path: root/Applied_Thermodynamics/Chapter13.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 13: Nozzles"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1, page no. 584"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from __future__ import division\n",
      "  \n",
      "#Variable Declaration: \n",
      "p1 = 10 #Pressure of dry steam(in bar):\n",
      "C1 = 100 #Velocity of steam entering(in m/s):\n",
      "C2 = 300 #Velocity of steam leaving the nozzle(in m/s):\n",
      "p2 = 5 #Pressure of steam at exit(in bar):\n",
      "m = 16 #Mass flow rate(in kg/s):\n",
      "q = 10 #Heat loss to surroundings(in kJ/kg):\n",
      "#From steam tables:\n",
      "h1 = 2778.1                 #kJ/kg\n",
      "hf = 640.23                 #kJ/kg\n",
      "hfg = 2108.5                #kJ/kg\n",
      "\n",
      "#Calculations:\n",
      "dh = (q*10**3+(C1**2-C2**2)/2)/1000\t#Heat drop in the nozzle(in kJ/kg):\n",
      "dQ = -dh*m #Total heat drop(in kJ/s):\n",
      "h2 = h1+dh #Enthalpy at state 2(in kJ/kg):\n",
      "x2 = (h2-hf)/hfg #Dryness fraction at state 2:\n",
      "\n",
      "#Results: \n",
      "print \"Heat drop in the nozzle: \",round(-dh,2),\"kJ/kg\" \n",
      "print \"Total heat drop: \",round(dQ,2),\"kJ/s\"\n",
      "print \"Dryness fraction at exit: \",round(x2,4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat drop in the nozzle:  30.0 kJ/kg\n",
        "Total heat drop:  480.0 kJ/s\n",
        "Dryness fraction at exit:  0.9997\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2, page no. 585"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from __future__ import division\n",
      "   \n",
      "from math import sqrt\n",
      "\n",
      "#Variable Declaration: \n",
      "p1 = 10 #Steam entering at pressure(in bar):\n",
      "p2 = 6 #Pressure at which steam leaves(in bar):\n",
      "A2 = 20 #Cross-section area of exit of nozzle(in cm**2):\n",
      "#From steam tables:\n",
      "h1 = 3478.5                 #kJ/kg \n",
      "s1 = 7.7622                 #kJ/kg.K\n",
      "T2 = 418.45                 #C(by interpolation)\n",
      "h2 = 3309.51                #kJ/kg\n",
      "v2 = 0.5281                 #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "s2 = s1\n",
      "C2 = sqrt(2*(h1-h2)*10**3) #Velocity at exit(in m/s):\n",
      "m = A2*10**(-4)*C2/v2     #Mass flow rate(in kg/s):\n",
      "\n",
      "#Result: \n",
      "print \"Mass flow rate: \",round(m,3),\"kg/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mass flow rate:  2.202 kg/s\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3, page no. 587"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from __future__ import division\n",
      "\n",
      "from math import sqrt \n",
      "\n",
      "#Variable Declaration: \n",
      "p1 = 12 #Pressure of steam entering(in bar):\n",
      "p2 = 6 #Pressure at exit(in bar):\n",
      "m1 = 5 #Mass flow rate(in kg/s):\n",
      "m2 = m1\n",
      "m3 = m1\n",
      "C3a = 500 #Exit velocity(in m/s):\n",
      "#From steam tables:\n",
      "h1 = 3045.8                 #kJ/kg \n",
      "h2 = 2900.05                #kJ/kg\n",
      "s2 = 7.0317                 #kJ/kg.K\n",
      "v2 = 0.3466                 #m**3/kg\n",
      "h3 = 2882.55                #kJ/kg\n",
      "v3 = 0.3647                 #m**3/kg\n",
      "n = 1.3     #For superheated steam:\n",
      "\n",
      "#Calculations:\n",
      "s1 = s2\n",
      "s3 = s2\n",
      "p2 = p1*(2/(n+1))**(n/(n-1)) #Pressue at state 2(in bar):\n",
      "C2 = sqrt(2*(h1-h2)*10**3) #Velocity at throat(in m/s):\n",
