e54.ipynb

{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "<script>\n",
    "  function code_toggle() {\n",
    "    if (code_shown){\n",
    "      $('div.input').hide('500');\n",
    "      $('#toggleButton').val('Show Code')\n",
    "    } else {\n",
    "      $('div.input').show('500');\n",
    "      $('#toggleButton').val('Hide Code')\n",
    "    }\n",
    "    code_shown = !code_shown\n",
    "  }\n",
    "\n",
    "  $( document ).ready(function(){\n",
    "    code_shown=true;\n",
    "    $('div.input').show()\n",
    "  });\n",
    "</script>\n",
    "<form action=\"javascript:code_toggle()\"><input type=\"submit\" id=\"toggleButton\" value=\"Hide Code\"></form>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8s4sp-qtRsZ4"
   },
   "source": [
    "# Ejercicio 54\n",
    "\n",
    "![54.png](data:image/png;base64,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)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "30p5YfIVfDQT"
   },
   "source": [
    "Hallar:\n",
    "\n",
    "1. $\\Delta S_u$\n",
    "2. $\\eta_{ex,proc}$\n",
    "3. $\\eta_{iso,c}$\n",
    "\n",
    "------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Xnbf3ALheSV3"
   },
   "source": [
    "## Solución"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tCrw_1MwMkCZ"
   },
   "source": [
    "### Turbina"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0AaIdFSVhKox"
   },
   "source": [
    "__Datos:__\n",
    "\n",
    "$\n",
    "\\begin{array}{l}\n",
    "\\hline\n",
    "\\dot{m}_3 = 2,1 \\mbox{ [kg/s]}, \\; P_3 = 4 \\mbox{ bar}, \\; t_3 = 200^\\circ \\mbox{C} \\\\\n",
    "P_4 = 1,4 \\mbox{ bar} \\\\ \n",
    "\\eta_{iso} = 0,85 \\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "executionInfo": {
     "elapsed": 1620,
     "status": "ok",
     "timestamp": 1616677680901,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "XqEftiDyMkCh"
   },
   "outputs": [],
   "source": [
    "# Datos:\n",
    "m_3 = 2.1 # [kg/s]\n",
    "P_3 = 4e5 # [Pa]\n",
    "T_3 = 200 + 273.15 # [K]\n",
    "m_4 = m_3\n",
    "P_4 = 1.4e5 # [Pa]\n",
    "n_iso = 0.85"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kYC2bHxEMkCj"
   },
   "source": [
    "Desarrollo teórico:\n",
    "\n",
    "$\\begin{array}{|l|l|c|}\n",
    "\\hline\n",
    "n^\\circ & \\mbox{Ecuación} & \\mbox{Incógnita} \\\\\n",
    "\\hline\n",
    "1) & h_3 = f(P_3,t_3) \\quad \\mbox{(de tabla)} & h_3 \\\\\n",
    "2) & s_3 = f(P_3,t_3) \\quad \\mbox{(de tabla)} & s_3 \\\\\n",
    "3) & s_{4id} = s_3 \\quad \\mbox{(por isoentrópico)} & s_{4id} \\\\\n",
    "4) & s'_4 = f(P_4) \\quad \\mbox{(líq. saturado)} & s'_4 \\\\\n",
    "5) & s''_4 = f(P_4) \\quad \\mbox{(vap. saturado)} & s''_4 \\\\\n",
    "6) & h'_4 = f(P_4) \\quad \\mbox{(líq. saturado)} & h'_4 \\\\\n",
    "7) & h''_4 = f(P_4) \\quad \\mbox{(vap. saturado)} & h''_4 \\\\\n",
    "8) & \\displaystyle x_{4id} = \\frac{s_{4id} - s'_4}{s''_4 - s'_4} & x_{4id} \\\\\n",
    "9) & h_{4id} = x_{4id} (h''_4 - h'_4) + h'_4 & h_{4id} \\\\\n",
    "10) & \\displaystyle \\eta_{iso} = \\frac{W_{real}}{W_{ideal}} = \\frac{\\dot{m}_3 (h_3 - h_4)}{\\dot{m}_3 (h_3 - h_{4id})} = \\frac{h_3 - h_4}{h_3 - h_{4id}} & \\\\\n",
    "    & \\mbox{Despejando } h_4: & \\\\\n",
    "    & h_4 = \\eta_{iso} (h_{4id} - h_3) + h_3 & h_4 \\\\  \n",
    "11) & T_4 = f(P_4,h_4) & T_4 \\\\\n",
    "12) & s_4 = f(P_4,h_4) & s_4 \\\\\n",
    "13) & \\dot{W}_T = \\dot{m}_3 (h_3 - h_4) & \\dot{W}_T \\\\\n",
