1re Spé - Loi de la statique des fluides V2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# On détaille ici un programme python affichant les points expérimentaux des mesures de pression P en fonction de la différence d'altitude $ \\Delta z$.\n",
    "### Dans cet exercice il faudra :\n",
    "###     1. Compléter les listes P et z avec les valeurs expérimentales.\n",
    "###     2. Calculer les écarts d'altitude $\\Delta z$\n",
    "###     2. Ajuster la valeur du coefficient directeur \"a\" et de l'ordonnée à l'origine \"b\" pour faire correspondre au mieux le modèle aux points expérimentaux."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chaque partie de code est précédée d'un titre.\n",
    "### Certaines parties de code sont à modifier par vous, cela est indiqué par la mention $\\color {red} {\"A\\: VOUS\\: DE\\: JOUER\\,!\"}$ dans le titre de la partie."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 0 : Initialisation des bibliothèques python nécessaires"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.close() # On ferme les fenêtres graphiques éventuellement ouvertes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 1 : On entre les coordonnées des valeurs expérimentales."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\color {red} {A\\: VOUS\\: DE\\: JOUER\\,!}$ \n",
    "### Compléter les listes P (en Pa) et z (en m) ci-dessous avec les valeurs expérimentales, les valeurs sont séparées par une virgule.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = [] #liste contenant les valeurs de la pression P en Pa\n",
    "z = [] #liste contenant les valeurs de l'altitude z en m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 2 : Calcul de la variation d'altitude $\\Delta z$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   ### 1. Définition de la fonction \"delta\" de calcul de la variation de l'altitude\n",
    "   ### $\\color {red} {A\\: VOUS\\: DE\\: JOUER\\,!}$\n",
    "   ### Compléter la formule permettant de calculer la variation d'altitude au point n° i\n",
    "   ### on précise que $\\Delta z$ du point i = $z_i$ - $z_0$ où $z_0$ est l'atitude la plus basse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta(liste): #la fonction se nomme delta et a une liste comme argument\n",
    "    deltaliste=[] #on crée la liste qui stockera les valeurs des variations de la grandeur\n",
    "    for i in range(0,len(liste)): #la boucle for balaie tous les termes de la liste\n",
    "        terme = (\"A modifier\") #on calcule la variation entre la première valeur et la i-ème la valeur\n",
    "        deltaliste.extend([terme]) #on ajoute le résultat à la liste deltaliste des variations de la gandeur\n",
    "    return deltaliste #la fonction retourne la liste deltaliste contenant les variations de la grandeur"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   ### 2. Calcul des variations $\\Delta z$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltaZ = delta(z) #on calcule les valeurs de variation de l'altitude, on les stocke dans la liste deltaZ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 4 : On modélise la répartition des points $\\Delta P$ en fonction de $\\Delta z$ par une droite affine de la forme y = ax + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "max() arg is an empty sequence",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-44-04d8d79427f7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m100000\u001b[0m \u001b[0;31m#Valeur de l'ordonnée à l'origine de la droite modèle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mpas\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdeltaZ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdeltaZ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m100\u001b[0m \u001b[0;31m#pas générant les abscisses du mmodèle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mabs_debut\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdeltaZ\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m5\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mpas\u001b[0m \u001b[0;31m#Abscisse de début du graphique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: max() arg is an empty sequence"
     ]
    }
   ],
   "source": [
    "a = -10 #Valeur du coefficient directeur de la droite modèle\n",
    "b = 100000 #Valeur de l'ordonnée à l'origine de la droite modèle\n",
    "\n",
    "pas = (max(deltaZ)-min(deltaZ))/100 #pas générant les abscisses du mmodèle\n",
    "\n",
    "abs_debut = min(deltaZ) - 5 * pas #Abscisse de début du graphique\n",
    "\n",
    "abs_fin = 0 + 110 * pas #Abscisse de fin du graphique\n",
    "\n",
    "X_modele = np.arange(abs_debut, abs_fin, pas) #On génère les abscisses du modèle\n",
    "                                                        # 10 x pas permet d'obtenir une droite qui dépasse à droite\n",
    "for i in X_modele:\n",
    "    Y_modele = a * X_modele + b #On génère les ordonnées du modèle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 5 : On trace le graphique contenant les points expérimentaux et le modèle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\color {red} {A\\: VOUS\\: DE\\: JOUER\\,!}$\n",
    "### Si nécessaire, modifier les valeurs de \"a\" et de \"b\", dans l'étape 4, pour que le modèle s'ajuste au mieux à la répartition des points expérimentaux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "max() arg is an empty sequence",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-45-25ff5ca1454c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_modele\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY_modele\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'b'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'Modèle'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#Affiche le modèle mathématique, ici une droite affine\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mx_Eq\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_Eq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdeltaZ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdeltaZ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m3\u001b[0m \u001b[0;31m#Calcule les coordonnées d'affichage de l'équation du modèle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_Eq\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_Eq\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\"y = \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\"*\"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\"x\"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\" + \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m22\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'b'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbbox\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mboxstyle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"round\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mec\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"k\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"w\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#Affiche l'équation de la droite dans un encadré\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: max() arg is an empty sequence"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8)) #Définit la taille de l'affichage du graphique\n",
    "plt.grid() # Affiche une grille sur le graphique\n",
    "plt.title(\"A modifier\", size=22) #Définit le titre du graphique\n",
    "plt.ylabel(\"A modifier\", size=18) #Affiche le titre des ordonnées\n",
    "plt.xlabel(\"A modifier\", size=18) #Affiche le titre des abscisses\n",
    "plt.xlim(abs_debut, abs_fin) #Définit le début et la fin des abscisses.\n",
    "plt.plot(deltaZ,P, 'o', color ='red', label = 'Points issus de la mesure') #Affiche les points expérimentaux\n",
    "plt.plot(X_modele, Y_modele, color = 'b', label = 'Modèle') #Affiche le modèle mathématique, ici une droite affine\n",
    "\n",
    "x_Eq,y_Eq = (max(deltaZ)-min(deltaZ))/2, min(P) + (max(P)-min(P))*2/3 #Calcule les coordonnées d'affichage de l'équation du modèle\n",
    "\n",
    "plt.text(x_Eq,y_Eq,\"y = \" + str(a) + \"*\" + \"x\" + \" + \" + str(b), size=22, color='b', bbox=dict(boxstyle=\"round\", ec=(\"k\"), fc=(\"w\"))) #Affiche l'équation de la droite dans un encadré\n",
    "plt.legend(fontsize=18)# Affiche la légende\n",
    "plt.show() #Affiche le graphique"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}