GS1-Trabajo Practico Integrador-Segunda Parte.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cbac6550",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## **3. Interpolación**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "69b26373",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02d11fc4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Se conoce la presión de vapor del agua a las siguientes temperaturas: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "78eaeecf",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Presión de vapor [bar]</th>\n",
       "      <th>Temperatura [K]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>372.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>393.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>416.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>431.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>443.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>10</td>\n",
       "      <td>453.03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Presión de vapor [bar]  Temperatura [K]\n",
       "0                       1           372.75\n",
       "1                       2           393.36\n",
       "2                       4           416.76\n",
       "3                       6           431.98\n",
       "4                       8           443.56\n",
       "5                      10           453.03"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Agua = pd.Series(['Temperatura [°C]', 'Presión [bar]'])\n",
    "Temperatura_agua = pd.Series([99.6, 120.21, 143.61, 158.83, 170.41, 179.88])\n",
    "Presion_agua = pd.Series([1, 2, 4, 6, 8, 10])\n",
    "\n",
    "pd.DataFrame({'Presión de vapor [bar]': Presion_agua, 'Temperatura [K]': Temperatura_agua + 273.15})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e255ae8a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**3. Obtener la temperatura del agua a una presión de 3 bar. Elegir un método de interpolación, justificar su elección y graficar resultados.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9b96d95",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Ecuación general del método de Lagrange mejorado:\n",
    "\n",
    "$$ P_n(x)=\\sum^n_{i=0}f(x_i)\\frac{L(x)w_i}{x-x_i}=L(x)\\sum^n_{i=0}f(x_i)\\frac{w_i}{x-x_i},$$\n",
    "\n",
    "#### Ecuación del polinomio L (Cte dentro de la sumatoria):\n",
    "\n",
    "$$ L(x)=(x-x_0)(x-x_1)\\ldots(x-x_n)$$ \n",
    "\n",
    "#### Ecuación de los pesos baricéntricos:\n",
    "\n",
    "$$ w_i=\\prod^n_{\\substack{k=0 \\\\k\\neq i}}\\frac{1}{x_i-x_k}, \\text{  para todo  }i=0;1;\\ldots;n. $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "c7bc8abd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "#Generamos un array llamado data que almacene la información provista por la consigna:\n",
    "data = [[1,372.75],[2,393.36],[4,416.76],[6,431.98],[8,443.56],[10,453.03]]\n",
    "#(x,y) = (P,T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "204b5917",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def lagrangeMejorado_GS1(x,data):\n",
    "    w_lista = []\n",
    "    l = 1\n",
    "    sumatoria = 0\n",
    "    for i in range(0, len(data)):\n",
    "        l *= (x - data[i][0])\n",
    "        w = 1\n",
    "        for j in range(0, len(data)):\n",
    "            if j != i:\n",
    "                w *= 1 / (data[i][0] - data[j][0])\n",
    "        w_lista.append(w)\n",
    "    for i in range(0,len(data)):\n",
    "        sumatoria += data[i][1] * (w_lista[i] / (x - data[i][0]))\n",
    "    return l * sumatoria"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "d4b2ea8a",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame(data, columns = ['x', 'y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "11301c57",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def LagrangeMejorado_práctica(x,df):\n",
    "    N=len(df)\n",
    "    W=np.zeros(N)\n",
    "    P=0\n",
    "    L=1\n",
    "    PB=0\n",
    "    for i in range (0,N):\n",
    "        if x==df['x'][i]:         #Para que no divida por cero .\n",
    "            return df['y'][i]\n",
    "        L*=x-df['x'][i] #Productoria que define a L\n",
    "        w=1\n",
    "        for j in range (0,N):\n",
    "            if j != i:\n",