    "\\hline\n",
    "\\end{array}$\n",
    "\n",
    "13 ecuaciones - 13 incógnitas, tiene solución."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "executionInfo": {
     "elapsed": 5128,
     "status": "ok",
     "timestamp": 1616677684491,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "jS9377AhMkCk"
   },
   "outputs": [],
   "source": [
    "import CoolProp.CoolProp as cp  # (importa bilioteca termodinámica)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "executionInfo": {
     "elapsed": 5102,
     "status": "ok",
     "timestamp": 1616677684495,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "dwO5sq8RMkCk"
   },
   "outputs": [],
   "source": [
    "h_3 = cp.PropsSI('H','P',P_3,'T',T_3,'Water') #  (1)\n",
    "s_3 = cp.PropsSI('S','P',P_3,'T',T_3,'Water') #  (2)\n",
    "s_4id = s_3                                   #  (3)\n",
    "s_f4 = cp.PropsSI('S','P',P_4,'Q',0,'Water')  #  (4)\n",
    "s_g4 = cp.PropsSI('S','P',P_4,'Q',1,'Water')  #  (5)\n",
    "h_f4 = cp.PropsSI('H','P',P_4,'Q',0,'Water')  #  (6)\n",
    "h_g4 = cp.PropsSI('H','P',P_4,'Q',1,'Water')  #  (7)\n",
    "x_4id = (s_4id - s_f4)/(s_g4 - s_f4)          #  (8)\n",
    "h_4id = x_4id*(h_g4 - h_f4) + h_f4            #  (9)\n",
    "h_4 = n_iso*(h_4id - h_3) + h_3               # (10)\n",
    "T_4 = cp.PropsSI('T','P',P_4,'H',h_4,'Water') # (11)\n",
    "s_4 = cp.PropsSI('S','P',P_4,'H',h_4,'Water') # (12)\n",
    "W_T = m_3*(h_3 - h_4)                         # (13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 5083,
     "status": "ok",
     "timestamp": 1616677684501,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "qGdsJNMVMkCl",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "b937f3c6-5a84-4094-e463-dcb2e6670e8d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Turbina:\n",
      "h_3 = 2860.93 [kJ/kg]\n",
      "s_3 = 7.17230 [kJ/(kg·K)]\n",
      "s_4id = 7.17230 [kJ/(kg·K)]\n",
      "s_f4 = 1.41100 [kJ/(kg·K)]\n",
      "s_g4 = 7.24606 [kJ/(kg·K)]\n",
      "h_f4 = 458.42 [kJ/kg]\n",
      "h_g4 = 2689.98 [kJ/kg]\n",
      "x_4id = 0.9874\n",
      "h_4id = 2661.78 [kJ/kg]\n",
      "h_4 = 2691.65 [kJ/kg]\n",
      "T_4 = 383.23 [K]\n",
      "s_4 = 7.25041 [kJ/(kg·K)]\n",
      "W_T = 355.48 [kJ/s]\n"
     ]
    }
   ],
   "source": [
    "#@title Resultados:\n",
    "print('Turbina:')\n",
    "print('h_3 = %.2f [kJ/kg]'%(h_3/1000))\n",
    "print('s_3 = %.5f [kJ/(kg·K)]'%(s_3/1000))\n",
    "print('s_4id = %.5f [kJ/(kg·K)]'%(s_4id/1000))\n",
    "print('s_f4 = %.5f [kJ/(kg·K)]'%(s_f4/1000))\n",
    "print('s_g4 = %.5f [kJ/(kg·K)]'%(s_g4/1000))\n",
    "print('h_f4 = %.2f [kJ/kg]'%(h_f4/1000))\n",
    "print('h_g4 = %.2f [kJ/kg]'%(h_g4/1000))\n",
    "print('x_4id = %.4f'%x_4id)\n",
    "print('h_4id = %.2f [kJ/kg]'%(h_4id/1000))\n",
    "print('h_4 = %.2f [kJ/kg]'%(h_4/1000))\n",
    "print('T_4 = %.2f [K]'%T_4)\n",
    "print('s_4 = %.5f [kJ/(kg·K)]'%(s_4/1000))\n",
    "print('W_T = %.2f [kJ/s]'%(W_T/1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CN-PSb_eMkCo"
   },
   "source": [
    "### Compresor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qfIn3xyDMkCo"
   },
   "source": [
    "__Datos:__\n",
    "\n",
    "$\\begin{array}{l}\n",
    "\\hline\n",
    "W_c = W_T \\\\\n",
    "P_0 = 1 \\mbox{ bar}, \\; T_0 = 300^\\circ \\mbox{C} \\\\\n",
    "m_1 = 3,5 \\mbox{ kg/s}, \\; P_1=P_0, \\; T_1 = T_0 \\\\\n",
    "P_2 = 2 \\mbox{ bar} \\\\\n",
    "c_{p,aire} = 1,0047 \\mbox{ [kJ/(kg·K)]} \\\\\n",
