path: root/Gas_Dynamics_and_Jet_Propulsion_by_P._Murugaperumal/ch3.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 3 : Flow through constant area duct adiabatic flow"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.1 page : 11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M1 = 0.25 \t\t\t\t#Mach number at entrance\n",
      "M2 = 1 \t\t\t\t#Mach number at exit\n",
      "D = 0.04 \t\t\t\t#inner tude diameter in m\n",
      "f = 0.002 \t\t\t\t#frictional factor\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "X1 = 8.537 \t\t\t\t#frictional consmath.tant fanno parameter at entry from gas tables @M1 = 0.25\n",
      "X2 = 0 \t\t\t\t#frictional consmath.tant fanno parameter at exit from gas tables @M2 = 1\n",
      "X = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter i.e. (4*f*L)/D\n",
      "L = (X*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the pipe is %3.3f m'%(L)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the pipe is 42.685 m\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.2 page : 11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M1 = 0.1 \t\t\t\t#Mach number at entrance\n",
      "M2 = 0.5 \t\t\t\t#Mach number at a section\n",
      "M3 = 1 \t\t\t\t#Mach number at critical condition\n",
      "D = 0.02 \t\t\t\t#Diameter of duct in m\n",
      "f = 0.004 \t\t\t\t#Frictional factor\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "X1 = 66.922 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M1 = 0.1\n",
      "X2 = 1.069 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M2 = 0.5\n",
      "X3 = 0 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M3 = 1\n",
      "X4 = X1-X3 \t\t\t\t#\t\t\t\t#frictional consmath.tant fanno parameter from M2 = 0.1 to M3 = 1\n",
      "L1 = (X4*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "X5 = X2-X3 \t\t\t\t#frictional consmath.tant fanno parameter from M2 = 0.5 to M3 = 1\n",
      "L2 = (X5*D)/(4*f) \t\t\t\t#Addition length of the pipe required to accelerate into critical condition in m\n",
      "L = L1-L2 \t\t\t\t#Length of the pipe required to accelerate the flow from M1 = 0.1 to M2 = 0.5 in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Output \n",
      "print 'A)Length of the pipe required to accelerate the flow from M1 = %3.1f to M2 = %3.1f is %3.3f m \\\n",
      "\\nB)Additional length required to accelerate into critical condition is %3.5f m'%(M1,M2,L,L2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the pipe required to accelerate the flow from M1 = 0.1 to M2 = 0.5 is 82.316 m \n",
        "B)Additional length required to accelerate into critical condition is 1.33625 m\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3 page : 12"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "D = 0.05 \t\t\t\t#inner pipe diameter in m\n",
      "Po = 10 \t\t\t\t#Stagnation Pressure at reservoir in bar\n",
      "To = 400 \t\t\t\t#Stagnation temperature at reservoir in K\n",
      "f = 0.002 \t\t\t\t#frictional factor \n",
      "M1 = 3 \t\t\t\t#Mach number at entrance\n",
      "M2 = 1 \t\t\t\t#Mach number at end of pipe\n",
      "R = 287 \t\t\t\t#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",
      "#Calculation\n",
      "X1 = 0.522 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M1 = 3\n",
      "X2 = 0 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M2 = 1\n",
      "X = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L = (X*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "p1 = 0.0272 \t\t\t\t#Pressure ratio from gas tables (M = 3,k = 1.4,isentropiC)\n",
      "P1 = p1*Po \t\t\t\t#Static pressure at entrance in bar\n",
      "t1 = 0.3571 \t\t\t\t#Temperature ratio from gas tables (M = 3,k = 1.4,isentropic)\n",
      "T1 = t1*To \t\t\t\t#Static temperature at entrance in K\n",
      "d1 = (P1*10**5)/(R*T1) \t\t\t\t#Density of air in kg/m**3, P1 in Pa\n",
      "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity in m/s\n",
      "C1 = a1*M1 \t\t\t\t#air velocity in m/s\n",
      "A1 = (math.pi*D**2)/4 \t\t\t\t#Cross sectional area of pipe in m**2\n",
      "m = d1*A1*C1 \t\t\t\t#Mass flow rate in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the pipe is %3.2f m \\\n",
      "\\nB)Mass flow rate is %3.4f kg/s'%(L,m)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the pipe is 3.26 m \n",
        "B)Mass flow rate is 0.9363 kg/s\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.4 page : 13"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "C1 = 235. \t\t\t\t#Velocity at entrance in m/s\n",
      "P1 = 13. \t\t\t\t#Static Pressure at entry in bar\n",
      "P2 = 10. \t\t\t\t#Static Pressure at a point in duct in bar\n",
      "T1 = 543. \t\t\t\t#Static temperature at entry in Kelvin\n",
      "D = 0.15 \t\t\t\t#inner duct diameter in m\n",
      "f = 0.005 \t\t\t\t#frictional factor\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#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 in m/s\n",
      "M1 = C1/a1 \t\t\t\t#Mach number at entry\n",
      "p1 = 2.138 \t\t\t\t#Static Pressure ratio from gas tables (fanno flow tables,k = 1.4,M = 0.5)\n",
      "Pt = P1/p1 \t\t\t\t#Static critical pressure in bar\n",
      "t1 = 1.143 \t\t\t\t#Static temperature ratio from gas tables (fanno flow tables,k = 1.4,M = 0.5) \n",
      "Tt = T1/t1 \t\t\t\t#Static critical temperature in K\n",
      "c1 = 0.534 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,M = 0.5)\n",
      "Ct = C1/c1 \t\t\t\t#Critical velocity in m/s\n",
      "p2 = 1.644 \t\t\t\t#Pressure ratio from gas tables (fanno flow tables,k = 1.4)\n",
      "M2 = 0.64 \t\t\t\t#Mach number from gas tables (fanno flow tables,k = 1.4,p2)\n",
      "c2 = 0.674 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,p2)\n",
      "C2 = Ct*c2 \t\t\t\t#Air velocity at P2 in m/s\n",
      "t2 = 1.109 \t\t\t\t#Temperature ratio from gas tables (fanno flow tables,k = 1.4,p2)\n",
      "T2 = t2*Tt \t\t\t\t#Satic temperature at P2 is K\n",
      "X1 = 1.06922 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M1\n",
      "X2 = 0.353 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M2\n",
