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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 5 : First Law Applied to Flow Processes"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.1 Page No : 101"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V1 = 0.95;\n",
      "P1 = 100e03;  #initial pressure Pa\n",
      "v1 = 7.;      #initial velocity m/s\n",
      "V2 = 0.19;    #final velocity m/s\n",
      "P2 = 700e03;  #final pressure Pa\n",
      "v2 = 5.;\n",
      "w = 0.5;\n",
      "u21 = 90e03; \t\t\t# u21 = u2-u1\n",
      "Q = -58e03; \t\t\t# As heat is added Q = dQ/dt\n",
      "\n",
      "# Calculation and Results\n",
      "W =  - w*( u21 + (P2*V2-P1*V1) + ((v2**2-v1**2)/2) ) + Q; \t\t\t# W = dW/dt  \n",
      "print \"The rate of work input is\",round(W/1000),\"kW\"\n",
      "\n",
      "# Part (b)\n",
      "A = (v2/v1)*(V1/V2); \t\t\t# A = A1./A2\n",
      "d = math.sqrt(A); \t\t\t# d = d1./d2\n",
      "print \"The ratio of the inlet pipe diameter and outer pipe diameter is %.2f\"%d\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The rate of work input is -122.0 kW\n",
        "The ratio of the inlet pipe diameter and outer pipe diameter is 1.89\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.2 Page No : 102"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "V1 = 0.37;    #specific volume m^3/kg\n",
      "P1 = 600.e03;\n",
      "v1 = 16.;\n",
      "V2 = 0.62; \n",
      "P2 = 100.e03;\n",
      "v2 = 270.;\n",
      "Z1 = 32.;\n",
      "Z2 = 0;\n",
      "g = 9.81; \n",
      "Q = -9.e03; \t\t\t# heat loss Q = dQ/dt\n",
      "W = 135.e03; \t\t\t# Work done W = dW/dt\n",
      "\n",
      "# Calculation\n",
      "U12 = (P2*V2-P1*V1) + ((v2**2-v1**2)/2.) + (Z2-Z1)*g + W - Q; \t\t\t# U12 = U1-U2\n",
      "\n",
      "# Results\n",
      "print \"The internal energy decreases by\",round(U12/1000,3),\"Joule\"\n",
      "\n",
      "# note : rounding off error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The internal energy decreases by 20.008 Joule\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.3 Page No : 103"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "P1 = 4e06;\n",
      "t1 = 400.;\n",
      "h1 = 3213e03;\n",
      "V1 = 0.073;\n",
      "P2 = 3.5e06;\n",
      "t2 = 392.;\n",
      "h2 = 3202e03;\n",
      "V2 = 0.084;\n",
      "Q = -8.5e03;\n",
      "\n",
      "# Calculation\n",
      "v1 = math.sqrt((2*(h1-h2+Q))/(1.15**2-1));\n",
      "A1 = (math.pi/4)*0.2**2;\n",
      "w = (A1*v1)/V1;\n",
      "\n",
      "# Results\n",
      "print \"The stean flow rate is %.1f Kg/s\"%w\n",
      "\n",
      "# rounding off error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The stean flow rate is 53.6 Kg/s\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.4 Page No : 104"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import sys\n",
      "from numpy import *\n",
      "from sympy import Symbol\n",
      "\n",
      "# Variables\n",
      "h1 = 313.93;\n",
      "h2 = 2676.;\n",
      "h3 = 419.;\n",
      "w1 = 4.2;\n",
      "\n",
      "# Calculation\n",
      "w = Symbol('w') \t\t\t# w = w2\n",
      "P = w1*h1 + w*h2 - h3*(4.2+w)\n",
      "def stress(a,b,f):\n",
      "    N = 100;\n",
      "    eps = 1e-5;\n",
      "    if((f(a)*f(b))>0):\n",
      "        print ('no root possible f(a)*f(b)>0');\n",
      "        sys.exit(0)\n",
      "    if(abs(f(a))<eps):\n",
      "        print ('solution at a');\n",
      "        sys.exit(0)\n",
      "    if(abs(f(b))<eps):\n",
      "        print ('solution at b');\n",
      "        sys.exit(0)\n",
      "\n",
      "    while(N>0):\n",
      "        c = (a+b)/2.\n",
      "        if(abs(f(c))<eps):\n",
      "            x = c ;\n",
      "            return x;\n",
      "        if((f(a)*f(c))<0 ):\n",
      "            b = c ;\n",
      "        else:\n",
      "            a = c ;\n",
      "        N = N-1;\n",
      "    print ('no convergence');\n",
      "    sys.exit(0)\n",
      "\n",
      "def p(w): \n",