    "                w*=1/(df['x'][i]-df['x'][j])\n",
    "        W[i]=w\n",
    "        P+=(w*df['y'][i])/(x-df['x'][i])\n",
    "    PB=L*P\n",
    "    return PB,L,W, print(\"El valor despejado de T[k] con el método programado en clase es: \",PB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "60faa419",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El valor despejado de T[k] con el método programado en clase es:  424.8667410714287\n",
      "\n",
      "\n",
      "El valor despejado de T[k] con el método programado por el grupo es:  424.8667410714287\n"
     ]
    }
   ],
   "source": [
    "#Cálculo del valor de T[K] con la función vista en la clase práctica.\n",
    "x = 5\n",
    "LagrangeMejorado_práctica(x,df)\n",
    "#-------------------------------------------------------------------------------------------------------------------------#\n",
    "print(\"\\n\")\n",
    "#-------------------------------------------------------------------------------------------------------------------------#\n",
    "#Cálculo del valor de T[K] con la función programada por el grupo.\n",
    "t = lagrangeMejorado_GS1(x,data)\n",
    "print(\"El valor despejado de T[k] con el método programado por el grupo es: \",t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "b595f3ba",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Grafico Lagrange(mejorado)')"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Ploteo hecho por el grupo\n",
    "\n",
    "plt.xlabel(\"Presion [BAR]\")\n",
    "plt.ylabel(\"Temperatura Agua [°C]\")\n",
    "\n",
    "ejeX = np.linspace(0, 12, 500)\n",
    "ejeY = []\n",
    "for xi in ejeX:\n",
    "    ejeY.append(lagrangeMejorado_GS1(xi, data))\n",
    "\n",
    "plt.plot(ejeX, ejeY, linewidth = 2, color = \"green\")\n",
    "plt.scatter(3, lagrangeMejorado_GS1(3, data))\n",
    "plt.axvline(1, linewidth=2, color='blue',linestyle='dashed')\n",
    "plt.axvline(10, linewidth=2, color='blue',linestyle='dashed')\n",
    "plt.legend([\"Lagrange (mejorado)\", \"1\", \"10\", \"Valor especifico en 3\"], fontsize = 10)\n",
    "plt.title(\"Grafico Lagrange(mejorado)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a7c1f33",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## **Integración numérica**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33a2a8c6",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "La corriente metanol-agua (F1) debe ser precalentada previo al ingreso del tanque de mezclado. Para ello se utiliza vapor de agua. El intercambio calórico se lleva a cabo en un intercambiador de tubos concéntricos. <br>\n",
    "La longitud del equipo está dada por la siguiente ecuación: $L = \\frac{m}{D\\pi}\\int_{T_1}^{T} \\frac {Cp(T)}{h(T_s-T)}\\,dT$<br>\n",
    "Siendo: <br>m: caudal másico<br>D: diámetro del tubo<br>\n",
    "h: coeficiente de transferencia de calor<br>\n",
    "Ts: temperatura del vapor de agua<br>\n",
    "Cp: calor específico<br><br>\n",
    "\n",
    "$h = \\alpha(kCp)^{0.33}$<br><br>\n",
    "El calor específico está dado por la siguiente expresión:<br>\n",
    "$Cp(T) = aT^3+bT^2+cT+d$  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "8f0a3dc4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "#DATOS DEL PROBLEMA \n",
    "diametro = 0.08 #m Diámetro del tubo\n",
    "tEntrada = 5 #°C Temperatura de ingreso de la corriente F1\n",
    "tSalida = 15 #°C Temperatura de salida de la corriente F1\n",
    "\n",
    "#Coeficientes para h \n",
    "kappa = 0.0086\n",
    "alpha = 3630.4\n",
    "\n",
    "#Coeficientes del Cp para la corriente F1\n",
    "a = 0.00000006\n",
    "b = 0.000006\n",
    "c = 0.0008\n",
    "d = 0.05806\n",
    "\n",
    "#Información del vapor de agua\n",
    "Presion_vapor = 3 #bar (Del ejercicio 3, se saca que la temperatura del agua es:)\n",
    "temperaturaAgua = 424.8667410714287\n",
    "caudalMasicoF1 = 56000 # kg/h (Del ejercicio 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "6f13e1c8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "#Funciones que se van a utilizar\n",
    "def cp(t):\n",
    "    return ((a * t**3) + (b * t**2) + (c * t) + d)\n",
    "\n",
    "def h(t):\n",
    "    return (alpha * (kappa * cp(t))**0.33) \n",
    "\n",
    "def f(t):\n",
