ex-12-087.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6e963640",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from oetils import init_plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "af0eba87",
   "metadata": {},
   "outputs": [],
   "source": [
    "W = init_plotting(latex=True, sans=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e6b73ffd",
   "metadata": {},
   "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>p</th>\n",
       "      <th>R</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>50.65</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>101.30</td>\n",
       "      <td>6.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>202.60</td>\n",
       "      <td>8.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>303.90</td>\n",
       "      <td>9.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>405.20</td>\n",
       "      <td>10.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        p     R\n",
       "0   50.65   5.4\n",
       "1  101.30   6.5\n",
       "2  202.60   8.2\n",
       "3  303.90   9.7\n",
       "4  405.20  10.9"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = 9.81\n",
    "H = 50e-2\n",
    "data = pd.DataFrame({\n",
    "    'p': [0.50, 1.00, 2.00, 3.00, 4.00],  # [atm]\n",
    "    'R': [5.4, 6.5, 8.2, 9.7, 10.9]       # [m]\n",
    "})\n",
    "data.p = data.p * 1.013e5 / 1e3  # Convert atm to kPa\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "971c3497",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Least squares fit\n",
    "x = np.stack([np.ones(len(data)), data.p]).T\n",
    "y = data.R ** 2\n",
    "w = np.linalg.lstsq(x, y, rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a432ed21",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3000x2086.34 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel(r\"$p_g\\quad/\\quad\\mathrm{kPa}$\")\n",
    "ax.set_ylabel(r\"$R^2\\quad/\\quad\\mathrm{m^2}$\")\n",
    "ax.plot(data.p, data.R**2, 'r.', label=\"Data\")\n",
    "x = np.linspace(data.p.min(), data.p.max())\n",
    "ax.plot(x, sum(w[i] * x**i for i in range(2)), label=\"Fit\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7624da7e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Height of liquid: h = 8.2 m\n"
     ]
    }
   ],
   "source": [
    "# Compute h\n",
    "h = w[0] / (4 * H)\n",
    "print(f\"Height of liquid: h = {h:.2g} m\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "831f3c42",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Density of liquid: 0.8 g / cm^3\n"
     ]
    }
   ],
   "source": [
    "rho = 4 * H / (g * w[1])\n",
    "print(f\"Density of liquid: {rho:.2g} g / cm^3\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}