From 02ebf9776819227ee6052992b0a1df2b7856889c Mon Sep 17 00:00:00 2001 From: Toto Date: Fri, 19 Oct 2018 19:03:14 -0700 Subject: [PATCH 1/2] notebooks --- .../Ordinary Differential Equations.ipynb | 192 ++++++++++++++++-- 1 file changed, 175 insertions(+), 17 deletions(-) diff --git a/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb b/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb index c213aa0..9ba8ea5 100644 --- a/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb +++ b/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb @@ -58,32 +58,34 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Comparing Analytical solutions with Numerical Solver\n", + "## Comparing Analytical solutions with Numerical Solvers \n", + "### Stepsizes are important! \n", + "\n", + "When using numerical solvers, it is important to consider the step size that the solver is operating at. Discrete methods are stepsize dependent. The code below illustrates what happens to a simple ode solver at low and high step sizes compared to the analytical equation.\n", "\n", - "Be\n", "\n" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 1, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -95,7 +97,7 @@ "\n", "import matplotlib.pyplot as plt \n", "import numpy as np\n", - "from scipy import integrate\n", + "from scipy.integrate import odeint\n", "%matplotlib inline\n", "\n", "y0 = 0.1 \n", @@ -106,12 +108,19 @@ "\n", "## using simple RK method\n", "t = np.linspace(0,tot,stepsize) # creating a time vector\n", + "t2 = np.linspace(0,tot,stepsize*50) # creating a time vector\n", "dt = t[1]-t[0] # establishing dt\n", + "dt2 = t2[1]-t2[0] # establishing dt\n", "y = np.zeros(len(t)) # creating a Cell density vector \n", + "y2 = np.zeros(len(t2)) # creating a Cell density vector \n", "y[0] = y0\n", + "y2[0] = y0\n", + "\n", "\n", "for i in range (1, len(t)):\n", " y[i] = y[i-1] + ug*y[i-1]*dt\n", + "for i in range (1, len(t2)):\n", + " y2[i] = y2[i-1] + ug*y2[i-1]*dt2\n", "\n", "## using analytical solution \n", " X = np.exp(ug*(t))*y0\n", @@ -120,31 +129,110 @@ "plt.xlabel('time,h')\n", "plt.ylabel('Cell density (g/L)')\n", "plt.title ('Comparing Analytical solution to RK')\n", - "plt.plot(t,y,'-x',label='Numerical')\n", + "plt.plot(t,y,'-x',label='Numerical step = 10')\n", + "plt.plot(t2,y2,'-x',label='Numerical step = 500')\n", "plt.plot(t,X,'-or',label = 'Analytical')\n", "plt.legend()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using Scipy's ODE solver\n", + "\n", + "More complicated ODE solvers can be derived and have been. One of the common solvers comes from SciPy's Integrate library. The function is called ```odeint ```. More can be read about the numerical method here: [Adams-Bashforths method](https://www.math.utah.edu/~vshankar/5620/LinearMultistepI.pdf)\n", + "\n", + "```odeint``` takes the following arguements ```odeint(function,intial_value,time_vector) ```. It is important to note that the function to input into python is an actual python function that returns the derivative of the system. \n", + "\n", + "Using the cell growth model for the last time... A function is created to return the derivative of the cell growth: $ \\frac{dX}{dt} = \\mu _g X $" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "ug = 0.5 \n", + "def dxdt(X,t):\n", + " return ug*X" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, a time vector is created and the initial concentration is set." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "tfinal = 12 \n", + "time = np.linspace(0,tfinal,200) # from 0 hours to 20 hours in 200 intervals \n", + "y0 = 2 # initial cell concentration is 2 g/L" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These values are subsequently input into the ```odeint``` function, which is stored into a vector and plotted out. " + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "After 12 hours, the final cell density is [806.85766419] g/L\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = odeint(dxdt,y0,time)\n", + "plt.plot(time,X)\n", + "print (\"After {} hours, the final cell density is {} g/L\".format(tfinal,X[-1]) )" + ] + }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 4, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -152,12 +240,12 @@ } ], "source": [ - "C0 = 50 # g/L\n", - "t = np.linspace(0,40,200) # minutes \n", + "C0 = 500 # g/L\n", + "t = np.linspace(0,100,200) # minutes \n", "dt= t[1]-t[0]\n", "\n", "def dcdt(C,t):\n", - " return (2.5-0.2333*C)\n", + " return (600/700-30/700*C)\n", "\n", "sol = integrate.odeint(dcdt,C0,t)\n", "\n", @@ -166,6 +254,76 @@ "plt.plot(t,sol)" ] }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "print(type(X))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "500" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(t2)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def dvdt(V,t):\n", + " return (-20)\n", + "vol = integrate.odeint(dvdt,700,t)\n", + "plt.plot(t,vol)" + ] + }, { "cell_type": "code", "execution_count": null, From 009de594649aede1400735b4cdb8c3cd66e91d5a Mon Sep 17 00:00:00 2001 From: ngai to Date: Sun, 21 Oct 2018 23:18:25 -0700 Subject: [PATCH 2/2] Ode tutorial is 'playable' will add system of ODE at later time ' --- .../Tutorial_2 Algebraic Systems.ipynb | 14 +- ...ry Differential Equations-checkpoint.ipynb | 164 ++++++++++++++++-- .../Ordinary Differential Equations.ipynb | 160 +++++++---------- 3 files changed, 221 insertions(+), 117 deletions(-) diff --git a/Notebooks/Tutorial 2/Tutorial_2 Algebraic Systems.ipynb b/Notebooks/Tutorial 2/Tutorial_2 Algebraic Systems.ipynb index 5606e1a..8475b6b 100644 --- a/Notebooks/Tutorial 2/Tutorial_2 Algebraic Systems.ipynb +++ b/Notebooks/Tutorial 2/Tutorial_2 Algebraic Systems.ipynb @@ -49,7 +49,9 @@ { "cell_type": "code", "execution_count": 56, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Import relevant packages\n", @@ -269,7 +271,9 @@ { "cell_type": "code", "execution_count": 62, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "A3 = np.array([[1,1,1],[2,1,1],[-1,2,4],[1,2,5]])\n", @@ -370,7 +374,9 @@ { "cell_type": "code", "execution_count": 87, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Now let's find the solution:\n", @@ -432,7 +438,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.4" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/Notebooks/Tutorial 5/.ipynb_checkpoints/Ordinary Differential Equations-checkpoint.ipynb b/Notebooks/Tutorial 5/.ipynb_checkpoints/Ordinary Differential Equations-checkpoint.ipynb index c213aa0..66c18a3 100644 --- a/Notebooks/Tutorial 5/.ipynb_checkpoints/Ordinary Differential Equations-checkpoint.ipynb +++ b/Notebooks/Tutorial 5/.ipynb_checkpoints/Ordinary Differential Equations-checkpoint.ipynb @@ -58,9 +58,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Comparing Analytical solutions with Numerical Solver\n", + "## Comparing Analytical solutions with Numerical Solvers \n", + "### Stepsizes are important! \n", + "\n", + "When using numerical solvers, it is important to consider the step size that the solver is operating at. Discrete methods are stepsize dependent. The code below illustrates what happens to a simple ode solver at low and high step sizes compared to the analytical equation.\n", "\n", - "Be\n", "\n" ] }, @@ -72,7 +74,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 1, @@ -81,9 +83,9 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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hrSTev9b2Jl76kt0XFBYQvYm9lUsgMMYsMcZc7ywfMcb0N8a0NcZcZYw5Wh5p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\nd8r96xRV/CHgCrbzBhz6JaCagfoa2mH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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -95,7 +97,7 @@ "\n", "import matplotlib.pyplot as plt \n", "import numpy as np\n", - "from scipy import integrate\n", + "from scipy.integrate import odeint\n", "%matplotlib inline\n", "\n", "y0 = 0.1 \n", @@ -106,12 +108,19 @@ "\n", "## using simple RK method\n", "t = np.linspace(0,tot,stepsize) # creating a time vector\n", + "t2 = np.linspace(0,tot,stepsize*50) # creating a time vector\n", "dt = t[1]-t[0] # establishing dt\n", + "dt2 = t2[1]-t2[0] # establishing dt\n", "y = np.zeros(len(t)) # creating a Cell density vector \n", + "y2 = np.zeros(len(t2)) # creating a Cell density vector \n", "y[0] = y0\n", + "y2[0] = y0\n", + "\n", "\n", "for i in range (1, len(t)):\n", " y[i] = y[i-1] + ug*y[i-1]*dt\n", + "for i in range (1, len(t2)):\n", + " y2[i] = y2[i-1] + ug*y2[i-1]*dt2\n", "\n", "## using analytical solution \n", " X = np.exp(ug*(t))*y0\n", @@ -120,31 +129,144 @@ "plt.xlabel('time,h')\n", "plt.ylabel('Cell density (g/L)')\n", "plt.title ('Comparing Analytical solution to RK')\n", - "plt.plot(t,y,'-x',label='Numerical')\n", + "plt.plot(t,y,'-x',label='Numerical step = 10')\n", + "plt.plot(t2,y2,'-x',label='Numerical step = 500')\n", "plt.plot(t,X,'-or',label = 'Analytical')\n", "plt.legend()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using Scipy's ODE solver\n", + "\n", + "More complicated ODE solvers can be derived and have been. One of the common solvers comes from SciPy's Integrate library. The function is called ```odeint ```. More can be read about the numerical method here: [Adams-Bashforths method](https://www.math.utah.edu/~vshankar/5620/LinearMultistepI.pdf)\n", + "\n", + "```odeint``` takes the following arguements ```odeint(function,intial_value,time_vector) ```. It is important to note that the function to input into python is an actual python function that returns the derivative of the system. \n", + "\n", + "Using the cell growth model for the last time... A function is created to return the derivative of the cell growth: $ \\frac{dX}{dt} = \\mu _g X $" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "ug = 0.5 \n", + "def dxdt(X,t):\n", + " return ug*X" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, a time vector is created and the initial concentration is set." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "tfinal = 12 \n", + "time = np.linspace(0,tfinal,200) # from 0 hours to 20 hours in 200 intervals \n", + "y0 = 2 # initial cell concentration is 2 g/L" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These values are subsequently input into the ```odeint``` function, which is stored into a vector and plotted out. " + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "After 12 hours, the final cell density is [ 806.85766419] g/L\n" + ] + }, { "data": { + "image/png": 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G8ifTLmTiBQMZnx/5ys1OD/EKRGJPQS8JpbW9g+ojJ6k8dILKQ8epOnyCqkMn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\n", "text/plain": [ - "[]" + "" ] }, - "execution_count": 4, "metadata": {}, - "output_type": "execute_result" + "output_type": "display_data" + } + ], + "source": [ + "X = odeint(dxdt,y0,time)\n", + "plt.plot(time,X)\n", + "print (\"After {} hours, the final cell density is {} g/L\".format(tfinal,X[-1]) )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem 1: \n", + "\n", + "A tank of $ 700 L $ contains a solution of $ 50 \\frac{g}{L} $ NaOH. 2 inlet valves and 1 oulet valve are opened. One inlet have inputs a solution of $ 12 \\frac{g}{L} $ at $ 10 \\frac{L}{hr} $. The other inlet stream is pure water running at $ 15 \\frac{L}{hr} $. The outlet stream is set to maintain an equal flow to that of the inlet streams. \n", + "\n", + "Plot the concentration of the tank as a function of time. What concentration of NaOH will the tank have at 30hrs?