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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 2 : pipe flow of gasses and gas liquid mixtures\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "example 2.1 page no : 27"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "from scipy.optimize import fsolve\n",
      "from math import *\n",
      "\n",
      "# Initialization of Variable\n",
      "pi = 3.1428\n",
      "mmm = 16.04/1000            #molar mass of methane\n",
      "mV = 22.414/1000            #molar volume\n",
      "R = 8.314\n",
      "mu = 1.08/10**5\n",
      "r = 4.2/100                 #radius\n",
      "rr = 0.026/2/r              #relative roughness\n",
      "Pfinal = 560.*1000.\n",
      "tfinal = 273+24\n",
      "l = 68.5\n",
      "m = 2.35                    #mass flow rate\n",
      "\n",
      "#calculation\n",
      "A = pi*r**2\n",
      "A = round(A*10.**5)/10.**5\n",
      "rho = mmm/mV\n",
      "rho24 = mmm*Pfinal*273/mV/101.3/tfinal          #density at 24'C\n",
      "u = m/rho24/A\n",
      "Re = u*rho24*2*r/mu\n",
      "\n",
      "#from graph\n",
      "phi = 0.0032\n",
      "#for solving using fsolve we copy numerical value of constant terms\n",
      "#using back calculation\n",
      "#as pressure maintained should be more than Pfinal so guessed value is Pfinal\n",
      "\n",
      "def eqn(x):\n",
      "    y = m**2/A**2*log(x/Pfinal)+(Pfinal**2-x**2)/2/R/tfinal*mmm+4*phi*l/2/r*m**2/A**2\n",
      "    return y\n",
      "x = fsolve(eqn,560*10**3)\n",
      "print \"pressure maintained at compressor in (kN/m**2):\",x[0]/1000\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "pressure maintained at compressor in (kN/m**2): 960.06917347\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "example 2.2 pageno : 29"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "from math import *\n",
      "from numpy import *\n",
      "from scipy.optimize import fsolve\n",
      "\n",
      "# Initialization of Variable\n",
      "M = 28.8/1000\n",
      "mu = 1.73/10**5\n",
      "gamm = 1.402\n",
      "P1 = 107.6*10**3\n",
      "V = 22.414/1000\n",
      "R = 8.314\n",
      "temp = 285.\n",
      "d = 4./1000\n",
      "rr = 0.0008\n",
      "phi = 0.00285\n",
      "l = 68.5  \n",
      "\n",
      "#calculation\n",
      "#constant term of equation\n",
      "#part1\n",
      "\n",
      "a = 1.-8*phi*l/d            #constant term in deff\n",
      "def f(x):\n",
      "    return log(x**2)-x**2+2.938\n",
      "    \n",
      "x = fsolve(f,1)\n",
      "print x\n",
      "z = 1./x[0]\n",
      "z = round(z*1000.)/1000\n",
      "print \"ratio of Pw/P1 : %.4f\"%z\n",
      "\n",
      "#part2\n",
      "Pw = z*P1\n",
      "nuw = V*P1*temp/Pw/M/273.\n",
      "Uw = sqrt(nuw*Pw)\n",
      "print \"maximum velocity in (m/s): %.4f\"%Uw\n",
      "\n",
      "#part3\n",
      "Gw = pi*d**2/4*Pw/Uw\n",
      "print \"maximum mass flow rate in(kg/s): %.4f\"%Gw\n",
      "\n",
      "#part4\n",
      "G = 2.173/1000\n",
      "J = G*Uw**2/2\n",
      "print \"heat taken up to maintain isothermal codition(J/s): %.4f\"%J\n",
      "\n",
      "#part5\n",
      "nu2 = 2.79              #found from graph\n",
      "nu1 = R*temp/M/P1\n",
      "P2 = P1*(nu1/nu2)**gamm\n",
      "print \"crtical pressure ratio in adiabatic condition: %.4f\"%(P2/P1)\n",
      "\n",
      "#part6\n",
      "Uw = sqrt(gamm*P2*nu2)\n",
      "print \"velocity at adiabatic condition in (m/s): %.4f\"%Uw\n",
      "\n",
      "#part7\n",
