{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "e501f69c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit, fsolve\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "505ed473",
   "metadata": {},
   "source": [
    "# question 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b2baaf03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3200000.0000000005"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = 2\n",
    "nu = 1e-6\n",
    "l = 1.6\n",
    "\n",
    "re = (u*l)/nu\n",
    "re"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fe6c3dd",
   "metadata": {},
   "source": [
    "this shows that the flow is probably turbulent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b5543777",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0304"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = (l * 0.38)/re** 0.2\n",
    "delta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e580f779",
   "metadata": {},
   "source": [
    "the boundary layer is 30mm. This needs a margin of error becuase it is an empirical guess"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3219ab49",
   "metadata": {},
   "source": [
    "# question 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e93da678",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.58060331 -4.38330176]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f91c6a259a0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# reads in file\n",
    "u = []\n",
    "y = []\n",
    "with open(\"laminar_profile.csv\", 'r') as file:\n",
    "    for line in file:\n",
    "        if line[0] == 'W':\n",
    "            continue\n",
    "        line = line.strip()\n",
    "        data = line.split(',')\n",
    "        u.append(float(data[1]))\n",
    "        y.append(float(data[0]))\n",
    "\n",
    "        \n",
    "#plotting and finding some things\n",
    "u=np.array(u)\n",
    "y=np.array(y)\n",
    "u_inf = np.array(u[-1])\n",
    "delta = np.interp(0.99,u/u_inf,y)\n",
    "\n",
    "\n",
    "# curve fitting\n",
    "def func(x, a, b):\n",
    "    return a**x + b*x\n",
    "\n",
    "u=u[np.where(u<u_inf)]\n",
    "y=y[:11]\n",
    "popt, pcov = curve_fit(func,u/u_inf,y/delta)\n",
    "\n",
    "print(popt)\n",
    "x=np.linspace(0,1)\n",
    "plt.plot(func(x, 2.5, -1.7), x)\n",
    "plt.plot(u/u_inf, y/max(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "614102a9",
   "metadata": {},
   "source": [
    "# all the stuff above this is useless"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "17a0cf12",
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "functions to use later, might have confused momentum and displacement thickness\n",
    "'''\n",
    "\n",
    "def re(U, l, nu): # reynolds number for nu\n",
    "    return (U*l)/nu\n",
    "\n",
    "def re2(U, l, rho, mu): # reynolds number for mu and rho\n",
    "    return (rho * U * l)/(mu)\n",
    "\n",
    "def theta_lam(x, re_x): # momentum thickness for laminar flow\n",
    "    top = 0.664 * x\n",
    "    bottom = np.sqrt(re_x)\n",
    "    return top/bottom\n",
    "\n",
    "def theta_turb(x, re_x):# momentum thickness for turbulent flow\n",
    "    top = 0.0037 * x\n",
    "    bottom = re_x**0.2\n",
    "    return top/bottom\n",
    "\n",
    "def virtual_origin(x_t, re_xt): # finds the virtual origin from the transition point and the reynolds number\n",
    "    return x_t * (1-38.22 * re_xt**(-3/8))\n",
    "\n",
    "def drag(rho, U, theta_x): # drag from density, velocity and momentum thickness\n",
    "    return rho * (U**2) * theta_x\n",
    "\n",
    "def C_F(L, re_L):\n",
    "    return (2 * theta_turb(L, re_L))/L\n",
    "\n",
    "def U_tau(U_inf, C_F):\n",
    "    frac = C_F / 2\n",
    "    part = np.sqrt(frac)\n",
    "    return U_inf * part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "5d28aa89",
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "setting up values for q1, calculations in the box below\n",
    "'''\n",
    "U_inf = 59\n",
    "chord = 1\n",
    "nu = 1.529e-5\n",
    "rho = 1.19\n",
    "span = 16.9\n",
    "mu = rho * nu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "68da0d7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "47.32749313996018"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "actual calculations for q1\n",
    "'''\n",
    "reynolds = re(U_inf, chord, nu) # using re2 gives the same answer\n",
    "drag = (U_inf ** 2) * rho * theta_lam(chord, reynolds) * 2\n",
    "drag * span "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d1c2d198",
   "metadata": {},
   "outputs": [],
   "source": [
    "span = 3.4\n",
    "chord = 1.0\n",
    "U_inf = 6.3\n",
    "nu = 1.01e-6\n",
    "rho = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "082661b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43.69058910080194"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reynolds = re(U_inf, chord, nu)\n",
    "drag = (U_inf ** 2) * rho * theta_turb(chord, reynolds) * 2\n",
    "drag * span "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "b96e82ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.06031864992180838"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chord = 4\n",
    "U_inf = 6\n",
    "rho = 1.2\n",
    "nu = 1.48e-5\n",
    "x_t = chord * 0.3\n",
    "re_xt = re(U_inf, x_t, nu)\n",
    "x_0 = virtual_origin(x_t, re_xt)\n",
    "\n",
    "(U_inf ** 2) * rho * theta_turb(chord - x_0, re(U_inf, chord - x_0, nu)) * 2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "7bd13256",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4363636.363636363"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "re(40, 1.2, 0.000011)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "2ea8458b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2.143944115339496"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = 5.9e-3\n",