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution: \n", + "\n", + "Let $ x_1 $ be the concentration of NaOH at the exit stream. Setting up the differential:\n", + "\n", + "$$ \\dot m_{out} = 10 + 15 = 25 \\frac{L}{hr} $$ \n", + "\n", + "\n", + "$$ \\frac{d(Vx)}{dt} = (12)*(10) + (0)*(15) - (x_1)(25) $$ \n", + "\n", + "Since V is held constant: \n", + "\n", + "$$ \\frac{d(x)}{dt} = \\frac{(12)*(10)}{V} + \\frac{(0)*(15)}{V} - \\frac{(x_1)(25)}{V} $$ \n", + "\n", + "$$ \\frac{d(x)}{dt} = \\frac{(12)*(10)}{700} + \\frac{(0)*(15)}{700} - \\frac{(x_1)(25)}{700} $$ \n", + "\n", + "Coupled with the initial Concentration $ C_0 = 50 $, the ODE can be solved. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 4.8]\n" + ] }, { "data": { - "image/png": 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MioFfAje6+37gh8AZQD2wC7itj+ctNrNGM2tsbm4ehsgjLxox/va8KbyydS8rt7eFHUdEpFcJFbqZ5RIv8/vc/REAd9/t7l3uHgN+BCzo7bnufqe7N7h7Q1VV1XDlHnHXNNRSkp/D//vj5rCjiIj0KpGjXAy4C1jr7t/ttrym22ofAlYPf7zUUVKQy9+cN5knVu9iY5N+aCQiqSeRPfTzgU8Bi3ocovhvZrbKzFYCFwP/I5lBU8Fnzp9CQU6U/3huY9hRREROkdPfCu7+AmC9PJSRhymeTkVxPp88dxJ3/3krN14yg0kVhWFHEhE5Qb8UHaDPXjiVaMT44R+1ly4iqUWFPkDVpQX814aJPLx0OzvbjoQdR0TkBBX6IHzuoqm4ww+f2xR2FBGRE1Tog1A7upBrzpnIA6+8yZuth8OOIyICqNAH7YZLphMx4/an14cdRUQEUKEPWnVpAZ8+fwq/Wr6Dtbv2hx1HRESFPhSfv+gMSvJz+F9/eD3sKCIiKvShKCvM5fPvmcaz65r465Y9YccRkSynQh+ivz2vjurSfL7xxFpiOl+6iIRIhT5Eo/KifO2yWazY1sYjr+4IO46IZDEV+jC4un4CZ08q59u/W6drj4pIaFTowyASMW79L2fSeqid7z+rUwKISDhU6MNk3sRyrnnnRO5+cQubmnV6XREZeSr0YfTVy2ZSkBPl1l+vwV1fkIrIyFKhD6PK4ny+8v6ZPL+hhUf1BamIjDAV+jD71MLJzJ9Uzr88/hotB9vDjiMiWUSFPswiEeM7H5nLofZO/uU3r4UdR0SySCLXFJ1oZkvMbK2ZrTGzG4LlY8zsKTPbENyPTn7c9DC9uoQvXDyNX6/YybPrdocdR0SyRCJ76J3Al919NrAQ+IKZzQFuBp5x9+nAM8G8BP77e6Yxo7qYf3hkNW2HO8KOIyJZoN9Cd/dd7r4smD4ArAUmAB8E7g1Wuxe4Olkh01FeToTbPlZPy8F2/vHR1TrqRUSSbkBj6GZWB5wNvAxUu/suiJc+MLaP5yw2s0Yza2xubh5a2jRzVm0ZX3rfDH67ahe/XKajXkQkuRIudDMrBn4J3OjuCZ8A3N3vdPcGd2+oqqoaTMa09rkLz2DBlDH882OrdXUjEUmqhArdzHKJl/l97v5IsHi3mdUEj9cATcmJmN6iEeO718wjEjFufPBVjnXFwo4kIhkqkaNcDLgLWOvu3+320K+B64Lp64DHhj9eZqgdXci3PnwWy95s45tPrA07johkqJwE1jkf+BSwysyWB8v+Afg28JCZXQ+8CXwsOREzw5Vzx7P0jb3c/eJWzp40mqvmjQ87kohkmH4L3d1fAKyPhy8Z3jiZ7ZYPzGbl9n3c/MuVzB5XwvTqkrAjiUgG0S9FR1BeToQ7PjGfwrwon/v5UvYd1rnTRWT4qNBH2LiyAu74xHy27TnM5+9bqi9JRWTYqNBDcO7UCr714bn8eVMr//Qr/ehIRIZHIl+KShJ89J21bGk5yB1LNjGlsojPXXRG2JFEJM2p0EP05ffOZGvLYb71u3VUFufzkXfWhh1JRNKYCj1EkYhx2zXz2Hu4g5t+uZKSghzed+a4sGOJSJrSGHrICnKj3Pk3DZw1oYwv/uJVXtzYEnYkEUlTKvQUUJyfwz2fPocplUV89qeN/GVTa9iRRCQNqdBTRHlhHj/7uwVMKB/Fp+/5Ky9s0J66iAyMCj2FjC0p4P7FC6mrKOIz977CknU635mIJE6FnmIqi/O5/7MLmT62mMU/a+Sx5TqPuogkRoWegkYX5fGLzy7k7EmjueGB5dz5p0368ZGI9EuFnqLKRuXy088s4Iq5NXzziXV8/Tev0RVTqYtI33QcegoryI3y/WvPZlxpAXe9sIXNLYf4/rVnU1aYG3Y0EUlB2kNPcZGI8U9XzuFbHz6Lv2xq4ao7XmD97gNhxxKRFKRCTxMfXzCJ+z+7kEPtXXzojhf1ZamInCKRS9D9xMyazGx1t2W