    "R_{aire} = 0,287 \\mbox{ [kJ/(kg·K)]} \\\\\n",
    "\\hline\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "executionInfo": {
     "elapsed": 5049,
     "status": "ok",
     "timestamp": 1616677684506,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "cHZB6_ONMkCq"
   },
   "outputs": [],
   "source": [
    "# Datos:\n",
    "W_c = -W_T\n",
    "P_0 = 1e5 # [Pa]\n",
    "T_0 = 300 # [K]\n",
    "m_1 = 3.5 # [kg/s]\n",
    "P_1 = P_0\n",
    "T_1 = T_0\n",
    "P_2 = 2e5 # [Pa]\n",
    "cp_aire = 1.0047e3 # [J/(kg·K)]\n",
    "R_aire = 0.287e3 # [J/(kg·K)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "executionInfo": {
     "elapsed": 5032,
     "status": "ok",
     "timestamp": 1616677684512,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "ydM9ekzMMkCs"
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "S_8gjzDAMkCq"
   },
   "source": [
    "$\\begin{array}{|l|l|c|}\n",
    "\\hline\n",
    "n^\\circ & \\mbox{Ecuación} & \\mbox{Incógnita} \\\\\n",
    "\\hline\n",
    "1) & |\\dot{W}_c| = |\\dot{W}_T| = \\dot{m}_3 (h_3 - h_4) & \\dot{W}_c \\\\\n",
    "2) &  \\Delta H_{12} = - \\dot{W}_c & \\Delta H_{12} \\\\\n",
    "3) & \\Delta H_{12} = \\dot{m} c_{p,aire} \\Delta T_{12} \\\\\n",
    " & \\mbox{Despejando } \\Delta T_{12}: \\\\\n",
    " & \\displaystyle \\Delta T_{12} = \\frac{\\Delta H_{12}}{\\dot{m}_1  c_{p,aire}} & \\Delta T_{12} \\\\\n",
    "4) & T_2 = T_1 + \\Delta T_{12} & T_2 \\\\\n",
    "5) & \\displaystyle \\Delta S_{12} = \\dot{m}_1 \\left( c_{p,aire} \\ln \\frac{T_2}{T_1} - R_{aire} \\ln \\frac{P_2}{P_1} \\right) & \\Delta S_{12} \\\\\n",
    "\\hline\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "executionInfo": {
     "elapsed": 5005,
     "status": "ok",
     "timestamp": 1616677684517,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "S2Ny2vfLMkCs"
   },
   "outputs": [],
   "source": [
    "DH_12 = -W_c                                                  # (2)\n",
    "DT_12 = DH_12/(m_1*cp_aire)                                   # (3)\n",
    "T_2 = T_1 + DT_12                                             # (4)\n",
    "DS_12 = m_1*(cp_aire*np.log(T_2/T_1) - R_aire*np.log(P_2/P_1))# (5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 4982,
     "status": "ok",
     "timestamp": 1616677684521,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "QKOlVfxqMkCs",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "90b183d6-9761-485a-8265-249b2b7a384d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compresor:\n",
      "W_c = -355.48 [kJ/s]\n",
      "DT_12 = 101.09 [K]\n",
      "T_2 = 401.09 [K]\n",
      "DS_12 = 0.32494 [kJ/K]\n"
     ]
    }
   ],
   "source": [
    "#@title Resultados:\n",
    "print('Compresor:')\n",
    "print('W_c = %.2f [kJ/s]'%(W_c/1000))\n",
    "print('DT_12 = %.2f [K]'%DT_12)\n",
    "print('T_2 = %.2f [K]'%T_2)\n",
    "print('DS_12 = %.5f [kJ/K]'%(DS_12/1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6D8mo1CEMkCs"
   },
   "source": [
    "### Intercambiador de calor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Hya1d8hUMkCs"
   },
   "source": [
    "__Datos:__\n",
    "\n",
    "$\\begin{array}{l}\n",
    "\\hline\n",
    "P_4 \\mbox{ y del ítem anterior averiguamos, } T_4,h_4,s_4 \\\\\n",
    "P_5,x_5 \\\\\n",
    "P_6,t_6 \\\\\n",
    "P_7,t_7 \\\\\n",
    "c_{p,O_2} = 0,9185  \\mbox{ [kJ/(kg·K)]} \\\\\n",
    "\\hline\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "executionInfo": {