      "A2 = m2*v2/C2 #Cross-sectional area at throat(in m**2):\n",
      "C3 = sqrt(2*(h1-h3)*10**3) #Ideal velocity at exit(in m/s):\n",
      "A3 = m3*v3/C3a #Cross-sectional area at exit(in m**2):    \n",
      "r = C3a/C3  #Coefficient of velocity:\n",
      "\n",
      "#Results: \n",
      "print \"Cross-sectional area at throat: \",round(A2*10**3,3),\" x 10^-3 m^2\"\n",
      "print \"Cross-sectional area at exit: \",round(A3*10**3,3),\" x 10^-3 m^2\"\n",
      "print \"Coefficient of velocity: \",round(r,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Cross-sectional area at throat:  3.21  x 10^-3 m^2\n",
        "Cross-sectional area at exit:  3.647  x 10^-3 m^2\n",
        "Coefficient of velocity:  0.875\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4, page no. 588"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from __future__ import division\n",
      "\n",
      "from math import sqrt\n",
      "\n",
      "#Variable Declaration: \n",
      "p1 = 16 #Pressure of steam entering(in bar):\n",
      "p3 = 5 #Pressure at exit(in bar):\n",
      "m1 = 1 #Mass flow rate(in kg/s):\n",
      "m2 = m1\n",
      "m3 = m1\n",
      "#From steam tables:\n",
      "#For case 1:\n",
      "h1 = 3034.8                 #kJ/kg\n",
      "s1 = 6.8844                 #kJ/kg.K\n",
      "v1 = 0.15862                #m**3/kg\n",
      "n = 1.3\n",
      "h2 = 2891.39                #kJ/kg\n",
      "h3 = 2777                   #kJ/kg\n",
      "v2 = 0.2559                 #m**3/kg\n",
      "v3 = 0.3882                 #m**3/kg\n",
      "#For case 2:\n",
      "h2a = 2905.73               #kJ/kg\n",
      "v2a = 0.2598                #m**3/kg\n",
      "v3a = 0.40023               #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "p2 = p1*(2/(n+1))**(n/(n-1)) #Pressure at the throat of nozzle(in bar):\n",
      "q12 = h1-h2 #Heat drop up to throat section(in kJ/kg):\n",
      "C2 = sqrt(2*(h1-h2)*10**3) #Velocity at throat(in m/s):\n",
      "q23 = h2-h3 #Heat drop from exit(in kJ/kg):\n",
      "C3 = sqrt(2*(h2-h3)*10**3+C2**2) #Velocity at exit(in m/s):\n",
      "A2 = m2*v2/C2 #Throat area(in m**2):\n",
      "A3 = m3*v3/C3 #Exit area(in m**2):\n",
      "q12a = 0.9*q12 #Considering expansion to have 10% friction loss:\n",
      "C2a = sqrt(2*q12a*10**3) #Actual velocity at throat(in m/s):\n",
      "A2a = m2*v2a/C2a #Actual throat area(in m**2):\n",
      "q23a = 0.9*q23 #Actual drop at the exit of the nozzle(in kJ/kg):\n",
      "h3a = h2a-q23a #Actual enthalpy at state 3(in kJ/kg):\n",
      "C3a = sqrt(2*q23a*10**3+C2a**2) #Actual velocity at exit(in m/s):\n",
      "A3a = m3*v3a/C3a #Actual area at exit(in m**2):\n",
      "\n",
      "#Results:\n",
      "print \"Throat area, without friction consideration: \",round(A2*10**4,2),\"cm**2\"\n",
      "print \"Exit area, without friction consideration: \",round(A3*10**4,2),\"cm**2\"\n",
      "print \"Throat area, with friction consideration: \",round(A2a*10**4,2),\"cm**2\"\n",
      "print \"Exit area, with friction consideration: \",round(A3a*10**4,3),\"cm**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Throat area, without friction consideration:  4.78 cm**2\n",
        "Exit area, without friction consideration:  5.41 cm**2\n",
        "Throat area, with friction consideration:  5.11 cm**2\n",
        "Exit area, with friction consideration:  5.875 cm**2\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5, page no. 590"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from __future__ import division\n",
      " \n",
      "from math import sqrt,pi\n",