      "X = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L = (X*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Temperature and velocity at section of the duct where the pressure has dropped to %3i bar \\\n",
      "\\ndue to friction are %3.1f K and %3.2f m/s \\\n",
      "\\nB)The Distance between two section is %3.3f m'%(P2,T2,C2,L)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Temperature and velocity at section of the duct where the pressure has dropped to  10 bar \n",
        "due to friction are 526.8 K and 296.61 m/s \n",
        "B)The Distance between two section is 5.372 m\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.5 page : 14"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P1 = 120. \t\t\t\t#Static pressure at entrance in bar\n",
      "T1 = 313. \t\t\t\t#Static temperature at entry in Kelvin\n",
      "M1 = 2.5 \t\t\t\t#Mach number at entrance\n",
      "M2 = 1.8 \t\t\t\t#Mach number at exit\n",
      "D = 0.2 \t\t\t\t#inner pipe diameter in m\n",
      "f = 0.01/4 \t\t\t\t#frictional factor\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#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 in m/s\n",
      "C1 = a1*M1 \t\t\t\t#air velocity in m/s\n",
      "p1 = 0.292 \t\t\t\t#Static Pressure ratio from gas tables (fanno flow tables,k = 1.4,M = 2.5)\n",
      "Pt = P1/p1 \t\t\t\t#Static critical pressure in kPa\n",
      "t1 = 0.533 \t\t\t\t#Static temperature ratio from gas tables (fanno flow tables,k = 1.4,M = 2.5)\n",
      "Tt = T1/t1 \t\t\t\t#Static critical temperature in K\n",
      "c1 = 1.826 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,M = 2.5)\n",
      "Ct = C1/c1 \t\t\t\t#Critical velocity in m/s\n",
      "X1 = 0.432 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1 = 3\n",
      "X2 = 0 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables @M2 = 1\n",
      "X3 = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L1 = (X3*D)/(4*f) \t\t\t\t#Maximum length of the pipe in m\n",
      "p2 = 0.474 \t\t\t\t#Static Pressure ratio from gas tables (fanno flow tables,k = 1.4,M = 1.8)\n",
      "P2 = Pt*p2 \t\t\t\t#Static pressure in kPa\n",
      "t2 = 0.728 \t\t\t\t#static temperature ratio from gas tables (fanno flow tables,k = 1.4,M = 1.8)\n",
      "T2 = Tt*t2 \t\t\t\t#Static temperature in K\n",
      "c2 = 1.536 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,M = 1.8)\n",
      "C2 = c2*Ct \t\t\t\t#Critical velocity in m/s\n",
      "X4 = 0.242 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M = 1.8\n",
      "X5 = X4-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L2 = (X5*D)/(4*f) \t\t\t\t#Length between sonic and oulet section\n",
      "L = L1-L2 \t\t\t\t#Length of the pipe in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Maximum length of the pipe is %3.2f m \\\n",
      "\\nB)Properties of air at sonic condition:    \\\n",
      "\\nPressure is %3i kPa    \\\n",
      "\\nTemperature is %3.2f K    \\\n",
      "\\nVelocity is %3.1f m/s \\\n",
      "\\nC)Length of the pipe is %3.1f m \\\n",
      "\\nD)Properties of air at M2 = %3.1f:    \\\n",
      "\\nPressure is %3i kPa    \\\n",
      "\\nTemperature is %3.2f K    \\\n",
      "\\nVelocity is %3.2f m/s'%(L1,Pt,Tt,Ct,L,M2,P2,T2,C2)\n",
      "\n",
      "# note : rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Maximum length of the pipe is 8.64 m \n",
        "B)Properties of air at sonic condition:    \n",
        "Pressure is 410 kPa    \n",
        "Temperature is 587.24 K    \n",
        "Velocity is 485.5 m/s \n",
        "C)Length of the pipe is 3.8 m \n",
        "D)Properties of air at M2 = 1.8:    \n",
        "Pressure is 194 kPa    \n",
        "Temperature is 427.51 K    \n",
        "Velocity is 745.77 m/s\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.6 page :  15"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M1 = 0.25 \t\t\t\t#Mach number at entrance\n",
      "ds = 0.124 \t\t\t\t#Change in entropy in kJ/kg-K\n",
      "P1 = 700. \t\t\t\t#Static pressure at entrance in bar\n",
      "T1 = 333. \t\t\t\t#Static temperature at entry in Kelvin\n",
      "D = 0.05 \t\t\t\t#inner pipe diameter in m\n",
      "f = 0.006 \t\t\t\t#frictional factor\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 0.287 \t\t\t\t#Gas consmath.tant in kJ/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p1 = math.exp(ds/R) \t\t\t\t#Ratio of Stagnation pressure at inlet to outlet \n",
      "t1 = 0.987 \t\t\t\t#Ratio of Static Temperature to Stagnation temperature at entry from gas tables @M1\n",
      "To1 = T1/t1 \t\t\t\t#Stagnation temperature at entry in K\n",
      "p2 = 0.957 \t\t\t\t#Ratio of Static pressure to Stagnation pressure at entry from gas tables @M1\n",
      "Po1 = P1/p2 \t\t\t\t#Stagnation pressure at entry in kPa\n",
      "Po2 = Po1/p1 \t\t\t\t#Stagnation pressure at exit in kPa\n",
      "a1 = math.sqrt(k*R*10**3*T1) \t\t\t\t#Sound velocity in m/s, R in J/kg\n",
      "C1 = a1*M1 \t\t\t\t#air velocity in m/s\n",
      "p3 = 4.3615 \t\t\t\t#Static Pressure ratio from gas tables (fanno flow tables,k = 1.4,M = 0.25)\n",
      "Pt = P1/p3 \t\t\t\t#Static critical pressure in kPa\n",
      "t1 = 1.185 \t\t\t\t#Static temperature ratio from gas tables (fanno flow tables,k = 1.4,M = 0.25)\n",
      "Tt = T1/t1 \t\t\t\t#Static critical temperature in K\n",
      "c1 = 0.272 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,M = 0.25)\n",
      "Ct = C1/c1 \t\t\t\t#Critical velocity in m/s\n",
      "p4 = 2.4065 \t\t\t\t#Pressure ratio at entry from gas tables @M1,k\n",
      "Pot = Po1/p4 \t\t\t\t#Stagnation pressure at critical state in kPa\n",
      "X1 = 8.537 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k\n",
      "p5 = Po2/Pot \t\t\t\t#Pressure ratio \n",
      "M2 = 0.41 \t\t\t\t#Mach number at exit from gas tables @p5\n",
      "p6 = 2.629 \t\t\t\t#Pressure ratio at exit from gas tables @p5\n",
      "P2 = Pt*p6 \t\t\t\t#Exit pressure in kPa\n",
      "t2 = 1.161 \t\t\t\t#Temperature ratio at exit from gas tables @p5\n",
      "T2 = Tt*t2 \t\t\t\t#Exit temperature in K\n",