    "    return (cp(t) / h(temperaturaAgua - t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "e72f814f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#Metodo de Simpson Compuesto hecho por el grupo---------------------------------------------------------------------------#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "1de98113",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def simpsonCompuesto_GS1(tEntrada,tSalida,n):\n",
    "    paso = (tSalida-tEntrada) / (2*n)\n",
    "    sc = (1/3) * paso * f(tEntrada) + (1/3)* paso *f(tSalida)\n",
    "    for i in range(1, 2*n):\n",
    "        if i % 2 == 0:\n",
    "            sc += (2/3)* paso *f(tEntrada + i * paso)\n",
    "        if i % 2 != 0:\n",
    "            sc += (4/3)* paso *f(tEntrada + i * paso)\n",
    "    return sc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "212bdd52",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la integracion mediante GS1-Simpson Compuesto es:  0.0004975672392314942\n",
      "y el resultado es:  110.86639990199188\n"
     ]
    }
   ],
   "source": [
    "print(\"la integracion mediante GS1-Simpson Compuesto es: \", simpsonCompuesto_GS1(5, 15, 1000))\n",
    "print(\"y el resultado es: \", (caudalMasicoF1 / (diametro*np.pi)) * simpsonCompuesto_GS1(5, 15, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "8a429c61",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "#Optimización del método de Simpson compuesto mediante el uso de booleans en reemplazo del operador \" % \""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "dc6de62d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def simpsonCompuesto_GS1_optimizado(tEntrada,tSalida,n):\n",
    "    par = False\n",
    "    paso = (tSalida-tEntrada) / (2*n)\n",
    "    sc = (1/3) * paso * f(tEntrada) + (1/3)* paso *f(tSalida)\n",
    "    for i in range(1, 2*n):\n",
    "        if(par):\n",
    "            sc += (2/3)* paso *f(tEntrada + i * paso)\n",
    "            par = False\n",
    "        else:\n",
    "            sc += (4/3)* paso *f(tEntrada + i * paso)\n",
    "            par = True\n",
    "    return sc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "575c4d3b",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la integracion mediante GS1-Simpson Compuesto es:  0.0004975672392314942\n",
      "y el resultado es:  110.86639990199188\n"
     ]
    }
   ],
   "source": [
    "print(\"la integracion mediante GS1-Simpson Compuesto es: \", simpsonCompuesto_GS1_optimizado(5, 15, 1000))\n",
    "print(\"y el resultado es: \", (caudalMasicoF1 / (diametro*np.pi)) * simpsonCompuesto_GS1_optimizado(5, 15, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "0e6ac8be",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#Cuadratura de Gauss-Legendre---------------------------------------------------------------------------------------------#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "b6c4738d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def gaussLegendre(tMax, tMin, f, n):\n",
    "    resultado = 0 \n",
    "    sumatoria = 0\n",
    "    ti, ci = np.polynomial.legendre.leggauss(n)\n",
    "    for i in range (0, n):\n",
    "        tActual = ((tMax - tMin) / 2) * ti[i] + ((tMin + tMax) / 2)\n",
    "        sumatoria += ci[i] * (f(tActual))\n",
    "    resultado = ((tMax-tMin)/2) * sumatoria \n",
    "    return resultado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "af61314c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La integracion mediante Gauss Legendre es:  0.0004975672392314943\n",
      "y el resultado es:  110.86639990199191\n"
     ]
    }
   ],
   "source": [
    "print(\"La integracion mediante Gauss Legendre es: \", gaussLegendre(15, 5, f, 10))\n",
    "print(\"y el resultado es: \", (caudalMasicoF1 / (diametro * np.pi)) * gaussLegendre(15, 5, f, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "1706f7e5",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Funcion prueba (for debugging) -----------------------------------------------------------------------------------------#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "f5d8a33c",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#def Gauss2(tMax, tMin, f,cp, h, a, b, c, d, alpha, k, n ): #Viejo, antes de prolijar.\n",
    "#    resultado=0 \n",
    "#    sumatoria=0\n",