      "#Variable Declaration: \n",
      "P = 1 #Power of turbine(in MW):\n",
      "p1 = 20 #Pressure of steam entering(in bar):\n",
      "m = 8 #Steam consumption rate(in kg/kW.h):\n",
      "p3 = 0.2 #Pressure at which steam leaves(in bar):\n",
      "d = 0.01 #Throat diameter(in m):\n",
      "#From Mollier diagram:\n",
      "q12 = 142              #kJ/kg \n",
      "v2 = 0.20              #m**3/kg\n",
      "q13 = 807              #kJ/kg\n",
      "v3 = 7.2               #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "C2 = sqrt(2*q12*10**3) #Velocity at throat(in m/s):\n",
      "m2 = pi*d**2/4*C2/v2 #Mass flow rate:\n",
      "m3 = m2\n",
      "n = 10**3*m/(3600*m2) #Number of nozzles:\n",
      "q13a = 0.90*q13 #Useful heat drop:\n",
      "C3 = sqrt(2*10**3*q13a)#Velocity at exit(in m/s):\n",
      "A3 = m3*v3/C3 #Area at exit(in m**2):\n",
      "\n",
      "#Results: \n",
      "print \"Number of nozzles required: \",round(n) \n",
      "print \"Area at exit: \",round(A3*10**4,2),\"cm**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Number of nozzles required:  11.0\n",
        "Area at exit:  12.5 cm**2\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6, page no. 591"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "from math import pi, atan, sqrt\n",
      "#Variable Declaration: \n",
      "p1 = 0.7 #Pressure at which steam is supplied(in MPa):\n",
      "l = 0.06 #Length of diverging nozzle(in m):\n",
      "d = 0.005 #Throat diameter(in mm):\n",
      "p3 = 0.1 #Pressure at which steam leaves the nozzle(in MPa):\n",
      "#From Mollier diagram:\n",
      "q12 = 138                   #kJ/kg\n",
      "v2 = 0.58                   #m**3/kg\n",
      "T = 203                     #\u00b0C\n",
      "q23 = 247                   #kJ/kg\n",
      "q23a = 209.95               #kJ/kg\n",
      "v3a = 1.7                   #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "C2 = sqrt(2*q12*10**3) #Velocity at throat(in m/s):\n",
      "m1 = pi*d**2/4*C2/v2   #Mass flow rate(in kg/s):\n",
      "m2 = m1\n",
      "m3 = m1\n",
      "q = q12+q23a   #Total heat drop(in kJ/kg):\n",
      "C3 = sqrt(2*10**3*q) #Velocity at exit(in m/s):\n",
      "A3 = m3*v3a/C3 #Area at exit(in m**2):\n",
      "d1 = (sqrt(A3*4/pi))*10**3 #Diameter at exit(in mm):\n",
      "a = atan((d1-d*10**3)/(2*60))*180/pi\n",
      "\n",
      "#Results: \n",
      "print \"With no losses, temperature at throat: \",round(T,2),\"\u00b0C\"\n",
      "print \"Velocity at throat: \",round(C2,2),\"m/s\"\n",
      "print \"With losses, cone angle: \",round(2*a,2),\"\u00b0\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "With no losses, temperature at throat:  203.0 \u00b0C\n",
        "Velocity at throat:  525.36 m/s\n",
        "With losses, cone angle:  1.71 \u00b0\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7, page no. 593"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "from math import sin,pi,sqrt\n",
      "\n",
      "#Variable Declaration:\n",
      "P = 5000 #Power of the turbine(in hp):\n",
      "m = P*6/3600 #Steam required(in kg of steam/hp-hr):\n",
      "n = 0.90 #Efficiency of nozzle:\n",
      "a = 12 #Nozzle angle:\n",
      "p = 5 #Pitch(in cm):\n",
      "t = 0.3 #Thickness(in cm):\n",
      "#From steam tables:\n",
      "h1 = 2794                   #kJ/kg\n",
      "s1 = 6.4218                 #kJ/kg.K\n",
      "x2 = 0.9478\n",
      "h2 = 2662.2                 #kJ/kg\n",
      "x2a = 0.9542\n",
      "v2a = 0.2294                #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "s2 = s1\n",