     "elapsed": 4958,
     "status": "ok",
     "timestamp": 1616677684537,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "a0KmMS6ZkpMY"
   },
   "outputs": [],
   "source": [
    "# Datos:\n",
    "P_5 = 1.2e5 # [Pa]\n",
    "x_5 = 0.5\n",
    "P_6 = 2e5 # [Pa]\n",
    "P_7 = P_6\n",
    "T_6 = 27 + 273.15 # [K]\n",
    "T_7 = 67 + 273.15 # [K]\n",
    "cp_O2 = 0.9185e3 # [J/(kg·K)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kcWo_uyJMkCt"
   },
   "source": [
    "$\\begin{array}{|l|c|}\n",
    "\\hline\n",
    "\\mbox{Ecuación} & \\mbox{Incógnita} \\\\\n",
    "\\hline\n",
    "h'_5 = f(P_5) \\quad \\mbox{ (de tabla)} & h'_5 \\\\\n",
    "h''_5 = f(P_5) \\quad \\mbox{ (de tabla)} & h''_5 \\\\\n",
    "h_5 = x_5(h''_5 - h'_5) + h'_5 & h_5 \\\\\n",
    "s'_5 = f(P_5) \\quad \\mbox{ (de tabla)} & s'_5 \\\\\n",
    "s''_5 = f(P_5) \\quad \\mbox{ (de tabla)} & s''_5 \\\\\n",
    "s_5 = x_5(s''_5 - s'_5) + s'_5 & s_5\\\\\n",
    "\\hline\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "executionInfo": {
     "elapsed": 4933,
     "status": "ok",
     "timestamp": 1616677684542,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "M5giGIfmMkCt"
   },
   "outputs": [],
   "source": [
    "h_f5 = cp.PropsSI('H','P',P_5,'Q',0,'Water')\n",
    "h_g5 = cp.PropsSI('H','P',P_5,'Q',1,'Water')\n",
    "\n",
    "h_5 = x_5*(h_g5 - h_f5) + h_f5\n",
    "\n",
    "s_f5 = cp.PropsSI('S','P',P_5,'Q',0,'Water')\n",
    "s_g5 = cp.PropsSI('S','P',P_5,'Q',1,'Water')\n",
    "\n",
    "s_5 = x_5*(s_g5 - s_f5) + s_f5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 4913,
     "status": "ok",
     "timestamp": 1616677684546,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "WYG12-XCmTgQ",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "a7560bdc-a610-4aea-f6b5-ff0fb52aa1ec"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h_5 = 1561.21 [kJ/kg]\n",
      "s_5 = 4.32930 [kJ/(kg·K)]\n"
     ]
    }
   ],
   "source": [
    "print('h_5 = %.2f [kJ/kg]'%(h_5/1000))\n",
    "print('s_5 = %.5f [kJ/(kg·K)]'%(s_5/1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sep4ZdqhRkn5"
   },
   "source": [
    "__Variación de entropían en 6-7__\n",
    "\n",
    "$$ \\Delta S_{67} = \\dot{m}_6 \\left( c_{p,O_2} \\ln \\frac{T_7}{T_6} - R_{O_2} \\ln \\frac{P_7}{P_6} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wl0-0ukMRkn5"
   },
   "source": [
    "Tenemos que $P_6 = P_7$, entonces se simplifica:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VXttiF7iRkn5"
   },
   "source": [
    "$$ \\Delta S_{67} = \\dot{m}_6 \\left( c_{p,O_2} \\ln \\frac{T_7}{T_6} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KALKR6YMRkn6"
   },
   "source": [
    "Averiguamos $\\dot{m}_6$, sabiendo que\n",
    "\n",
    "$$ |\\Delta H_{45}| = \\dot{m}_6 |\\Delta h_{67}| $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tfN1_71iRkn6"
   },
   "source": [
    "Entonces:\n",
    "$$ \\dot{m}_6 = \\left| \\frac{\\Delta H_{45}}{\\Delta h_{67}} \\right| = \\left| \\frac{\\dot{m}_4 (h_5 - h_4)}{c_{p,O_2} (T_7 - T_6)} \\right| $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "quJOxHHUvEEN"
   },
   "source": [
    "Luego, calculamos la variación de entropía entra el punto 3 y 5\n",
    "\n",
    "$$ \\Delta S_{35} = \\dot{m}_3 (s_5 - s_3) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "executionInfo": {
     "elapsed": 4888,
     "status": "ok",
     "timestamp": 1616677684550,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "R2IKEC18cTJp"