      "\t return  - 441.294 + 2257*w \n",
      "\n",
      "w = stress(0.1,0.2,p);\n",
      "\n",
      "# Results\n",
      "print \"The amount of heat that should be supplied is %.0fKg/h\"%(w*3600)\n",
      "\n",
      "# rounding off error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The amount of heat that should be supplied is 704Kg/h\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.5 Page No : 104"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "t1 = 15.\n",
      "t2 = 800. \n",
      "t3 = 650.\n",
      "t4 = 500.;\n",
      "v1 = 30.; \n",
      "v2 = 30. \n",
      "v3 = 60.; \n",
      "w = 2.;\n",
      "cp = 1005.;\n",
      "\n",
      "# Calculation and Results\n",
      "Q1_2 = w*cp*(t2-t1);\n",
      "print \"The rate of heat transfer to the air in the heat exchanger is %.0f KJ/s\"%(round(Q1_2/1000,-1)),\"KJ/s\"\n",
      "W_T = w*( ((v2**2-v3**2)/2) + cp*(t2-t3));\n",
      "print \"The power output from the turbine assuming no heat loss\",W_T/1000,\"KW\"\n",
      "v4 = math.sqrt( (v3**2) + (2*cp*(t3-t4)) );\n",
      "print \"The velocity at the exit of the nozzle is %.0f m/s\"%v4\n",
      "\n",
      "# rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The rate of heat transfer to the air in the heat exchanger is 1580 KJ/s KJ/s\n",
        "The power output from the turbine assuming no heat loss 298.8 KW\n",
        "The velocity at the exit of the nozzle is 552 m/s\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.6 Page No : 106"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "# Variables\n",
      "w = 5.\n",
      "h1 = 900\n",
      "h2 = 400\n",
      "v1 = 50. \n",
      "v2 = 150.\n",
      "Q = -25*5. \t\t\t# Q = dQ/dt for w = 5kg\n",
      "\n",
      "# Calculation and Results\n",
      "W = (w*( (h1-h2) + ((v1**2-v2**2)/2)*10**-3 )) + Q; \t\t\t# W = dW/dt\n",
      "print \"The power output of the turbine is %.0f kW\"%(W)\n",
      "R = 285.\n",
      "T1 = 300.\n",
      "P1 = 100e03;\n",
      "V = (w*R*T1)/P1; \t\t\t# V = dV/dt\n",
      "A1 = V/v1; \n",
      "D1 = math.sqrt((4*A1)/math.pi);\n",
      "print \"The diameter of the inlet pipe is %.2f m\"%D1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The power output of the turbine is 2325 kW\n",
        "The diameter of the inlet pipe is 0.33 m\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.7 Page No : 107"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "ha = 260.; \t\t\t    # Enthalpy of air\n",
      "hg = 912.; \t\t    \t# Enthalpy of gas\n",
      "Va = 270.; \t    \t\t# Velocity of air\n",
      "f = 0.0190; \t\t\t# Fuel to air ratio wf/wa\n",
      "Ef = 44500.; \t\t\t# Chemical energy of fuel in kJ/kg\n",
      "Q = 21.;     \t\t\t# Heat loss from the engine\n",
      "\n",
      "# Calculation\n",
      "Eg = 0.05*f*Ef/(1+f)    \t# As 5% of chemical energy is not released in reaction\n",
      "Vg = math.sqrt(2000*(((ha+(Va**2*0.001)/2+(f*Ef)-Q)/(1+f))-hg-Eg));\n",
      "\n",
      "# Results\n",
      "print \"Velocity of exhaust gas is %.0f m/s\"%Vg\n",
      "\n",
      "# rounding off error. please check."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Velocity of exhaust gas is 541 m/s\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.9 Page No : 108"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from hornerc import horner\n",
      "\n",
      "# Variables\n",
      "u0 = 0.718*273*1e03;\n",
      "#t = poly(0,'t');\n",
      "#u = u0+718*t; \t\t\t# in SI unit\n",
      "#hp = u + 285*(t+273); \t\t\t# \"\"\n",
      "hp =  [273819, 1003]\n",
      "\n",
      "# Calculation\n",
      "h = horner(hp,150); \t\t\t# h = hp(150)\n",
      "W = 100.; \t\t\t# W = dW/dt\n",
      "m = W/h;\n",
      "\n",
      "# Results\n",
      "print \"The rate at which air flows out of the tank %.3f kg/h\"%(m*3600)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The rate at which air flows out of the tank 0.849 kg/h\n"
       ]
      }
     ],
     "prompt_number": 13
    }
   ],
   "metadata": {}
  }
 ]
}