      "h12 = h1-h2 #Change in enthalpy(in kJ/kg):\n",
      "h12a = n*h12 #Actual change(in kJ/kg):\n",
      "C2 = sqrt(2*h12a*10**3) #Velocity at inlet(in m/s):\n",
      "A2 = m*v2a/C2*10**4 #Area at exit of nozzle(in cm**2):\n",
      "l = 60*pi/3  #Approximate length of the nozzle(in cm):\n",
      "n = int(l/p)+1 #Number of nozzles:\n",
      "l1 = n*p #Correct length of nozzle arc:\n",
      "h = A2/((p*sin(a*pi/180)-t)*n)#Radial height of nozzle(in cm):\n",
      "\n",
      "#Results:\n",
      "print \"Length of nozzle: \",round(l1,2),\"cm\"\n",
      "print \"Radial height of nozzle: \",round(h,2),\"cm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Length of nozzle:  65.0 cm\n",
        "Radial height of nozzle:  4.08 cm\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8, page no. 594"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "from math import sqrt\n",
      "\n",
      "#Variable Declaration: \n",
      "p1 = 13 #Pressure at which steam enters(in bar):\n",
      "p2 = 6 #Pressure at which steam leaves(in bar):\n",
      "T1 = 150+273 #Temperature of steam entering(in K):\n",
      "r = 1.4 #Adibatic insex of compression:\n",
      "\n",
      "#Calculations:\n",
      "T2 = T1*(p2/p1)**((r-1)/r) #Final temperature of steam(in K):\n",
      "C2 = sqrt(2*1.005*(T1-T2)) #Exit velocity(in m/s):\n",
      "\n",
      "#Results: \n",
      "print \"Exit velocity: \",round(C2,2),\"m/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exit velocity:  12.98 m/s\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9, page no. 595"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "from math import sqrt\n",
      "\n",
      "#Variable Declaration: \n",
      "F = 350 #Force on the plate(in N):\n",
      "p1 = 8 #Initial pressure(in bar):\n",
      "p3 = 1 #Final pressure(in bar):\n",
      "A2 = 5*10**(-4) #Throat cross-sectional area(in m**2):\n",
      "#From steam tables:\n",
      "h1 = 2769.1                 #kJ/kg\n",
      "s1 = 6.6628                 #kJ/kg.K\n",
      "x2 = 0.9717\n",
      "h2 = 2685.17                #kJ/kg\n",
      "v2 = 0.3932                 #m**3/kg\n",
      "x3 = 0.8238\n",
      "h3 = 2277.6                 #kJ/kg\n",
      "\n",
      "#Calculations:\n",
      "s2 = s1\n",
      "s3 = s1\n",
      "h12 = h1-h2 #Enthalpy change(in kJ/kg):\n",
      "C2 = sqrt(2*h12*10**3) #Velocity at throat(in m/s):\n",
      "m = A2*C2/v2 #Discharge at throat(in kg/s):\n",
      "C3a = F/m #Actual exit velocity(in m/s):\n",
      "h23 = h2-h3 #Theoretical enthalpy drop(in kJ/kg):\n",
      "n = C3a**2/(2*h23*10**3) #Nozzle efficiency:\n",
      "\n",
      "#Results:\n",
      "print \"Discharge at throat: \",round(m,3),\"kg/s\"\n",
      "print \"Nozzle efficiency: \",round(n*100,2),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Discharge at throat:  0.521 kg/s\n",
        "Nozzle efficiency:  55.37 %\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10, page no. 597"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "   \n",
      "from math import sqrt,pi\n",
      "\n",
      "#Variable Declaration: \n",
      "m = 5/60 #Mass flow rate(in kg/s):\n",
      "p3 = 1 #Pressure at which steam is discharged(in bar):\n",
      "p1 = 10 #Initial pressure(in bar):\n",
      "T1 = 200+273 #Initial temperature(in K)\n",
      "n = 1.3 #Adiabatic index of compression:\n",
      "\n",
      "#From steam tables:\n",
      "h1 = 2827.9                 #kJ/kg\n",
      "s1 = 6.6940                 #kJ/kg.K\n",
      "v1 = 0.2060                 #m**3/kg\n",
      "h2a = 2711.23               #kJ/kg\n",