      "c2 = 0.4415 \t\t\t\t#Velocity ratio at exit from gas tables @p5\n",
      "C2 = Ct*c2 \t\t\t\t#Exit velocity in m/s\n",
      "X2 = 2.141 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k\n",
      "X3 = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L = (X3*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Mach number at exitsection 2) is %3.2f  \\\n",
      "\\nB)Properties at exitsection 2):    \\\n",
      "\\nPressure is %3.2f kPa    \\\n",
      "\\nTemperature is %3i K    \\\n",
      "\\nVelocity is %3.3f m/s \\\n",
      "\\nC)Length of the duct is %3.3f m'%(M2,P2,T2,C2,L)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Mach number at exitsection 2) is 0.41  \n",
        "B)Properties at exitsection 2):    \n",
        "Pressure is 421.94 kPa    \n",
        "Temperature is 326 K    \n",
        "Velocity is 148.432 m/s \n",
        "C)Length of the duct is 13.325 m\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.7 page : 17"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M1 = 0.25 \t\t\t\t#Initial Mach number \n",
      "M2 = 0.75 \t\t\t\t#Final mach number \n",
      "P1 = 1.5 \t\t\t\t#Inlet pressure in bar\n",
      "T1 = 300. \t\t\t\t#Inlet temperature in K\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 0.287 \t\t\t\t#Gas consmath.tant in kJ/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "a1 = math.sqrt(k*R*10**3*T1) \t\t\t\t#Sound velocity in m/s, R in J/kg\n",
      "C1 = a1*M1 \t\t\t\t#air velocity in m/s\n",
      "p1 = 4.3615 \t\t\t\t#Pressure ratio at entry from gas tables @M1,k\n",
      "Pt = P1/p1 \t\t\t\t#Static critical pressure in kPa\n",
      "c1 = 0.272 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,M1)\n",
      "Ct = C1/c1 \t\t\t\t#Critical velocity in m/s\n",
      "p2 = 1.385 \t\t\t\t#Pressure ratio at exit from gas tables @M2,k\n",
      "P2 = Pt*p2 \t\t\t\t#Exit pressure in bar\n",
      "c2 = 0.779 \t\t\t\t#Velocity ratio at exit from gas tables @M2,k\n",
      "C2 = Ct*c2 \t\t\t\t#Exit velocity in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Final pressure and velocity are %3.4f bar and %3.2f m/s'%(P2,C2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Final pressure and velocity are 0.4763 bar and 248.58 m/s\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.8 page : 17"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "T1 = 333. \t\t\t\t#Inlet temperature in K\n",
      "D = 0.05 \t\t\t\t#inner duct diameter in m\n",
      "f = 0.005/4 \t\t\t\t#frictional factor\n",
      "L = 5. \t\t\t\t#Length of the pipe in m\n",
      "Pt = 101. \t\t\t\t#Exit pressure in kPa, Pt = P2 Since flow is choked \n",
      "M2 = 1. \t\t\t\t#Mach number at exit math.since pipe is choked \n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 0.287 \t\t\t\t#Gas consmath.tant in kJ/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "X = (4*f*L)/D \t\t\t\t#frictional consmath.tant fanno parameter \n",
      "M1 = 0.6 \t\t\t\t#Inlet mach number \n",
      "t1 = 1.119 \t\t\t\t#Temperature ratio at entry from fanno flow gas tables @M1,k\n",
      "Tt = T1/t1 \t\t\t\t#Static critical temperature in K\n",
      "at = math.sqrt(k*R*10**3*Tt) \t\t\t\t#Sound velocity in m/s, R in J/kg\n",
      "Ct = at \t\t\t\t#air velocity in m/s\n",
      "d_t = Pt/(R*Tt) \t\t\t\t#Density at exit in kg/m**3\n",
      "At = math.pi*D**2/4 \t\t\t\t#Critical area in m**2\n",
      "m = d_t*At*Ct \t\t\t\t#Mass flow rate in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Mach number at inlet is %3.1f  \\\n",
      "\\nB)Mass flow rate is %3.5f kg/s \\\n",
      "\\nC)Exit temperature is %3.3f K'%(M1,m,Tt)\n",
      "\n",
      "# note : rouding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Mach number at inlet is 0.6  \n",
        "B)Mass flow rate is 0.80291 kg/s \n",
        "C)Exit temperature is 297.587 K\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.9 page : 18"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "m = 8.25 \t\t\t\t#Mass flow rate in kg/s\n",
      "M1 = 0.15 \t\t\t\t#Mach number at entrance\n",
      "M2 = 0.5 \t\t\t\t#Mach number at exit\n",
      "P1 = 345. \t\t\t\t#Static pressure at entrance in kPa\n",
      "T1 = 38.+273 \t\t\t\t#Static temperature at entry in Kelvin\n",
      "f = 0.005 \t\t\t\t#frictional factor\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 0.287 \t\t\t\t#Gas consmath.tant in kJ/kg-K\n",
      "\n",
      "#calculation\n",
      "d1 = (P1*10**3)/(R*10**3*T1) \t\t\t\t#Density of air in kg/m**3, P1 in Pa\n",
      "a1 = math.sqrt(k*R*10**3*T1) \t\t\t\t#Sound velocity in m/s, R in J/kg\n",
      "C1 = a1*M1 \t\t\t\t#air velocity in m/s\n",
      "A1 = m/(d1*C1) \t\t\t\t#Inlet area in m**2\n",
      "D = (math.sqrt((4*A1)/(math.pi)))*10**3 \t\t\t\t#inner duct diameter in mm\n",
      "p1 = 7.3195 \t\t\t\t#Static Pressure ratio from gas tables (fanno flow tables,k = 1.4,M = 0.15)\n",
      "Pt = P1/p1 \t\t\t\t#Static critical pressure in kPa\n",
      "t1 = 1.1945 \t\t\t\t#Static temperature ratio from gas tables (fanno flow tables,k = 1.4,M = 0.15)\n",
      "Tt = T1/t1 \t\t\t\t#Static critical temperature in K\n",
      "c1 = 0.164 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,M = 0.15)\n",
      "Ct = C1/c1 \t\t\t\t#Critical velocity in m/s\n",
      "p2 = 0.984 \t\t\t\t#Pressure ratio at entry from gas tables (fanno flow tables,k = 1.4,M = 0.15)\n",
      "Po1 = P1/p2 \t\t\t\t#Stagnation pressure at entry in kPa\n",
      "p3 = 3.928 \t\t\t\t#Stagnation pressure ratio at entry from gas tables (fanno flow tables,k = 1.4,M = 0.15)\n",
      "Pot = Po1/p3 \t\t\t\t#Stagnation pressure at critical state in kPa\n",
      "X1 = 28.354 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k\n",
      "p5 = 2.138 \t\t\t\t#Pressure ratio at exit from gas tables (fanno flow tables,k = 1.4,M2)\n",
      "P2 = Pt*p5 \t\t\t\t#Exit pressure in kPa\n",
      "t2 = 1.143 \t\t\t\t#Temperature ratio at exit from gas tables (fanno flow tables,k = 1.4,M2)\n",
      "T2 = Tt*t2 \t\t\t\t#Exit temperature in K\n",
      "c2 = 0.534 \t\t\t\t#Velocity ratio at exit from gas tables (fanno flow tables,k = 1.4,M2) \n",
