{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gravity Drain Tank Modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pysketcher import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import HTML, SVG, display, clear_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact, FloatSlider, Button"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import pi\n",
    "import numpy as np\n",
    "from ipywidgets import VBox, FloatSlider, Output, Button, Label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experiment, Simulation (x10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "myfig={}\n",
    "sketch = Sketch(myfig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sketch.file2Sketch(\"drainingtank.yml\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tank(h):\n",
    "    sketch.container['h'] = h\n",
    "    sketch.refresh('interieur')\n",
    "    sketch.refresh('contenu')\n",
    "    sketch.refresh('hc')\n",
    "    sketch.refresh('V')\n",
    "    sketch.refresh('Y')\n",
    "    sketch.refresh('jet')\n",
    "    sketch.refresh('dim')\n",
    "    sketch.refresh('tank')\n",
    "    drawing_tool.erase()\n",
    "    sketch.container['tank'].draw()\n",
    "    display(SVG(Sketch.matplotlib2SVG()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b45518327af34b0b8f3eb769326c7b3d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.5, description='h', max=2.0, min=0.12), Output()), _dom_classes=('wi…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.tank(h)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "024ee43ca2594a5b93ecccfc213eed8d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Simulate', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = FloatSlider(min=sketch.container['d_o']*1.2, max=sketch.container['H'], step=0.1, value=sketch.container['h'])\n",
    "b = Button(description=\"Simulate\")\n",
    "i = interact(tank, h=w)\n",
    "display(i,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xSIqWFm93OPg",
    "nbpages": {
     "level": 2,
     "link": "[2.2.2 Torricelli's law](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.2-Torricelli's-law)",
     "section": "2.2.2 Torricelli's law"
    }
   },
   "source": [
    "## Torricelli's law\n",
    "\n",
    "Torricelli's law states the velocity of an incompressible liquid stream exiting a liquid tank at level $h$ below the surface is \n",
    "\n",
    "$$v = \\sqrt{2gh}$$ \n",
    "\n",
    "This is the same velocity as an object dropped from a height $h$. The derivation is straightforward. From Bernoulli's principle,\n",
    "\n",
    "$$\\frac{v^2}{2} + gh + \\frac{P}{\\rho} = \\text{constant}$$\n",
    "\n",
    "Applying this principle, compare a drop of water just below the surface of the water at distance $h$ above the exit, to a drop of water exiting the tank\n",
    "\n",
    "$$gh + \\frac{P_{atm}}{\\rho} = \\frac{v^2}{2} + \\frac{P_{atm}}{\\rho}$$\n",
    "\n",
    "$$\\implies v^2 = 2gh$$\n",
    "$$\\implies v = \\sqrt{2gh}$$\n",
    "\n",
    "Torricelli's law is an approximation that doesn't account for the effects of fluid viscosity, the specific flow geometry near the exit, or other flow non-idealities. Nevertheless it is a useful first approximation for flow from a tank."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "H8dmoxAJ3OPk",
    "nbpages": {
     "level": 2,
     "link": "[2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.3-Mass-Balance-for-Tank-with-Constant-Cross-Sectional-Area)",
     "section": "2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area"
    }
   },
   "source": [
    "# Mass Balance for Tank with Constant Cross-Sectional Area\n",
    "\n",
    "For a tank with constant cross-sectional area, such as a cylindrical or rectangular tank, the liquid height is described by a differential equation\n",
    "\n",
    "$$A\\frac{dh}{dt} = q_{in}(t) - q_{out}(t)$$\n",
    "\n",
    "where $$q_{out}$$ is a function of liquid height. Torricelli's law tells the outlet flow from the tank is proportional to square root of the liquid height\n",
    "\n",
    "$$ q_{out}(h) = C_v\\sqrt{h} $$\n",
    "\n",
    "Dividing by area we obtain a nonlinear ordinary differential equation \n",
    "\n",
    "$$ \\frac{dh}{dt} = - \\frac{C_V}{A}\\sqrt{h} + \\frac{1}{A}q_{in}(t) $$\n",
    "\n",
    "in our standard form where the LHS derivative appears with a constant coefficient of 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Equation Solving"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construction parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "A   = pi * sketch.container['l']**2 / 4              # Tank area [meter^2]\n",
    "h0 = sketch.container['h']-sketch.container['d_o']   # tank initial height\n",
    "Cv  = 0.1/60                                         # Outlet valve constant [cubic meters/sec/meter^1/2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4\n"
     ]
    }
   ],
   "source": [
    "print(h0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Physical Constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = sketch.container['g']                         # gravity constant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Horizon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "horizon = 10 * 60   # simulation period"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qYEqVEsU3OPv",
    "nbpages": {
     "level": 3,
     "link": "[2.2.4.2 Step 2. Define parameters](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.2-Step-2.-Define-parameters)",
     "section": "2.2.4.2 Step 2. Define parameters"
    }
   },
   "source": [
    "## System Solving"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "nuIhX1VO3OPy",
    "nbpages": {
     "level": 3,
     "link": "[2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.3-Step-3.-Write-Functions-for-the-RHS-of-the-Differential-Equations)",
     "section": "2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations"
    }
   },
   "outputs": [],
   "source": [
    "# inlet flow rate in cubic meters/sec\n",
    "def qin(t):\n",
    "    return 0.0\n",
    "\n",
    "def deriv(h,t):\n",
    "    return qin(t)/A - Cv*np.sqrt(np.abs(h))/A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "HiA2HZcb3OP1",
    "nbpages": {
     "level": 3,
     "link": "[2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.4-Step-4.-Choose-an-Initial-Condition,-a-Time-Grid,-and-Integrate-the-Differential-Equation)",
     "section": "2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation"
    }
   },
   "outputs": [],
   "source": [
    "def solver():\n",
    "    global D,t,h,v0\n",
    "    D = 2 * np.sqrt(A/pi)\n",
    "    IC = [h0]\n",
    "    t = np.linspace(0,horizon,101)\n",
    "    h = odeint(deriv,IC,t)\n",
    "    v0 = np.sqrt(2*g*np.abs(h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "solver()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Animating Gravity Drain Tank"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulation(b):\n",
    "    global h, sketch, w\n",
    "    for hin in [hauteur for hauteur in h if hauteur > sketch.container['d_o']]:\n",
    "        w.value = hin\n",
    "        time.sleep(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "b.on_click(simulation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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