1re Spé - Loi de la statique des fluides V1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# On détaille ici un programme python affichant les points expérimentaux des mesures de l'écart de pression $\\Delta P$ 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 de pression $\\Delta P$ et $\\Delta z$\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": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "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": 60,
   "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 de pression $\\Delta P$ et de la variation d'altitude $\\Delta z$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   ### 1. Définition de la fonction \"delta\" de calcul de la variation d'une grandeur\n",
    "   ### $\\color {red} {A\\: VOUS\\: DE\\: JOUER\\,!}$\n",
    "   ### Compléter la formule permettant de calculer la variation de la grandeur\n",
    "   ### on précise que\n",
    "* la variation de pression $\\Delta P$ au point i se calcule par $\\Delta P = P_i - P_0$ avec $P_0$ la pression du point de plus faible altitude\n",
    "* la variation d'altitude $\\Delta z$ au point i se calcule par $\\Delta z = z_i - z_0$ avec $z_0$ l'altitude la plus faible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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 $\\Delta P$ et $\\Delta z$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltaP = delta(P) #on calcule les valeurs de variation de la pression, on les stocke dans la liste deltaP\n",
    "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": 63,
   "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-63-f3f90ba8508a>\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;36m0\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 = 0 #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": 64,
   "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-64-57dd73e3b625>\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[0mdeltaP\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[0mdeltaP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdeltaP\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,deltaP, '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(deltaP) + (max(deltaP)-min(deltaP))*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
}