      "C2 = Ct*c2 \t\t\t\t#Exit velocity in m/s\n",
      "p6 = 1.34 \t\t\t\t#Stagnation pressure ratio at exit from gas tables (fanno flow tables,k = 1.4,M2)\n",
      "Po2 = Pot*p6 \t\t\t\t#Stagnation pressure at exit in kPa\n",
      "SPL = Po1-Po2 \t\t\t\t#Stagnation Pressure lose in kPa\n",
      "X2 = 1.069 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k\n",
      "X3 = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L = (X3*D*10**-3)/(4*f) \t\t\t\t#Length of the duct in m\n",
      "\n",
      "\t\t\t\t#verification\n",
      "a2 = math.sqrt(k*R*10**3*T2) \t\t\t\t#Sound velocity in m/s, R in J/kg\n",
      "M2_v = C2/a2 \t\t\t\t#air velocity in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the duct is %3.2f m \\\n",
      "\\nB)Diameter of the duct is %3i mm \\\n",
      "\\nC)Pressure and diameter at exit are %3.2f kPa, and %3i mm respectively \\\n",
      "\\nD)Stagnation Pressure lose is %3i kPa \\\n",
      "\\nE)using exit velocity %3.2f m/s, \\\n",
      "\\ntemperature %3.2f K \\\n",
      "\\nMach number is found to be %3.2f'%(L,D,P2,D,SPL,C2,T2,M2_v)\n",
      "\n",
      "# note : rouding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the duct is 308.85 m \n",
        "B)Diameter of the duct is 226 mm \n",
        "C)Pressure and diameter at exit are 100.77 kPa, and 226 mm respectively \n",
        "D)Stagnation Pressure lose is 231 kPa \n",
        "E)using exit velocity 172.65 m/s, \n",
        "temperature 297.59 K \n",
        "Mach number is found to be 0.50\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.10 page : 19"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M1 = 0.25 \t\t\t\t#Mach number at entrance\n",
      "f = 0.01/4 \t\t\t\t#frictional factor\n",
      "D = 0.15 \t\t\t\t#inner pipe diameter in m\n",
      "p1 = 0.8 \t\t\t\t#Stagnation pressure ratio at exit to entry when loss in stagnation pressure is 20%\n",
      "M3 = 0.8 \t\t\t\t#Mach number at a section\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p2 = 2.4065 \t\t\t\t#Ratio of Stagnation pressure at entry from gas tables @M1,k = 1.4\n",
      "X1 = 8.537 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1\n",
      "p3 = p1*p2 \t\t\t\t#Ratio of Stagnation pressure at exit\n",
      "M2 = 0.32 \t\t\t\t#Exit mach number at p1 = 0.8\n",
      "X2 = 4.447 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2\n",
      "L1 = (X1*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "L2 = (X2*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "L = L1-L2 \t\t\t\t#Overall length of the duct in m\n",
      "p4 = 1.038 \t\t\t\t#Stagnation pressure ratio from M = 1 to M3\n",
      "PL = (1-(p4/p2))*100 \t\t\t\t#Percentage of stagnation pressure from inlet to section at which M3 in percent\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the pipe is %3.2f m \\\n",
      "\\nB)Mach number at this exit is %3.2f \\\n",
      "\\nC)Percentage of stagnation pressure from inlet to section at which M = %3.1f is %3.2f percent \\\n",
      "\\nD)Maximum length to reach choking condition is %3.3f m'%(L,M2,M3,PL,L1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the pipe is 61.35 m \n",
        "B)Mach number at this exit is 0.32 \n",
        "C)Percentage of stagnation pressure from inlet to section at which M = 0.8 is 56.87 percent \n",
        "D)Maximum length to reach choking condition is 128.055 m\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.11 page : 20"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "D = 0.3 \t\t\t\t#inner duct diameter in m\n",
      "P1 = 10. \t\t\t\t#Static pressure at entrance in bar\n",
      "T1 = 400. \t\t\t\t#Static temperature at entry in Kelvin\n",
      "M1 = 3. \t\t\t\t#Mach number at entrance\n",
      "M2 = 1. \t\t\t\t#Mach number at exit\n",
      "k = 1.3 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Specific Gas consmath.tant in J/kg-K, wrong printing in question\n",
      "f = 0.002 \t\t\t\t#frictional factor\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p1 = 0.233 \t\t\t\t#Pressure ratio from gas tables (M = 3,k = 1.4,isentropic)\n",
      "Pt = P1/p1 \t\t\t\t#Static pressure at entrance in bar\n",
      "t1 = 0.489 \t\t\t\t#Temperature ratio from gas tables (M = 3,k = 1.4,isentropic)\n",
      "Tt = T1/t1 \t\t\t\t#Static temperature at entrance in K\n",
      "X1 = 0.628 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.3\n",
      "L1 = (X1*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "d_t = (Pt*10**5)/(R*Tt) \t\t\t\t#Density at critical state in kg/m**3, Pt in Pa\n",
      "at = math.sqrt(k*R*Tt) \t\t\t\t#Sound velocity in m/s, R in J/kg \n",
      "Ct = at \t\t\t\t#air velocity in m/s\n",
      "At = (math.pi*D**2)/4 \t\t\t\t#Critical area in m**2\n",
      "m = d_t*At*Ct \t\t\t\t#Mass flow rate in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the pipe is %3.2f m \\\n",
      "\\nB)Mass flow rate is %3.3f kg/s'%(L1,m)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the pipe is 23.55 m \n",
        "B)Mass flow rate is 713.891 kg/s\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.12 page : 21"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "M1 = 0.25 \t\t\t\t#Mach number at entrance\n",
      "f = 0.04/4 \t\t\t\t#frictional factor\n",
      "D = 0.15 \t\t\t\t#inner duct diameter in m\n",
      "p1 = 0.9 \t\t\t\t#Stagnation pressure ratio at exit to entry when loss in stagnation pressure is 10%\n",
      "ds = 190 \t\t\t\t#/Change in entropy in J/kg-K\n",
      "k = 1.3 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287 \t\t\t\t#Specific Gas consmath.tant in J/kg-K, wrong printing in question\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p2 = 2.4064 \t\t\t\t#Ratio of stagnation pressures at inlet to critical state from gas tables fanno flow tables @M1,k = 1.3\n",
      "X1 = 8.537 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.3\n",
      "p3 = p1*p2 \t\t\t\t#Ratio of stagnation pressures at exit to critical state from gas tables fanno flow tables @M1,k = 1.3\n",
      "M2 = 0.28 \t\t\t\t#Mach number at p1 = 0.9 from gas tables @p3\n",