      "s2a = 6.6749                #kJ/kg.K\n",
      "h3 = 2420.08                #kJ/kg\n",
      "v3 = 1.5025                 #m**3/kg\n",
      "psat = 3.44                 #bar (at T = 138.18 \u00b0C)\n",
      "Tsat = 155.12               #C (at p = 5.45 bar)\n",
      "\n",
      "#Calculations:\n",
      "s3 = s2a\n",
      "p2 = p1*(2/(n+1))**(n/(n-1)) #Pressure at throat(in bar):\n",
      "C3 = sqrt(2*(h1-h3)*10**3) #Velocity at exit(in m/s):\n",
      "A3 = m*v3/C3 #Exit area(in m**2):\n",
      "d = sqrt(A3*4/pi) #Diameter of nozzle at exit(in m):\n",
      "T2 = T1*(p2/p1)**((n-1)/n) #Temperature at throat(in K):\n",
      "d1 = p2/psat #Degree of supersaturation:\n",
      "u = Tsat-(T2-273) #Amount of undercooling(in \u00b0C):\n",
      "\n",
      "#Results: \n",
      "print \"Degree of supersaturation: \",round(d1,2) \n",
      "print \"Amount of undercooling: \",round(u,2),\"\u00b0C\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Degree of supersaturation:  1.59\n",
        "Amount of undercooling:  16.82 \u00b0C\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11, page no. 599"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "\n",
      "#Variable Declaration: \n",
      "p1 = 4 #Initial pressure(in bar):\n",
      "T1 = 180+273 #Initial temperature(in K):\n",
      "p2 = 1.5 #Final pressure(in bar):\n",
      "n = 1.3 #Index of compression:\n",
      "nn = 0.95 #Efficiency due to heat loss:\n",
      "C = 2.174 #Specific heat(in kJ/kg.K):\n",
      "#From steam tables:\n",
      "v1 = 0.5088                 #m**3/kg \n",
      "Tsat = 111.37+273           #K (at p = 1.5 bar)\n",
      "\n",
      "#Calculations:\n",
      "h1 = p1*v1*10**2+2614      #Enthalpy at state 1(in kJ/kg):\n",
      "v2 = v1*(p1/p2)**(1/n) #Specific volume at state 2(in m**3/kg):\n",
      "h2 = p2*v2*10**2+2614 #Enthalpy at state 2(in kJ/kg):\n",
      "dh = nn*(h1-h2) #Actual heat drop(in kJ/kg):\n",
      "T2 = T1*(p2/p1)**((n-1)/n) #Temperature at state 2(in K):\n",
      "dT = (1-nn)*(h1-h2)/C #Temperature rise due to supersaturation:\n",
      "T2a = T2+dT #Actual temperature at state 2(in K):\n",
      "u = Tsat-T2a #Amount of undercooling(in \u00b0C):\n",
      "\n",
      "#Results:\n",
      "print \"Actual heat drop: \",round(dh,2),\"kJ/kg\"\n",
      "print \"Amount of undercooling: \",round(u,2),\"\u00b0C\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Actual heat drop:  39.16 kJ/kg\n",
        "Amount of undercooling:  22.18 \u00b0C\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12, page no. 600"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      " \n",
      "from math import sqrt\n",
      "\n",
      "#Variable Declaration: \n",
      "p1 = 14 #Initial pressure(in bar):\n",
      "T1 = 400+273 #Initial temperature(in K):\n",
      "N = 16 #Number of nozzles:\n",
      "p2 = 10 #Final pressure(in bar):\n",
      "m = 5  #Discharge(in kg/s):\n",
      "nn = 0.90 #Nozzle efficiency:\n",
      "C1 = 100 #Inlet velocity(in m/s):\n",
      "n = 1.3 #Insex of compression:\n",
      "\n",
      "#From steam tables:\n",
      "h1 = 3257.5                 #kJ/kg \n",
      "s1 = 7.3026                 #kJ/kg.K\n",
      "T2 = 350.46                 #\u00b0C\n",
      "h2 = 3158.7                 #kJ/kg\n",
      "v2 = 0.2827                 #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "h12 = (h1-h2)*nn #Actual enthalpy change(inn kJ/kg):\n",
      "C2 = sqrt(2*h12*10**3) #Velocity at exit(in m/s):\n",
      "A2 = m*v2/(C2*N)*10**4 #Cross-sectional area at exit(in cm**2):\n",