    "U = 4\n",
    "dydelta = delta * 0.001\n",
    "y = np.arange(0, delta+0.001, dydelta)\n",
    "u = np.arange(0, delta+0.001, dydelta)\n",
    "u[np.where(u>=delta)] = U\n",
    "u[np.where(u<delta)] = 4 * np.sin(np.pi * y[np.where(y<delta)]/(2 * delta))\n",
    "\n",
    "plt.plot(u/U, y/delta)\n",
    "plt.show()\n",
    "frac = u/U\n",
    "(np.trapz((1-frac))*dydelta)*1e3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "ba3fca18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6667000000000013"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dx = 0.01\n",
    "x = np.arange(-1,1+dx, dx)\n",
    "\n",
    "np.trapz(x**2)*dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "3fcb2199",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.02040816, 0.04081633, 0.06122449, 0.08163265,\n",
       "       0.10204082, 0.12244898, 0.14285714, 0.16326531, 0.18367347,\n",
       "       0.20408163, 0.2244898 , 0.24489796, 0.26530612, 0.28571429,\n",
       "       0.30612245, 0.32653061, 0.34693878, 0.36734694, 0.3877551 ,\n",
       "       0.40816327, 0.42857143, 0.44897959, 0.46938776, 0.48979592,\n",
       "       0.51020408, 0.53061224, 0.55102041, 0.57142857, 0.59183673,\n",
       "       0.6122449 , 0.63265306, 0.65306122, 0.67346939, 0.69387755,\n",
       "       0.71428571, 0.73469388, 0.75510204, 0.7755102 , 0.79591837,\n",
       "       0.81632653, 0.83673469, 0.85714286, 0.87755102, 0.89795918,\n",
       "       0.91836735, 0.93877551, 0.95918367, 0.97959184, 1.        ])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d38da998",
   "metadata": {},
   "outputs": [],
   "source": [
    "chord = 4\n",
    "x_0 = 1\n",
    "rho = 1.23\n",
    "U = 6\n",
    "Re_c = 64e4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "72045791",
   "metadata": {},
   "outputs": [],
   "source": [
    "laminar = pd.read_excel(\"LBLdata1.xlsx\")\n",
    "aa, ab = laminar.columns\n",
    "y=laminar[aa]\n",
    "u=laminar[ab]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "5a0a8e43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "delta: 1.4863636363636374\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "displacement thickness: 0.5409499999999999\n"
     ]
    }
   ],
   "source": [
    "U_inf = u.max()\n",
    "delta = np.interp(0.99*U_inf, u, y)\n",
    "print(f\"delta: {delta}\")\n",
    "plt.plot(u, y)\n",
    "plt.plot(0.99*U_inf, delta, \"ro\")\n",
    "plt.show()\n",
    "delta_star = np.trapz(1-(u/U_inf), y)\n",
    "print(f\"displacement thickness: {delta_star}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57ff2d69",
   "metadata": {},
   "source": [
    "# q4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "957d66de",
   "metadata": {},
   "outputs": [],
   "source": [
    "u = 6\n",
    "chord = 4\n",
    "x_t = 1\n",
    "nu = 3.75e-5\n",
    "rho = 1.23\n",
    "re_c = 64e4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "7acf95d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31.03469822371708"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_o = virtual_origin(1, re(u, x_t, nu))\n",
    "drag(rho, u, x_o)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81c9ead8",
   "metadata": {},
   "source": [
    "# q6\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "52b5106f",
   "metadata": {},
   "outputs": [],
   "source": [
    "chord = 3\n",
    "U = 6\n",
    "rho = 1.2\n",
    "nu = 1.48e-5\n",
    "x_t = 0.7 * chord"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "6a8caeab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2315109525128017"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_o = virtual_origin(1, re(u, x_t, nu))\n",
    "x_o * 0.3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a6d0eee",
   "metadata": {},
   "source": [
    "# q5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "d18e0bf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "U = 98\n",
    "nu = 0.000013\n",
    "x = 1\n",
    "y.plus = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "e850a5d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "reynolds = re(U, x, nu)\n",
    "coefficient = C_F(x, reynolds)\n",
    "U_t = U_tau(U, coefficient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "3ed4fbca",
   "metadata": {},
   "outputs": [],
   "source": [
    "l = nu / U_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "914da35e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.3126926430504054e-05"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5 * l"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aac15ef7",
   "metadata": {},
   "source": [
    "# q8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "6c59cc2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "chord = 0.5\n",
    "re_t = 3e5\n",
    "rho = 1.225\n",
    "nu = 1.5e-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "e6ab0b04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f91afa30820>]"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "laminar = pd.read_excel(\"LBLdata2.xlsx\")\n",
    "aa, ab = laminar.columns\n",
    "y=laminar[aa]\n",
    "u=laminar[ab]\n",
    "plt.plot(u, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "ba82cd75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.492929975\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "38.645710040000004"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U_inf = u.max()\n",
    "frac = u/U_inf\n",
    "\n",
    "theta = np.trapz(frac * (1-frac), y)\n",
    "print(theta)\n",
    "drag(rho, U_inf, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85cf6665",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}