    "#    ci, ti= np.polynomial.legendre.leggauss(n)\n",
    "#    for i in range (0, n):\n",
    "#        tActual= ((tMax-tMin)/n) * ti[i] + (tMin+tMax)/n\n",
    "#        #print(((tMax-tMin)/n) * ti[i])\n",
    "#        #print ((tMin+tMax)/n)\n",
    "#        #print (tActual)\n",
    "#        sumatoria+= ci[i] * (f(cp, h, a, b, c, d, alpha, k, tActual))\n",
    "#        #print(sumatoria)\n",
    "#        #print(f(cp, h, a, b, c, d, alpha, k, tActual))\n",
    "#        \n",
    "#        \n",
    "#    resultado= ((tMax-tMin)/n) * sumatoria \n",
    "#    return resultado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "fb5a7360",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#print(\"la integracion mediante Gauss Legendre es: \", Gauss2(15, 5, f,cp, h, a, b, c, d, alpha, k, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "e82df942",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#PRUEBA CON OTROS METODOS DE LA CATEDRA-----------------------------------------------------------------------------------#"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2090bbf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Comprobacion con otros metodos, programados por la catedra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "51a7d73b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def PuntoMedioC(A,B,n):\n",
    "    H = (B-A) / n  \n",
    "    Q = 0\n",
    "    for i in range (0,n):\n",
    "        Q += H * f(A+i*H+H/2)\n",
    "    return Q\n",
    "    \n",
    "def q(x,A,B):\n",
    "    H = B-A\n",
    "    return f(A+H/2)*x/x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "1db03385",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la integracion mediante Punto medio compuesto es:  0.000497567238604696\n",
      "y el resultado es:  110.86639976233064\n"
     ]
    }
   ],
   "source": [
    "print(\"la integracion mediante Punto medio compuesto es: \", PuntoMedioC(5, 15, 1000))\n",
    "print(\"y el resultado es: \", (caudalMasicoF1 / (diametro*np.pi)) * PuntoMedioC(5, 15, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "f7cf46cd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def TrapecioC(A,B,n):\n",
    "    H = (B-A) / n\n",
    "    Q = (H/2) * f(A)     \n",
    "    for i in range (1,n):\n",
    "        Q += H * f(A+i*H) \n",
    "    Q += (H/2) * f(B)\n",
    "    return Q\n",
    "    \n",
    "def q(x,a,b):\n",
    "    H = B-A\n",
    "    F01 = (f(B) - f(A)) / H \n",
    "    return f(A) + F01 * (x-A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "be03cfbb",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la integracion mediante trapecios compuestos es:  0.0004975672404850919\n",
      "y el resultado es:  110.86640018131467\n"
     ]
    }
   ],
   "source": [
    "print(\"la integracion mediante trapecios compuestos es: \", TrapecioC(5, 15, 1000))\n",
    "print(\"y el resultado es: \", (caudalMasicoF1 / (diametro*np.pi)) * TrapecioC(5, 15, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "14507b59",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def gaussLegendreCatedra (a0,b0,n):\n",
    "    H = (b0-a0)/n\n",
    "    Q = 0\n",
    "    ti, ci= np.polynomial.legendre.leggauss(n)\n",
    "    for j in range (0,n):\n",
    "        A = a0 + H*j\n",
    "        B = A + H\n",
    "        q = 0\n",
    "        for i in range (len(ti)):\n",
    "            xi = (B+A)/2 + H*ti[i]/2\n",
    "            q += ci[i] * f(xi)\n",
    "        Q += H*q/2\n",
    "    return (Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "1c78f7c8",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la integracion mediante Gauss Legendre es:  0.0004975672392314944\n",
      "y el resultado es:  110.86639990199194\n"
     ]
    }
   ],
   "source": [
    "print(\"la integracion mediante Gauss Legendre es: \", gaussLegendreCatedra(5, 15, 100))\n",
    "print(\"y el resultado es: \", (caudalMasicoF1 / (diametro*np.pi)) * gaussLegendreCatedra(5, 15, 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "7f37b2a7",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#-------------------------------------------------------------------------------------------------------------------------#"
   ]
  }
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