      "Gw = pi*d**2/4*Uw/nu2\n",
      "print \"mass flow rate at adiabatic condition in (kg/s): %.4f\"%Gw\n",
      "\n",
      "\n",
      "#part8\n",
      "#polynomial in T of the form ax**2+bx+c = 0\n",
      "c = gamm/(gamm-1)*P1*nu1+.5*Gw**2/pi**2/d**4*16*nu1**2\n",
      "b = gamm/(gamm-1)*R/M\n",
      "a = .5*Gw**2/pi**2/d**4*16*(R/M/P2)**2\n",
      "y = poly1d([a,b,-c],False)\n",
      "T2 = roots(y)\n",
      "print \"temperature of discharging gas in (Celcius) : %.4f\"%(T2[1]-273)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 1.0268468]\n",
        "ratio of Pw/P1 : 0.9740\n",
        "maximum velocity in (m/s): 295.6723\n",
        "maximum mass flow rate in(kg/s): 0.0045\n",
        "heat taken up to maintain isothermal codition(J/s): 94.9841\n",
        "crtical pressure ratio in adiabatic condition: 0.1629\n",
        "velocity at adiabatic condition in (m/s): 261.8257\n",
        "mass flow rate at adiabatic condition in (kg/s): 0.0012\n",
        "temperature of discharging gas in (Celcius) : -46.3847"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py:227: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
        "  improvement from the last ten iterations.\n",
        "  warnings.warn(msg, RuntimeWarning)\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "example 2.3 pageno : 35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "from scipy.optimize import fsolve \n",
      "import math \n",
      "\n",
      "# Initialization of Variable\n",
      "\n",
      "#1 refer to initial condition\n",
      "R=8.314\n",
      "P1=550.*10**3\n",
      "T1=273.+350\n",
      "M=18./1000\n",
      "d=2.4/100\n",
      "pi=3.1428\n",
      "A=pi*d**2./4\n",
      "gamm=1.33\n",
      "roughness=0.096/1000/d\n",
      "l=0.85\n",
      "phi=0.0035              #assumed value of friction factor\n",
      "\n",
      "#calculation\n",
      "nu1=R*T1/M/P1\n",
      "Pw=0.4*P1              #estimation\n",
      "nuw=(P1/Pw)**0.75*nu1\n",
      "enthalpy=3167*1000.\n",
      "Gw=math.sqrt(enthalpy*A**2/(gamm*nuw**2/(gamm-1)-nu1**2/2-nuw**2/2))\n",
      "def eqn(x):\n",
      "    return math.log(x/nu1)+(gamm-1)/gamm*(enthalpy/2*(A/Gw)**2*(1/x**2-1/nu1**2)+0.25*(nu1**2/x**2-1)-.5*math.log(x/nu1))+4*phi*l/d\n",
      "\n",
      "x=fsolve(eqn,0.2)\n",
      "\n",
      "if x[0] != nuw:\n",
      "    print \"we again have to estimate Pw/P1\"\n",
      "    print \"new estimate assumed as 0.45\"\n",
      "    Pw=0.45*P1                 #new estimation\n",
      "    nuw=(P1/Pw)**0.75*nu1\n",
      "    # & we equalise nu2 to nuw\n",
      "    nu2=nuw \n",
      "    Gw=math.sqrt(enthalpy*A**2/(gamm*nuw**2/(gamm-1)-nu1**2./2-nuw**2./2))\n",
      "    print \"mass flow rate of steam through pipe kg/s): %.2f\"%(Gw) \n",
      "    #part 2\n",
      "    print \"pressure of pipe at downstream end in (kPa):\",Pw/1000\n",
      "else:\n",
      "    print \"our estimation is correct\"\n",
      "\n",
      "#part3\n",
      "enthalpyw=2888.7*1000.      #estimated from steam table\n",
      "Tw=math.sqrt((enthalpy-enthalpyw+.5*Gw**2/A**2*nu1**2)*2*A**2/Gw**2/R**2*M**2*Pw**2)\n",
      "print \"temperature of steam emerging from pipe in (Celcius): %.4f\"%(Tw-273)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "we again have to estimate Pw/P1\n",
        "new estimate assumed as 0.45\n",
        "mass flow rate of steam through pipe kg/s): 0.46\n",
        "pressure of pipe at downstream end in (kPa): 247.5\n",