   },
   "outputs": [],
   "source": [
    "DH_45 = m_4*(h_5 - h_4)\n",
    "Dh_67 = cp_O2*(T_7 - T_6)\n",
    "\n",
    "m_6 = abs( DH_45/Dh_67 )\n",
    "DS_67 = m_6*(cp_O2*np.log(T_7/T_6))\n",
    "DS_35 = m_3*(s_5 - s_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 4871,
     "status": "ok",
     "timestamp": 1616677684553,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "Vo1nCJ__cVwT",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "c5c57d5b-6d23-47aa-ee43-802507876c72"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m_6 = 64.61 [kg/s]\n",
      "DS_12 = 0.32494 [kJ/K]\n",
      "DS_35 = -5.97030 [kJ/K]\n",
      "DS_67 = 7.42473 [kJ/K]\n"
     ]
    }
   ],
   "source": [
    "#@title Resultados:\n",
    "print('m_6 = %.2f [kg/s]'%m_6)\n",
    "print('DS_12 = %.5f [kJ/K]'%(DS_12/1000))\n",
    "print('DS_35 = %.5f [kJ/K]'%(DS_35/1000))\n",
    "print('DS_67 = %.5f [kJ/K]'%(DS_67/1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1gtAxqUGs3gW"
   },
   "source": [
    "### Variación de entropía del Universo\n",
    "$$ \\Delta S_u = \\Delta S_{12} + \\Delta S_{35} + \\Delta S_{67} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "executionInfo": {
     "elapsed": 4845,
     "status": "ok",
     "timestamp": 1616677684557,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "dYGaACFFmnGF"
   },
   "outputs": [],
   "source": [
    "DS_u = DS_12 + DS_35 + DS_67"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 4833,
     "status": "ok",
     "timestamp": 1616677684561,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "lCMGMvKnqtyV",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "24299a33-8858-45a2-cfb7-74a331eb11fc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DS_u  = 1.77936 [kJ/K]\n"
     ]
    }
   ],
   "source": [
    "#@title Resultado:\n",
    "print('DS_u  = %.5f [kJ/K]'%(DS_u/1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TmA71Wz9Rkn-"
   },
   "source": [
    "### Variación de exergías\n",
    "\n",
    "$\\begin{array}{l}\n",
    "\\Delta Ex_{12} = \\Delta H_{12} - T_0 \\Delta S_{12} \\\\\n",
    "\\Delta Ex_{34} = \\Delta H_{34} - T_0 \\Delta S_{34} \\\\\n",
    "\\Delta Ex_{45} = \\Delta H_{45} - T_0 \\Delta S_{45} \\\\\n",
    "\\Delta Ex_{67} = \\Delta H_{67} - T_0 \\Delta S_{67} \\\\\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "executionInfo": {
     "elapsed": 4810,
     "status": "ok",
     "timestamp": 1616677684565,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "FhRjCDuesG9C"
   },
   "outputs": [],
   "source": [
    "DH_34 = m_3*(h_4 - h_3)\n",
    "DH_67 = m_6*Dh_67\n",
    "DS_34 = m_3*(s_4 - s_3)\n",
    "DS_45 = m_4*(s_5 - s_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "executionInfo": {
     "elapsed": 4797,
     "status": "ok",
     "timestamp": 1616677684567,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "uI317CywVJiI"
   },
   "outputs": [],
   "source": [
    "DEx_12 = DH_12 - T_0*DS_12\n",
    "DEx_34 = DH_34 - T_0*DS_34\n",
    "DEx_45 = DH_45 - T_0*DS_45\n",
    "DEx_67 = DH_67 - T_0*DS_67"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 4788,
     "status": "ok",
     "timestamp": 1616677684573,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "jevYknD5V2tt",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "fa184def-603c-4fd3-dfb1-8f19750de860"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variación de entalpías:\n",