      "C2a = sqrt(2*h12*10**3+C1**2)#Modified velocity at nozzle exit(in m/s):\n",
      "ma = 16*2.13*433.41*10**(-4)/0.2827#ma = A2*C2a*N/v2*10**(-4) \n",
      "p = (ma-m)/m*100       #% increase in discharge:\n",
      "\n",
      "#Results: \n",
      "print \"Cross-sectional area at exit of nozzle: \",round(A2,2),\"cm**2\"\n",
      "print \"Percentage increase in discharge: \",round(p,2),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Cross-sectional area at exit of nozzle:  2.09 cm**2\n",
        "Percentage increase in discharge:  4.5 %\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 13, page no. 602"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "#Variable Declaration: \n",
      "p1 = 20       #Initial pressure(in bar):\n",
      "p3 = 5       #Final pressure(in bar):\n",
      "n = 1.3\n",
      "#From steam tables:\n",
      "T1 = 212.42+273         #K\n",
      "Tsat = 186.43+273       #K (at 11.6 bar)\n",
      "psat = 5.452            #bar (at 155.14 \u00b0C)\n",
      "h1 = 2799.5             #kJ/kg\n",
      "v1 = 0.009963           #m**3/kg\n",
      "s1 = 6.3409             #kJ/kg.K\n",
      "h2aa = 2693.98          #kJ/kg\n",
      "s2a = 6.5484            #kJ/kg.K\n",
      "h3a = 2632.76           #kJ/kg\n",
      "h3 = 2544.21            #kJ/kg\n",
      "p2 = p1*0.58 #Pressure at throat(in bar):\n",
      "\n",
      "#Calculations:\n",
      "s2aa = s1\n",
      "s3a = s2a\n",
      "s3 = s1\n",
      "T2 = T1*(p2/p1)**((n-1)/n)\t#Temperature at state 2(in K):\n",
      "d = p2/psat #Degree of supersaturation:\n",
      "d1 = Tsat-T2 #Degree of undercooling:\n",
      "h12 = (n/(n-1))*p1*10**2*v1*(1-(T2/T1)) #Isentropic enthalpy drop:\n",
      "h2 = h1-h12 #Enthalpy at state 2(in kJ/kg):\n",
      "h12aa = h1-h2aa #Heat drop with no saturation(in kJ/kg):\n",
      "L = h12aa-h12 #Loss of available heat drop(in kJ/kg):\n",
      "s12a = L/Tsat #Increase in entropy(in kJ/kg.K):\n",
      "L1 = h3a-h3 #Loss due to undercooling(in kJ/kg):\n",
      "p = L1/(h1-h3)*100 #Percentage loss:\n",
      "\n",
      "#Results: \n",
      "print \"Degree of supersaturation: \",round(d,2)\n",
      "print \"Degree of undercooling: \",round(d1,2),\"\u00b0C\"\n",
      "print \"Entropy change: \",round(s12a,4),\"kJ/kg.K\"\n",
      "print \"Loss due to undercooling: \",round(L1,2),\"kJ/kg\"\n",
      "print \"Percentage loss: \",round(p,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Degree of supersaturation:  2.13\n",
        "Degree of undercooling:  31.35 \u00b0C\n",
        "Entropy change:  0.2075 kJ/kg.K\n",
        "Loss due to undercooling:  88.55 kJ/kg\n",
        "Percentage loss:  34.69\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14, page no. 604"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "  \n",
      "from math import sqrt,pi\n",
      "\n",
      "#Variable Declaration: \n",
      "m1 = 150/60 #Mass flow rate(in kg/s):\n",
      "H = 5  #Height of water level from the axis of injector(in m):\n",
      "p4 = 20 #Pressuer at which steam is injected(in bar):\n",
      "Z4 = 0.8 #Water level in boiler from the injector(in m):\n",
      "x1 = 0.95 #Dryness fraction at state 1:\n",
      "C4 = 20 #Velocity in delivery pipe(in m/s):\n",
      "p3 = 1.013 #Atmospheric pressure(in bar):\n",
      "d = 10**3 #Density(in kg/m**3):\n",
      "g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
      "Cps = 3.18 #Specific heat of steam(in kJ/kg.K):\n",
      "Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
      "#From steam tables:\n",
      "T1 = 212.42                 #\u00b0C\n",