        "temperature of steam emerging from pipe in (Celcius): 209.9420\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "example 2.4 pageno : 39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "import math \n",
      "\n",
      "# Initialization of Variable\n",
      "M=28.05/1000\n",
      "gamm=1.23\n",
      "R=8.314\n",
      "atm=101.3*1000\n",
      "P1=3.*atm\n",
      "\n",
      "#calculation\n",
      "P2=P1*(2./(gamm+1))**(gamm/(gamm-1))\n",
      "print \"pressure at nozzle throat (kPa): %.4f\"%(P2/1000.)\n",
      "\n",
      "#part2\n",
      "temp=273.+50\n",
      "nu1=R*temp/P1/M\n",
      "G=18.                      #mass flow rate\n",
      "nu2=nu1*(P2/P1)**(-1/gamm)\n",
      "A=G**2*nu2**2*(gamm-1)/(2*gamm*P1*nu1*(1-(P2/P1)**((gamm-1)/gamm)))\n",
      "d=math.sqrt(4*math.sqrt(A)/math.pi)\n",
      "print \"diameter required at nozzle throat in (cm) : %.4f\"%(d*100)\n",
      "#part3\n",
      "vel=math.sqrt(2*gamm*P1*nu1/(gamm-1)*(1-(P2/P1)**((gamm-1)/gamm)))\n",
      "print \"sonic velocity at throat in(m/s): %.4f\"%vel\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "pressure at nozzle throat (kPa): 169.7903\n",
        "diameter required at nozzle throat in (cm) : 18.8847\n",
        "sonic velocity at throat in(m/s): 324.9787\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "example 2.5 page no : 41"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math \n",
      "\n",
      "# Initialization of Variable\n",
      "T=273.+15\n",
      "rho=999.\n",
      "rhom=13559.         #density of mercury\n",
      "g=9.81\n",
      "P2=764.3/1000*rhom*g\n",
      "R=8.314\n",
      "M=16.04/1000\n",
      "d=4.5/1000.\n",
      "A=math.pi*d**2/4.\n",
      "G=0.75/1000         #mass flow rate\n",
      "delP=(1-math.exp(R*T*G**2./2/P2**2/M/A**2))*P2\n",
      "h=-delP/rho/g\n",
      "print \"height of manometer in (cm) %.4f\"%(h*100)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "height of manometer in (cm) 16.7941\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "example 2.6 page no : 44"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "import math \n",
      "\n",
      "# Initialization of Variable\n",
      "rhol=931.\n",
      "mu=1.55/10000               #viscosity of water\n",
      "Vsp=0.6057                  #specific volume\n",
      "T=273+133.\n",
      "mug=1.38/100000             #viscosity of steam\n",
      "P=300*1000.\n",
      "d=0.075\n",
      "Gg=0.05                     #mass flow gas phase\n",
      "Gl=1.5                      #mass flow liquid phase\n",
      "A=math.pi*d**2./4\n",
      "rho = 999.\n",
      "#calculation\n",
      "rhog=1./Vsp\n",
      "rhog=round(rhog*1000)/1000.\n",
      "velg=Gg/A/rhog\n",
      "velg=round(velg*100)/100.\n",
      "Reg=rhog*velg*d/mug\n",
      "\n",
      "#using chart\n",
      "phig=0.00245                #friction factor gas phase\n",
      "l=1\n",
      "delPg=4*phig*velg**2*rhog/d\n",
      "\n",
      "#consider liquid phase\n",
      "vell=Gl/A/rho\n",
      "Rel=rho*vell*d/mu\n",
      "if Rel>4000 and Reg>4000:\n",
      "    print \"both liquid phase and solid phase in turbulent  motion\"\n",
      "    #from chart\n",
      "\n",
      "PHIg=5.\n",
      "delP=PHIg**2.*delPg\n",
      "print \"required pressure drop per unit length in (Pa) : %.4f\"%delP\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "both liquid phase and solid phase in turbulent  motion\n",
        "required pressure drop per unit length in (Pa) : 253.8050\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}