      "X2 = 6.357 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k = 1.3\n",
      "X3 = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L1 = (X3*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "p4 = math.exp(ds/R) \t\t\t\t#Ratio of Stagnation pressure at entry to Stagnation pressure where ds = 190 \n",
      "p5 = p1/p4 \t\t\t\t#Ratio of Stagnation pressures where ds = 190 to critical state\n",
      "M3 = 0.56 \t\t\t\t#Mach number where ds = 190\n",
      "X4 = 0.674 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M3,k = 1.3\n",
      "X5 = X1-X4 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L2 = (X5*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the pipe is %3.3f m \\\n",
      "\\nB)Length of the pipe would require to rise entropy by %3i J/kg-K is %3.5f m \\\n",
      "\\nC)Mach number is %3.2f'%(L1,ds,L2,M3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the pipe is 8.175 m \n",
        "B)Length of the pipe would require to rise entropy by 190 J/kg-K is 29.48625 m \n",
        "C)Mach number is 0.56\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.13 page : 22"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "Po1 = 200. \t\t\t\t#Stagantion pressure at inlet in kPa\n",
      "To1 = 303. \t\t\t\t#Stagnation temperature at inlet in K\n",
      "M1 = 0.2 \t\t\t\t#Inlet Mach number from diagram\n",
      "D = 0.025 \t\t\t\t#inner tude diameter in m(mismath.sing data)\n",
      "M2 = 0.8 \t\t\t\t#Outlet Mach number \n",
      "f = 0.005/4 \t\t\t\t#frictional factor\n",
      "R = 287. \t\t\t\t#Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "t1 = 0.992 \t\t\t\t#Static to Stagnation temperature ratio at entry from gas tables (M1,k = 1.4,isentropic)\n",
      "T1 = To1*t1 \t\t\t\t#Static temperature in K\n",
      "p1 = 0.973 \t\t\t\t#Static to Stagnation pressure ratio at entry from gas tables (M1,k = 1.4,isentropic)\n",
      "P1 = Po1*p1 \t\t\t\t#Static pressure in kPa\n",
      "p2 = 2.964 \t\t\t\t#Stagnation pressure ratio at inlet to critical state from gas tables (M1,k = 1.4,fanno flow)\n",
      "Pot = Po1/p2 \t\t\t\t#Stagnation pressure at critical state in kPa\n",
      "X1 = 14.533 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.4\n",
      "p3 = 1.038 \t\t\t\t#Stagnation pressure ratio at outlet to critical state from gas tables (M1,k = 1.4,fanno flow)\n",
      "Po2 = Pot*p3 \t\t\t\t#Stagnation pressure at exit in kPa\n",
      "X2 = 0.073 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k = 1.4\n",
      "X3 = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L1 = (X3*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "SPL = (1-(p3/p2))*100 \t\t\t\t#Percentage decrease in stagnation pressure in percent\n",
      "ds = R*math.log(Po1/Po2) \t\t\t\t#Change of entropy in kJ/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the pipe is %3.1f m \\\n",
      "\\nB)Percentage decrease in stagnation pressure is %3.2f percent \\\n",
      "\\nC)Change of entropy is %3.3f kJ/kg-K'%(L1,SPL,ds)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the pipe is 72.3 m \n",
        "B)Percentage decrease in stagnation pressure is 64.98 percent \n",
        "C)Change of entropy is 301.133 kJ/kg-K\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.14 page : 23"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "D1 = 0.03 \t\t\t\t#Inlet duct diameter in m\n",
      "D2 = 0.015 \t\t\t\t#Throat diameter of  duct in m \n",
      "Po1 = 750. \t\t\t\t#Stagantion pressure at inlet in kPa\n",
      "To1 = 450. \t\t\t\t#Stagnation temperature at inlet in K\n",
      "f = 0.02/4 \t\t\t\t#frictional factor\n",
      "L = 0.25 \t\t\t\t#Length of the duct in m\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "ar = (D1/D2)**2 \t\t\t\t#Ratio of areas\n",
      "M1 = 2.94 \t\t\t\t#Mach number at inlet from gas tables (ar,k = 1.4,isentropic)\n",
      "p1 = 0.0298 \t\t\t\t#Static to Stagnation pressure ratio at entry from gas tables (M1,k = 1.4,isentropic)\n",
      "P1 = Po1*p1 \t\t\t\t#Static pressure at inlet in kPa\n",
      "t1 = 0.367 \t\t\t\t#Static to Stagnation temperature ratio at entry from gas tables (M1,k = 1.4,isentropic)\n",
      "T1 = To1*t1 \t\t\t\t#Static temperature at inlet in K\n",
      "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity in m/s\n",
      "C1 = a1*M1 \t\t\t\t#Air velocity at inlet in m/s\n",
      "X1 = 0.513 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.4\n",
      "p2 = 0.226 \t\t\t\t#Static to Critical pressure ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "Pt = P1/p2 \t\t\t\t#Critical pressure in kPa\n",
      "c1 = 1.949 \t\t\t\t#Static to Critical velocity ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "Ct = C1/c1 \t\t\t\t#Critical velocity in m/s\n",
      "t2 = 0.439 \t\t\t\t#Static to Critical temperature ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "Tt = T1/t2 \t\t\t\t#Critical temperature in K\n",
      "L1 = (X1*D1)/(4*f) \t\t\t\t#Length of the pipe from inlet to critical state in m\n",
      "L2 = L1-L \t\t\t\t#Length of the pipe from required point to critical state in m\n",
      "X2 = (4*f*L2)/D2 \t\t\t\t#frictional consmath.tant fanno parameter\n",
      "M2 = 2.14 \t\t\t\t#Mach number at inlet from gas tables (X2,k = 1.4,fanno flow)\n",
      "p3 = 0.369 \t\t\t\t#Static to Critical pressure ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "P2 = Pt*p3 \t\t\t\t#Exit pressure in kPa\n",
      "c2 = 1.694 \t\t\t\t#Static to Critical velocity ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "C2 = Ct*c2 \t\t\t\t#Exit velocity in m/s\n",
      "t3 = 0.623 \t\t\t\t#Static to Critical temperature ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "T2 = t3*Tt \t\t\t\t#Exit temperature in K\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Maximum length of the pipe is %3.4f m \\\n",
      "\\nB)Condition of air at exit:    \\\n",
      "\\nPressure is %3.2f kPa    \\\n",
      "\\nVelocity is %3.2f m/s    \\\n",
      "\\nTemperature is %3.2f K'%(L1,P2,C2,T2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Maximum length of the pipe is 0.7695 m \n",