3mtkOM1se3C5PbkwBaKgbw+N/fwGzakq54YHl3PTwCg53dIYdS0RSRCJ76PcAl/Wy/HZ3rw9uTwxvLOnLuLICHly8kC9ePI3/XLqdq37wIqt37As7loikgH4L3d3/BOwZgSySoJxohK+8fyb3XX8uB44e44N3vMhtT75OR6culiGSzYYyhv5FM1sZDMmM7mslM1tsZo1m1tjc3DyEt5OezptWyZM3XsTV9RP4/rMbueoHL7Dszb1hxxKRkAy20H8InAHUA7uA2/pa0d3vdPcGd2+oqqoa5NtJX8oKc7ntmnncdV0DbYeP8eH/+DM3PbyCloPtYUcTkRE2qEJ3993u3uXuMeBHwILhjSUDdcnsap758kV87qKpPLJsBxf/7+e458UtdOqapSJZY1CFbmY13WY/BKzua10ZOUX5Odzygdn8/sYLmVdbzq2/eY3L//15/rDmLZ06QCQLWH9/0c3sfuA9QCWwG/jnYL4ecGAr8Dl339XfmzU0NHhjY+OQAkti3J0/rHmL7/z+dba0HGJubRlfft9MLpxeiZmFHU9EBsDMlrp7Q7/rjeSemwp95HV2xXjk1R38n6c3sKPtCAvqxvD3l0zjgmkqdpF0oUKXk7R3dvHQK9v4/rMbaTrQzqxxJfzdu6dy1bzx5OXoB8MiqUyFLr1q7+ziseU7uev5Lby++wBjS/K57rw6rmmYSFVJftjxRKQXKnQ5LXfnTxta+PHzm3l+Qws5EeOS2WO59pxJXDijimhEwzEiqSLRQtfpc7OUmXHRjCoumlHFpuaDPPTKNh5eup0/rNnNuNICPjR/AlfOrWFOTanG2kXShPbQ5YSOzhjPrtvNA69s4/kNLXTFnKmVRVw5t4Yr5o5nRnWxyl0kBBpykSHZc6iD369+i8dX7uSlza3EHCaNKWTRrLEsmjWWc6eOIT8nGnZMkaygQpdh03TgKE+u2c2z65p4cWML7Z0xCvOinHdGBQunxm+za0o17i6SJCp0SYqjx7r4y6ZWnlm3mxc3trKl5RAApQU5LJhSwcKpYzh3SgUzx5XocEiRYaIvRSUpCnKjXDxrLBfPGgvAW/uO8vKWVl7a3MpLm/fw9NrdAOTlRJhTU8q82jLm1pYzb2IZUyuLiWgvXiRptIcuw2rXviMsfWMvK7fvY8W2Nlbv2Mehji4AivKiTK8uYWZ1CTPGHb8vpqo4X1+2ipyGhlwkJXTFnM3NB1mxfR+rd+zj9bcO8PruA+w51HFinfLCXOoqiqirKGRScD85uB9TlKeyl6ynQpeU1nKwnfVBua/ffZA3Wg/xRuthdu47Qvc/ksX5OdSOHsX48lGMKyugprSAcWUFb8+XFVCYp5FDyWwaQ5eUVlmcT+W0fM6bVnnS8vbOLrbvPcIbrYfY2nKYN/ccZtuew+zad5Tl29pO2rM/rigvSkVxPhXFeVQU5VFRFEwX51NZHJ8vL8ylbFQupQW5FBfk6IgcyUgqdEkp+TlRzqgq5oyq4l4fP3qsi937j7Kz7Shv7T/CzrajtB7soPVQO60HO9i+9wgrt++j9VAHXbG+//VZkp9D6ahcSgri96UFuZSOyqG0IJei/CiFeTkU5kUpysthVF6Uwry3lxXmRSnMz6EwN0phfpS8aETDQpISVOiSVgpyo0yuKGJyRdFp14vFnP1Hj9FysIPWg+20HTnG/iPH2H+0M7g/xv4jncH9MbbvPcyBXfHHDnV0cprPglOYQV40Qn5OhLycKPk5x6e730d7zMfv86JRcqJGNGLkRoxoJEJO1MiJBMuiEaKR+HxONBLcH3/81HUjFp+OGETMsOA+foNIpNt0z8cjJ69r3daLRk59LX2IpR4VumSkSMQoL8yjvDCPaWN739vvi7vT3hnjcEcXhzs6OdLRxaEe00c6OoPHuzh6rIuOzhjtwS0+/fayjs4Yhzs6aTsSo/1YjI6u2EmPdcZidMWcY13pd1UpM7AT04YFywCMtx+0E+vaSc87/qFgwf9Oeq3TvDb0fLzv1z6xrFuunp9FPT+aevuwOmVJP6/R83W++aGzWDBlTC9rDZ9+C93MfgJcCTS5+zuCZWOAB4E64lcsusbddbl5yQhmRkFulILcKGOK8kb0vbtiflLBd8Wczq4YnTEPlsWCdZzOrvi6x6ePP9cdYu7EgnsPprtiHsyf+nhX7OR1jz8ef+zU14q5E4s5xz+C3MHxE19oe7AsPu0E/wXrerB+7889sU6/r+1vP97tvXp7bU567skfnD0/Rns7TuTUdU7/Gr0tLMpP/qkyEtlDvwf4AfDTbstuBp5x92+b2c3B/NeGP55IdolGjGhE58iRwen3t9nu/idgT4/FHwTuDabvBa4e5lwiIjJAgz3ZRvXxi0IH92OHL5KIiAxG0s+eZGaLzazRzBqbm5uT/XYiIllrsIW+28xqAIL7pr5WdPc73b3B3RuqqqoG+XYiItKfwRb6r4HrgunrgMeGJ46IiAxWv4VuZvcDfwFmmtl2M7se+DbwXjPbALw3mBcRkRD1e9iiu3+8j4cuGeYsIiIyBLqkjIhIhhjR0+eaWTPwxiCfXgm0DGOc4aJcA6NcA6NcA5OquWBo2Sa7e79HlYxooQ+FmTUmcj7gkaZcA6NcA6NcA5OquWBksmnIRUQkQ6jQRUQyRDoV+p1hB+iDcg2Mcg2Mcg1MquaCEciWNmPoIiJyeum0hy4iIqeRFoVuZpeZ2etmtjE4/3pKMLOtZrbKzJabWWOIOX5iZk1mtrrbsjFm9pSZbQjuR6dIrlvNbEewzZab2eUh5JpoZkvMbK2ZrTGzG4LloW6z0+QKdZuZWYGZ/dXMVgS5vh4sn2JmLwfb60EzG9GrgZwm1z1mtqXb9qofyVzd8