M1*a \t\t\t\t#Gas Velocity at section in m/s\n",
      "d = (P1*10**3)/(R*T1) \t\t\t\t#Density in kg/m**3\n",
      "A1 = math.pi*D**2/4 \t\t\t\t#Cross-sectional Area \n",
      "m = d*A1*C1 \t\t\t\t#Mass flow rate through nozzle in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)At section:    \\\n",
      "\\nMach number is %3.1f    \\\n",
      "\\nTemperature is %3.1f K    \\\n",
      "\\nVelocity is %3.3f m/s \\\n",
      "\\nB)Mass flow rate through nozzle is %3.3f kg/s'%(M1,T1,C1,m)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)At section:    \n",
        "Mach number is 1.8    \n",
        "Temperature is 145.3 K    \n",
        "Velocity is 404.790 m/s \n",
        "B)Mass flow rate through nozzle is 0.121 kg/s\n"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.37 page : 66"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "mol = 4. \t\t\t\t#Molecular weight of gas in kg/mol\n",
      "k = 1.3 \t\t\t\t#Adiabatic consmath.tant\n",
      "C1 = 150. \t\t\t\t#Gas Velocity at section-1 in m/s\n",
      "P1 = 100. \t\t\t\t#Pressure of duct at section-1 in kPa\n",
      "T1 = 15.+273 \t\t\t\t#Temperature at section-1 in K\n",
      "T2 = -10.+273 \t\t\t\t#Temperature at section-2 in K\n",
      "Ri = 8314. \t\t\t\t#Ideal gas consmath.tant in J/mol-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "R = Ri/mol \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity at section-1 in m/s\n",
      "M1 = C1/a1 \t\t\t\t#Mach number at section-1 \n",
      "t1 = 0.9955 \t\t\t\t#Static to Stagnation temperature ratio at entry from gas tables @M1,k = 1.3 \n",
      "To = T1/t1 \t\t\t\t#Stagantion temperature in K\n",
      "p1 = 0.9815 \t\t\t\t#Static to Stagnation pressure ratio at entry from gas tables @M1,k = 1.3 \n",
      "Po = P1/p1 \t\t\t\t#Stagnation pressure in kPa\n",
      "t2 = T2/To \t\t\t\t#Static to Stagnation temperature ratio at exit\n",
      "M2 = 0.82 \t\t\t\t#Amch number at section-2 from gas tables @t2,k = 1.3\n",
      "p2 = 0.659 \t\t\t\t#Static to Stagnation pressure ratio at exit from gas tables @M2,k = 1.3 \n",
      "P2 = Po*p2 \t\t\t\t#Pressure at section-2 in kPa\n",
      "a2 = math.sqrt(k*R*T2) \t\t\t\t#Sound velocity at section-2 in m/s\n",
      "C2 = M2*a2 \t\t\t\t#Gas Velocity at section-2 in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'At the second point:    \\\n",
      "\\nMach number is %3.2f    \\\n",
      "\\nPressure is %3.3f kPa    \\\n",
      "\\nVelocity is %3.2f m/s'%(M2,P2,C2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "At the second point:    \n",
        "Mach number is 0.82    \n",
        "Pressure is 67.142 kPa    \n",
        "Velocity is 691.26 m/s\n"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.38 page : 67"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "#Input data\n",
      "A1 = 10. \t\t\t\t#Inlet area in cm**2\n",
      "C1 = 80. \t\t\t\t#Inlet Air velocity in m/s\n",
      "T1 = 28.+273 \t\t\t\t#Inlet temperature in K\n",
      "P1 = 700. \t\t\t\t#Inlet Pressure in kPa\n",
      "P2 = 250. \t\t\t\t#Exit pressure in kPa\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity at inlet in m/s\n",
      "M1 = C1/a1 \t\t\t\t#Mach number at inlet\n",
      "t1 = 0.989 \t\t\t\t#Static to Stagnation temperature ratio at entry from gas tables @M1,k = 1.4\n",
      "To = T1/t1 \t\t\t\t#Stagantion temperature in K\n",
      "p1 = 0.964 \t\t\t\t#Static to Stagnation pressure ratio at entry from gas tables @M1,k = 1.4 \n",
      "Po = P1/p1 \t\t\t\t#Stagnation pressure in kPa\n",
      "p2 = P2/Po \t\t\t\t#Static to Stagnation pressure ratio \n",
      "M2 = 1.335 \t\t\t\t#Mach number at exit \n",
      "t2 = 0.737 \t\t\t\t#Static to Stagnation temperature ratio at exit from gas tables @M2,k = 1.4\n",
      "T2 = To*t2 \t\t\t\t#Stagnation temperatur in K\n",
      "a2 = math.sqrt(k*R*T2) \t\t\t\t#Sound velocity at exit in m/s\n",
      "C2 = M2*a2 \t\t\t\t#Exit Air velocity in m/s\n",
      "d1 = (P1*10**3)/(R*T1) \t\t\t\t#Density at inlet in kg/m**3\n",
      "m = d1*A1*C1*10**-4 \t\t\t\t#Mass flow rate in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Mass flow rate is %3.3f kg/s \\\n",
      "\\nB)Velocity at the exit is %3.2f m/s'%(m,C2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Mass flow rate is 0.648 kg/s \n",
        "B)Velocity at the exit is 400.78 m/s\n"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.39 page : 68"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "#Input data\n",
      "V = 5. \t\t\t\t#Volume of air in m**3\n",
      "Ae = 10.*10**-4 \t\t\t\t#Exit area in cm**2\n",
      "To = 60.+273 \t\t\t\t#Temperature inside in the math.tank in K\n",
      "Po1 = 40. \t\t\t\t#Intial total pressure in bar \n",
      "Po2 = 2. \t\t\t\t#Final total pressure in bar\n",
      "P = 1. \t\t\t\t#Discharge pressure in bar\n",
      "R = 287. \t\t\t\t#Specific gas consmath.tant in J/kg-K\n",
      "\n",
      "\n",
      "#Calculation\n",
      "#Here pressure ratios P/Po1 and P/Po2 are always less than critical pressure ratio therefore flow is choked i.e. M = 1 at exit\n",
      "Gp = (0.0404184*Ae)/math.sqrt(To) \t\t\t\t#Mass flow rate by Stagnation pressure i.e. m/Po\n",
      "#Differentiating m = (P*V)/(R*To) w.r.t. time and intrgrating resulting equation we get following expression.\n",
      "t = -(V/(R*To*Gp))*math.log(Po2/Po1) \t\t\t\t#The time required for math.tank pressure to decrease from Po1 to Po2 in sec\n",
      "\n",
      "\n",
      "#Output\n",
      "print 'The time required for tank pressure to decrease from %i bar to %i bar is %3.2f sec'%(Po1,Po2,t)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The time required for tank pressure to decrease from 40 bar to 2 bar is 70.76 sec\n"
       ]
      }
     ],
     "prompt_number": 78
    }
   ],
   "metadata": {}
  }
 ]
}