        "B)Condition of air at exit:    \n",
        "Pressure is 36.49 kPa    \n",
        "Velocity is 658.25 m/s    \n",
        "Temperature is 234.37 K\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.15 page : 25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "f = 0.002 \t\t\t\t#frictional factor\n",
      "C1 = 130. \t\t\t\t#Air velocity at inlet in m/s\n",
      "T1 = 400. \t\t\t\t#Inlet temperature at inlet in K\n",
      "P1 = 250. \t\t\t\t#Inlet pressure at inlet in kPa\n",
      "D = 0.16 \t\t\t\t#Inlet duct diameter in m\n",
      "p1 = 0.8 \t\t\t\t#Stagnation pressure ratio at exit to entry when loss in stagnation pressure is 20%\n",
      "L1 = 35. \t\t\t\t#Length of duct from inlet to required section\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#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 in m/s\n",
      "M1 = C1/a1 \t\t\t\t#Mach number at inlet\n",
      "p2 = 0.9295 \t\t\t\t#Static to Stagnation pressure ratio at entry from gas tables (M1,k = 1.4,isentropic)\n",
      "Po1 = P1/p2 \t\t\t\t#Stagantion pressure at inlet in kPa\n",
      "Po2 = 0.8*Po1 \t\t\t\t#Stagantion pressure at outlet in kPa\n",
      "p3 = 1.89725 \t\t\t\t#Stagnation pressure ratio at inlet to critical state from gas tables (M1,k = 1.4,fanno flow)\n",
      "Pot = Po1/p3 \t\t\t\t#Stagnation pressure at critical state in kPa\n",
      "X1 = 4.273 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.4\n",
      "p4 = 3.33725 \t\t\t\t#Static Pressure ratio from gas tables (fanno flow tables,k = 1.4,M = 0.5)\n",
      "Pt = P1/p4 \t\t\t\t#Static critical pressure in kPa\n",
      "t1 = 1.175 \t\t\t\t#Static temperature ratio from gas tables (fanno flow tables,k = 1.4,M = 0.5) \n",
      "Tt = T1/t1 \t\t\t\t#Static critical temperature in K\n",
      "c1 = 0.347 \t\t\t\t#Velocity ratio from gas tables (fanno flow tables,k = 1.4,M = 0.5)\n",
      "Ct = C1/c1 \t\t\t\t#Critical velocity in m/s\n",
      "p5 = Po2/Pot \t\t\t\t#Pressure ratio\n",
      "M2 = 0.43 \t\t\t\t#Mach number at p1 = 0.8\n",
      "X2 = 1.833 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k = 1.4\n",
      "X3 = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L2 = (X3*D)/(4*f) \t\t\t\t#Length of the pipe in m, (from required section to critical state) \n",
      "L3 = (X1*D)/(4*f) \t\t\t\t#Length of the pipe in m, (from required inlet to critical state) \n",
      "L4 = L3-L1 \t\t\t\t#Length of the pipe in m\n",
      "X4 = (4*f*L3)/D \t\t\t\t#frictional consmath.tant fanno parameter\n",
      "M3 = 0.39 \t\t\t\t#Mach number at L1 = 35m\n",
      "p6 = 2.767 \t\t\t\t#Static to Critical pressure ratio at outlet from gas tables,fanno flow tables @M3,k = 1.4\n",
      "P2 = Pt*p6 \t\t\t\t#Exit pressure in kPa\n",
      "t2 = 1.1645 \t\t\t\t#Static to Critical temperature ratio at outlet from gas tables,fanno flow tables @M3,k = 1.4\n",
      "T2 = Tt*t2 \t\t\t\t#Exit temperature in K\n",
      "c2 = 0.42087 \t\t\t\t#Static to Critical velocity ratio at outlet from gas tables,fanno flow tables @M3,k = 1.4\n",
      "C2 = Ct*c2 \t\t\t\t#Exit velocity in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of pipe required for p = %3.1f m is %3.3f m \\\n",
      "\\nB)Properties of air at section %3i from inlet:    \\\n",
      "\\nTemperature is %3.3f K    \\\n",
      "\\nPressure is %3.2f kPa    \\\n",
      "\\nVelocity is %3.1f m/s \\\n",
      "\\nC)Maximum length of the pipe is %3.2f m'%(p1,L2,L1,T2,P2,C2,L3)\n",
      "\n",
      "# rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of pipe required for p = 0.8 m is 48.800 m \n",
        "B)Properties of air at section  35 from inlet:    \n",
        "Temperature is 396.426 K    \n",
        "Pressure is 207.28 kPa    \n",
        "Velocity is 157.7 m/s \n",
        "C)Maximum length of the pipe is 85.46 m\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.16 page : 26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "D = 0.3 \t\t\t\t#inner pipe diameter in m\n",
      "Q = 1000. \t\t\t\t#Discharge in m**3/min\n",
      "P2 = 150. \t\t\t\t#Exit pressure in kPa\n",
      "T2 = 293. \t\t\t\t#Exit temperature in K\n",
      "L1 = 50. \t\t\t\t#Length of the pipe in m\n",
      "f = 0.005 \t\t\t\t#frictional factor\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "A = math.pi*D**2/4 \t\t\t\t#Area of duct in m**2 \n",
      "C2 = Q/(A*60) \t\t\t\t#Exit air velocity in m/s\n",
      "a2 = math.sqrt(k*R*T2) \t\t\t\t#Sound velocity in m/s\n",
      "M2 = C2/a2 \t\t\t\t#Exit mach number \n",
      "p1 = 1.54 \t\t\t\t#\t\t\t\t#Static to Critical pressure ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "Pt = P2/p1 \t\t\t\t#Critical pressure in kPa\n",
      "t1 = 1.10 \t\t\t\t#Static to Critical temperature ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "Tt = T2/t1 \t\t\t\t#Critical temperature in K\n",
      "X1 = 0.228 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k = 1.4\n",
      "L2 = (X1*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "L2 = L1+L2 \t\t\t\t#Overall length of pipe from inlet to critical state in m\n",
      "X2 = (4*f*L2)/D \t\t\t\t#frictional consmath.tant fanno parameter for M1\n",
      "M1 = 0.345 \t\t\t\t#Inlet Mach number from gas tables fanno flow tables @X2,k = 1.4\n",
      "p2 = 3.14 \t\t\t\t#Static to Critical pressure ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "P1 = Pt*p2 \t\t\t\t#Static pressure at inlet in kPa\n",
      "t2 = 1.17 \t\t\t\t#Static to Critical temperature ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "T1 = Tt*t2 \t\t\t\t#Static temperature at inlet in K\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Mach number at the exit is %3.3f \\\n",
      "\\nB)Inlet pressure and temperature are %3.3f kPa and %3.2f K'%(M2,P1,T1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Mach number at the exit is 0.687 \n",
        "B)Inlet pressure and temperature are 305.844 kPa and 311.65 K\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.17 page : 27"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "D = 0.0254 \t\t\t\t#inner pipe diameter in m\n",