      "DH_12 = 355.48 [kJ]\n",
      "DH_34 = -355.48 [kJ]\n",
      "DH_45 = -2373.93 [kJ]\n",
      "DH_67 = 2373.93 [kJ]\n",
      "Variación de entropías:\n",
      "DS_12 = 0.32494 [kJ/K]\n",
      "DS_34 = 0.16402 [kJ/K]\n",
      "DS_45 = -6.13432 [kJ/K]\n",
      "DS_67 = 7.42473 [kJ/K]\n",
      "Variación de exergías:\n",
      "DEx_12 = 258.00 [kJ]\n",
      "DEx_34 = -404.69 [kJ]\n",
      "DEx_45 = -533.63 [kJ]\n",
      "DEx_67 = 146.51 [kJ]\n"
     ]
    }
   ],
   "source": [
    "#@title Resultados:\n",
    "print('Variación de entalpías:')\n",
    "print('DH_12 = %.2f [kJ]'%(DH_12/1000))\n",
    "print('DH_34 = %.2f [kJ]'%(DH_34/1000))\n",
    "print('DH_45 = %.2f [kJ]'%(DH_45/1000))\n",
    "print('DH_67 = %.2f [kJ]'%(DH_67/1000))\n",
    "print('Variación de entropías:')\n",
    "print('DS_12 = %.5f [kJ/K]'%(DS_12/1000))\n",
    "print('DS_34 = %.5f [kJ/K]'%(DS_34/1000))\n",
    "print('DS_45 = %.5f [kJ/K]'%(DS_45/1000))\n",
    "print('DS_67 = %.5f [kJ/K]'%(DS_67/1000))\n",
    "print('Variación de exergías:')\n",
    "print('DEx_12 = %.2f [kJ]'%(DEx_12/1000))\n",
    "print('DEx_34 = %.2f [kJ]'%(DEx_34/1000))\n",
    "print('DEx_45 = %.2f [kJ]'%(DEx_45/1000))\n",
    "print('DEx_67 = %.2f [kJ]'%(DEx_67/1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Y3SAKTeMRkn-"
   },
   "source": [
    "### Rendimiento exergético del proceso\n",
    "\n",
    "$$ \\eta_{ex,proc} = \\frac{\\Delta Ex_{12} + \\Delta Ex_{67}}{|\\Delta Ex_{34} + \\Delta Ex_{45}|} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "executionInfo": {
     "elapsed": 4767,
     "status": "ok",
     "timestamp": 1616677684577,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "r0Y6O8QlXcm2"
   },
   "outputs": [],
   "source": [
    "n_exproc = (DEx_12 + DEx_67)/abs(DEx_34 + DEx_45)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 4756,
     "status": "ok",
     "timestamp": 1616677684581,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "8akyCN1fbcZB",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "e4d07cce-1cfb-4076-8bed-a0346849f459"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_exproc = 0.4311\n"
     ]
    }
   ],
   "source": [
    "#@title Resultado:\n",
    "print('n_exproc = %.4f'%n_exproc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V3c-CtFhXe8B"
   },
   "source": [
    "### Rendimiento isoentrópico del compresor\n",
    "\n",
    "$$ \\eta_{iso,c} = \\frac{W_{ideal}}{W_{real}} = \\frac{W_c}{W_c - T_0 \\Delta S_{12}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "executionInfo": {
     "elapsed": 4734,
     "status": "ok",
     "timestamp": 1616677684584,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "ZNiCkvZ2eIrk"
   },
   "outputs": [],
   "source": [
    "n_isoc = W_c/(W_c - T_0*DS_12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 4721,
     "status": "ok",
     "timestamp": 1616677684588,
     "user": {
      "displayName": "Daniel Lorenzo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiSyDLM9Gn1s7fTNG4HqC2LEoK_gQxFYnqlQkahFw=s64",
      "userId": "18370114327754096178"
     },
     "user_tz": 180
    },
    "id": "Bi6vVTFFY2FB",
    "jupyter": {
     "source_hidden": true
    },
    "outputId": "cfabbd3f-db0b-448e-916c-0a5a49168b2a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_isoc = 0.7848\n"
     ]
    }
   ],
   "source": [
    "#@title Resultado\n",
    "print('n_isoc = %.4f'%n_isoc)"
   ]
  }
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