      "Tw = 25                     #\u00b0C\n",
      "p2 = 0.7*p4\n",
      "h1 = 2704.95                #kJ/kg\n",
      "hfg1 = 1890.7               #kJ/kg\n",
      "s1 = 6.1462                 #kJ/kg.K\n",
      "x2 = 0.923\n",
      "h2 = 2639.10                #kJ/kg\n",
      "v2 = 0.13                   #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "s2 = s1\n",
      "C2 = sqrt(2*(h1-h2)*10**3) #Velocity of steam at throat(in m/s):\n",
      "C3 = sqrt(2*(g*Z4+p4*10**5/d+C4**2/2-p3*10**5/d))#Velocity at state 3(in m/s):\n",
      "m = (C2-C3)/(sqrt(2*g*H)+C3) #Mass of water pumped per kg of steam(in kg):\n",
      "m3 = m1+m1/m #Mass of mixture passing through state 3(in kg/s):\n",
      "A3 = m3/(d*C3)*10**4 #Area of throat of mixing nozzle(in cm**2):\n",
      "d3 = sqrt(A3*4/pi)     #Diameter of throat of the mixing nozzle(in cm):\n",
      "ms = m1/m #Mass of steam required for given flow rate(in kg/s):\n",
      "A2 = ms*v2/C2*10**4 #Area at state 2(in cm**2):\n",
      "d2 = sqrt(A2*4/pi) #Diameter of throat of steam nozzle(in cm):\n",
      "T3 = (x1*hfg1+Cps*T1+m*Cpw*Tw)/(m*Cpw+Cps)#Temperature of water coming out of the injector(in C):\n",
      "\n",
      "#Results: \n",
      "print \"Mass of water pumped per kg of steam: \",round(m,2),\"kg\"\n",
      "print \"Diameter of throat of the mixing nozzle: \",round(d3,3),\"cm\"\n",
      "print \"Diameter of throat of steam nozzle: \",round(d2,2),\"cm\"\n",
      "print \"Temperature of water coming out of the injector: \",round(T3,2),\"\u00b0C\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mass of water pumped per kg of steam:  3.98 kg\n",
        "Diameter of throat of the mixing nozzle:  0.783 cm\n",
        "Diameter of throat of steam nozzle:  1.69 cm\n",
        "Temperature of water coming out of the injector:  145.63 \u00b0C\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 15, page no. 607"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "from math import sqrt\n",
      "\n",
      "#Variable Declaration: \n",
      "p4 = 20 #Pressure at which steam is generated(in bar):\n",
      "p1 = 1.5 #Pressure at inlet(in bar):\n",
      "x1 = 0.9 #Dryness fraction:\n",
      "M = 5000 #Mass of water taken from feed water tank(in kg/hr):\n",
      "d = 10**3 #Density(in kg/m**3):\n",
      "#From steam tables:\n",
      "h1 = 2470.96                #kJ/kg \n",
      "s1 = 6.6443                 #kJ/kg.K\n",
      "s2 = s1\n",
      "x2 = 0.88\n",
      "h2 = 2396.72                #kJ/kg\n",
      "v2 = 1.7302                 #m**3/kg\n",
      "\n",
      "#Calculations:\n",
      "C2 = sqrt(2*(h1-h2)*10**3) #Steam velocity(in m/s):\n",
      "C3 = sqrt(1.2*p4*2*10**5/d) #Velocity at 3(in m/s):\n",
      "m = C2/C3-1  #Mass entrained per kg of steam:\n",
      "ms = M/(3600*m) #Mass of steam supplied per second(in kg/s):\n",
      "A2 = ms*v2/C2*10**4 #Area of steam nozzle(in cm**2):\n",
      "D = M/3600+ms #Total discharge from injector(in kg/s):\n",
      "A = D/(C3*d)*10**4 #Area of discharge orifice(in cm**2):\n",
      "\n",
      "#Results: \n",
      "print \"Mass of water pumped per kg of steam: \",round(m,2),\"kg water/kg of steam\"\n",
      "print \"Area of steam nozzle: \",round(A2,2),\"cm**2\"\n",
      "print \"Area of discharge orifice: \",round(A,3),\"cm**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mass of water pumped per kg of steam:  4.56 kg water/kg of steam\n",
        "Area of steam nozzle:  13.67 cm**2\n",
        "Area of discharge orifice:  0.244 cm**2\n"
       ]
      }
     ],
     "prompt_number": 29
    }
   ],
   "metadata": {}
  }
 ]
}