      "f = 0.003 \t\t\t\t#frictional factor\n",
      "M1 = 2.5 \t\t\t\t#Inlet Mach number \n",
      "To1 = 310. \t\t\t\t#Stagnation temperature at inlet in K\n",
      "P1 = 0.507 \t\t\t\t#Static pressure at inlet in kPa\n",
      "M2 = 1.2 \t\t\t\t#Exit mach number \n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "t1 = 0.4444 \t\t\t\t#Static to Stagnation temperature ratio at entry from gas tables (M1,k = 1.4,isentropic)\n",
      "T1 = To1*t1 \t\t\t\t#Static temperature at inlet in K\n",
      "p1 = 0.05853 \t\t\t\t#Static to Stagnation pressure ratio at entry from gas tables (M1,k = 1.4,isentropic)\n",
      "Po1 = P1/p1 \t\t\t\t#Stagantion pressure at inlet in kPa\n",
      "a1 = math.sqrt(k*R*T1) \t\t\t\t#Sound velocity at inlet in m/s, R in J/kg\n",
      "C1 = a1*M1 \t\t\t\t#air velocity at inlet in m/s\n",
      "c1 = 2.95804 \t\t\t\t#Static to Critical velocity ratio at inlet from gas tables,isothermal tables @M1,k = 1.4\n",
      "Ctt = C1/c1 \t\t\t\t#Critical velocity at isothermal state in m/s\n",
      "p2 = 0.33806 \t\t\t\t#Static to Critical pressure ratio at inlet from gas tables,isothermal @M1,k = 1.4\n",
      "Ptt = P1/p2 \t\t\t\t#Critical pressure at isothermal state in bar\n",
      "p3 = 3.61691 \t\t\t\t#Stagnation pressure ratio at inlet to isothermal state from gas tables,isothermal tables @M1,k = 1.4\n",
      "Pott = Po1/p3 \t\t\t\t#Critical pressure at isothermal state in K\n",
      "t2 = 1.968748 \t\t\t\t#Stagnation temperature ratio at inlet to isothermal state from gas tables,isothermal tables @M1,k = 1.4\n",
      "Tott = To1/t2 \t\t\t\t#Critical temperature at isothermal state in K\n",
      "X1 = 1.28334 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.4\n",
      "c2 = 1.4186 \t\t\t\t#Static to Critical velocity ratio at exit from gas tables,isothermal tables @M2,k = 1.4\n",
      "C2 = Ctt*c2 \t\t\t\t#Exit velocity in m/s\n",
      "p4 = 0.7043 \t\t\t\t#Static to Critical pressure ratio at inlet from gas tables,isothermal @M2,k = 1.4\n",
      "P2 = Ptt*p4 \t\t\t\t#Exit pressure in bar\n",
      "p5 = 1.07026 \t\t\t\t#Stagnation pressure ratio at inlet to isothermal state from gas tables,isothermal tables @M2,k = 1.4\n",
      "Po2 = Pott*p5 \t\t\t\t#Stagnation pressure at exit in bar \n",
      "t3 = 1.127 \t\t\t\t#Stagnation temperature ratio at inlet to isothermal state from gas tables,isothermal tables @M2,k = 1.4\n",
      "To2 = Tott*t3 \t\t\t\t#Stagnation temperature at exit in bar\n",
      "T2 = T1 \t\t\t\t#Exit temperature in K, Since isothermal flow\n",
      "X2 = 0.19715 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k = 1.4\n",
      "X3 = X1-X2 \t\t\t\t#Overall frictional consmath.tant fanno parameter\n",
      "L1 = (X3*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "d1 = (P1*10**5)/(R*T1) \t\t\t\t#Density of air in kg/m**3, P1 in Pa\n",
      "A1 = (math.pi*D**2)/4 \t\t\t\t#Cross sectional area of pipe in m**2\n",
      "m = d1*A1*C1 \t\t\t\t#Mass flow rate in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'At M = %3.1f : A)Static pressure and static temperature are %3.5f bar and %3.3f K respectively \\\n",
      "\\nB)Stagnation pressure and temperature are %3.4f bar and %3.3f K respectively \\\n",
      "\\nC)Velocity of air is %3.3f m/s \\\n",
      "\\nD)Distance of the section from innlet is %3.3f m \\\n",
      "\\nE)Mass flow rate is %3.5f kg/s'%(M2,P2,T2,Po2,To2,C2,L1,m)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "At M = 1.2 : A)Static pressure and static temperature are 1.05626 bar and 137.764 K respectively \n",
        "B)Stagnation pressure and temperature are 2.5632 bar and 177.458 K respectively \n",
        "C)Velocity of air is 282.078 m/s \n",
        "D)Distance of the section from innlet is 2.299 m \n",
        "E)Mass flow rate is 0.38217 kg/s\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.18 page : 29"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "D = 0.12 \t\t\t\t#inner duct diameter in m\n",
      "f = 0.004 \t\t\t\t#frictional factor\n",
      "M1 = 0.4 \t\t\t\t#Inlet Mach number \n",
      "P1 = 300. \t\t\t\t#Static pressure at inlet in kPa\n",
      "T1 = 310. \t\t\t\t#Static temperature at inlet in K\n",
      "M2 = 0.6 \t\t\t\t#Exit mach number\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p1 = 2.118 \t\t\t\t#Static to Critical pressure ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "Pt = P1/p1 \t\t\t\t#Critical pressure in kPa\n",
      "X1 = 1.968 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.4\n",
      "p2 = 1.408 \t\t\t\t#Static to Critical pressure ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "P2 = Pt*p2 \t\t\t\t#Exit pressure in kPa\n",
      "X2 = 0.299 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k = 1.4\n",
      "X3 = X1-X2 \t\t\t\t#Overall frictional consmath.tant fanno parameter\n",
      "L1 = (X3*D)/(4*f) \t\t\t\t#Length of the pipe in m\n",
      "T2 = T1 \t\t\t\t#Exit temperature in K, Since isothermal flow\n",
      "Ttt = T1 \t\t\t\t#Critical temperature at critical state, Since isothermal flow \n",
      "Mtt = 1/math.sqrt(k) \t\t\t\t#Limiting Mach number\n",
      "L2 = (X1*D)/(4*f) \t\t\t\t#Length of the duct required to attain limiting mach number in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Length of the duct required to chnage the mach number to %3.1f is %3.4f m \\\n",
      "\\nB)Pressure and temperature at M = %3.1f is %.f kPa and %3i K respectively \\\n",
      "\\nC)Length of the duct required to attain limiting mach number is %3.3f m \\\n",
      "\\nD)State of air at limiting mach number %3.3f is subsonic'%(M2,L1,M2,P2,T2,L2,Mtt)\n",
      "\n",
      "# rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Length of the duct required to chnage the mach number to 0.6 is 12.5175 m \n",
        "B)Pressure and temperature at M = 0.6 is 199 kPa and 310 K respectively \n",
        "C)Length of the duct required to attain limiting mach number is 14.760 m \n",
        "D)State of air at limiting mach number 0.845 is subsonic\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.19 page : 29"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from numpy import roots\n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "m = 0.32 \t\t\t\t#Mass flow rate in kg/s\n",
      "L = 140. \t\t\t\t#Length of the pipe in m\n",
      "P1 = 800. \t\t\t\t#Inlet pressure in N/m**2, wrong units in textbook\n",
      "T1 = 288. \t\t\t\t#Inlet temperature in K\n",
      "P2 = 600. \t\t\t\t#Outlet pressure in N/m**2, wrong units in textbook\n",
      "f = 0.006 \t\t\t\t#frictional factor\n",
      "R = 287. \t\t\t\t#Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "\t\t\t\t#Umath.sing Adiabatic Equation d = 1/((((((math.pi*(d/2)**2)**2)/(2*m**2*R*T))*(P1**2-P2**2))-(math.log(P1/P2)))/(2*f*L)) and converting into 5th degree polynomial of d\n",
      "a = (math.pi**2*(P1**2-P2**2))/(32*m**2*R*T1) \t\t\t\t#Coefficient of power 5\n",
      "b = math.log(P1/P2) \t\t\t\t#Coefficient of power 1\n",
      "c = 2*f*L \t\t\t\t#Coefficient of consmath.tant\n",
      "#p5 = poly([-c -b 0 0 0 a],'d','coeff') \t\t\t\t#Solving polynomial of degree 5\n",
      "d = roots([a,0,0,0,-b, -c]) \t\t\t\t#Command to find roots\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print (\"Possible values for diameter of pipe are:\") \t\t\t\t#Displays whatever within paranthesis \n",
      "print (d) \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t#To print lay roots\n",
      "print 'Therefore Diameter of the pipe is : %.1f m'%d[0].real\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Possible values for diameter of pipe are:\n",
        "[ 0.71338855+0.j          0.20228465+0.67301992j  0.20228465-0.67301992j\n",
        " -0.55897893+0.39355091j -0.55897893-0.39355091j]\n",
        "Therefore Diameter of the pipe is : 0.7 m\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.20 page: 30"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "Q = 225./60 \t\t\t\t#Discharge in m**3/s\n",
      "T2 = 293. \t\t\t\t#Exit temperature in K\n",
      "P2 = 1.25 \t\t\t\t#Exit pressure in bar\n",
      "L1 = 30. \t\t\t\t#Length of the pipe in m\n",
      "D = 0.15 \t\t\t\t#Duct diameter in m\n",
      "f = 0.02/4 \t\t\t\t#frictional factor\n",
      "k = 1.4 \t\t\t\t#Adiabatic consmath.tant\n",
      "R = 287. \t\t\t\t#Gas consmath.tant in J/kg-K\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "A = math.pi*D**2/4 \t\t\t\t#area in m**2\n",
      "C2 = Q/A \t\t\t\t#Exit air velocity in m/s\n",
      "a2 = math.sqrt(k*R*T2) \t\t\t\t#Exit sound velocity in m/s \n",
      "M2 = C2/a2 \t\t\t\t#Exit mach number \n",
      "p1 = 1.703 \t\t\t\t#Static to Critical pressure ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "Pt = P2/p1 \t\t\t\t#Critical pressure in bar\n",
      "c1 = 0.654 \t\t\t\t#Static to Critical velocity ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "Ct = C2/c1 \t\t\t\t#Critical velocity in m/s\n",
      "t1 = 1.114 \t\t\t\t#Static to Critical temperature ratio at outlet from gas tables,fanno flow tables @M2,k = 1.4\n",
      "Tt = T2/t1 \t\t\t\t#Critical temperature in K\n",
      "X1 = 0.417 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.4\n",
      "X2 = (4*f*L1)/D \t\t\t\t#frictional consmath.tant fanno parameter\n",
      "X3 = X1+X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "M1 = 0.32 \t\t\t\t#Mach number at entrance\n",
      "p2 = 3.385 \t\t\t\t#Static to Critical pressure ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "P1 = Pt*p2 \t\t\t\t#Static pressure at inlet in bar\n",
      "c2 = 0.347 \t\t\t\t#Static to Critical velocity ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "C1 = Ct*c2 \t\t\t\t#Air velocity at inlet in m/s\n",
      "t2 = 1.176 \t\t\t\t#Static to Critical temperature ratio at inlet from gas tables,fanno flow tables @M1,k = 1.4\n",
      "T1 = Tt*t2 \t\t\t\t#Static temperature at inlet in K\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'Required Inlet Condition:    \\\n",
      "\\nPressure is %3.4f bar    \\\n",
      "\\nVelocity is %3.3f m/s    \\\n",
      "\\nTemperature is %3.1f K'%(P1,C1,T1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Required Inlet Condition:    \n",
        "Pressure is 2.4846 bar    \n",
        "Velocity is 112.593 m/s    \n",
        "Temperature is 309.3 K\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.21 page : 31"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "D1 = 0.134 \t\t\t\t#Inlet duct diameter in m\n",
      "Po1 = 7 \t\t\t\t#Stagnation pressure at inlet in bar\n",
      "P1 = 0.245 \t\t\t\t#Static pressure at 5*D1 i.e. L1 in bar\n",
      "P2 = 0.5 \t\t\t\t#Static pressure at 33*D1 i.e. L2 in bar\n",
      "D2 = 0.0646 \t\t\t\t#throat diameter in m \n",
      "L1 = 5*D1 \t\t\t\t#Length of nozzle till section-1 in m\n",
      "L2 = 33*D1 \t\t\t\t#Length of nozzle till section-2 in m \n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "ar = (D1/D2)**2 \t\t\t\t#Ratio of areas\n",
      "p1 = P1/Po1 \t\t\t\t#Pressure ratio\n",
      "APR1 = p1*ar \t\t\t\t#Area Pressure ratio i.e. (A1*P1)/(At*Po1)\n",
      "M1 = 2.54 \t\t\t\t#Mach number at inlet from isentropic gas tables @APR1 \n",
      "X1 = 0.44 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M1,k = 1.4\n",
      "APR2 = 0.3073 \t\t\t\t#Area Pressure ratio i.e. (A2*P2)/(At*Po1)\n",
      "M2 = 1.54 \t\t\t\t#Exit mach number\n",
      "X2 = 0.151 \t\t\t\t#frictional consmath.tant fanno parameter from gas tables,fanno flow tables @M2,k = 1.4\n",
      "X3 = X1-X2 \t\t\t\t#overall frictional consmath.tant fanno parameter\n",
      "L3 = L2-L1 \t\t\t\t#Length of the nozzle (Section-1 to Section-2) in m \n",
      "f = (X3*D1)/(4*L3) \t\t\t\t#frictional factor\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)Mach number at %3.3f m and %3.3f m are %3.2f and %3.2f respectively \\\n",
      "\\nB)Mean value of friction between two sections is %3.5f'%(L1,L2,M1,M2,f)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)Mach number at 0.670 m and 4.422 m are 2.54 and 1.54 respectively \n",
        "B)Mean value of friction between two sections is 0.00258\n"
       ]
      }
     ],
     "prompt_number": 44
    }
   ],
   "metadata": {}
  }
 ]
}