kXN7FUzezyYT/728uAqJKl6A6LAJmAqkAesAOaEnSvIthWoTIEcFwLzgdXdlv0bcHMwfTPwnRTJdSvwlZC3Vw0wP5guAdYDc8LeZqfJFeo2I351teJgOhd4GVgIPARcGyz/v8DnUyTXPcBHw/wzFmT6EvAL4PFgPunbKx320BcAG919s7t3AA8Qv8CGBDxFL0LSR67Qufsud18WTB8A1gITCHmbnSZXqDzuYDCbG9wcWAQ8HCwPY3v1lSt0ZlYLXAH8OJg3RmB7pUOhTwC2dZvfTgr8IQ848KSZLTWzxWGH6SGVL0LyRTNbGQzJjPhQUHdmVgecTXzvLmW2WY9cEPI2C4YPlhM/VfZTxP/V3ObuncEqofy97JnL3Y9vr28E2+t2M8sf6VzA94CbgFgwX8EIbK90KPTeLqadEp/CwPnuPh/4APAFM7sw7EBp4IfAGUA9sAu4LawgZlYM/BK40d33h5Wjp15yhb7N3L3L3euBWuL/ap7d22ojm+rUXGb2DuAWYBZwDjCGEb7esZldCTS5+9Lui3tZddi3VzoU+nZgYrf5WmBnSFlO4u47g/sm4FHif9BTRcIXIRlJ7r47+EsYA35ESNvMzHKJl+Z97v5IsDj0bdZbrlTZZkGWNuA54mPV5WZ2/Iytof697JbrsmDoyt29Hbibkd9e5wNXmdlW4kPEi4jvsSd9e6VDob8CTA++Ic4DriV+gY1QmVmRmZUcnwbeB6w+/bNGVEpehOR4YQY+RAjbLBjPvAtY6+7f7fZQqNusr1xhbzMzqzKz8mB6FHAp8fH9JcBHg9XC2F695VrX7UPZiI9Tj+j2cvdb3L3W3euI99Wz7v5JRmJ7hf1NcILfFl9O/Bv/TcA/hp0nyDSV+BE3K4A1YeYC7if+T/FjxP9Fcz3xMbtngA3B/ZgUyfUzYBWwkniB1oSQ6wLi/9xdCSwPbpeHvc1OkyvUbQbMBV4N3n818D+D5VOBvwIbgf8E8lMk17PB9loN/JzgSJgwbsB7ePsol6RvL/1SVEQkQ6TDkIuIiCRAhS4ikiFU6CIiGUKFLiKSIVToIiIZQoUuIpIhVOgiIhlChS4ikiH+PxXgYEedFVsNAAAAAElFTkSuQmCC\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -152,24 +274,30 @@ } ], "source": [ + "\n", + "\n", "C0 = 50 # g/L\n", - "t = np.linspace(0,40,200) # minutes \n", + "t = np.linspace(0,1050,200) # minutes \n", "dt= t[1]-t[0]\n", "\n", "def dcdt(C,t):\n", - " return (2.5-0.2333*C)\n", + " return (120/700-25/700*C)\n", "\n", - "sol = integrate.odeint(dcdt,C0,t)\n", + "sol = odeint(dcdt,C0,t)\n", "\n", "\n", "# print(t)\n", - "plt.plot(t,sol)" + "plt.plot(t,sol)\n", + "\n", + "print(sol[-1])" ] }, { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [] } @@ -190,7 +318,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.4" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb b/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb index 9ba8ea5..66c18a3 100644 --- a/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb +++ b/Notebooks/Tutorial 5/Ordinary Differential Equations.ipynb @@ -68,24 +68,24 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 15, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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hrSTev9b2Jl76kt0XFBYQvYm9lUsgMMYsMcZc7ywfMcb0N8a0NcZcZYw5Wh5p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\nYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -150,8 +150,10 @@ }, { "cell_type": "code", - "execution_count": 16, - "metadata": {}, + "execution_count": 2, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "ug = 0.5 \n", @@ -168,8 +170,10 @@ }, { "cell_type": "code", - "execution_count": 23, - "metadata": {}, + "execution_count": 3, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "tfinal = 12 \n", @@ -186,21 +190,21 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "After 12 hours, the final cell density is [806.85766419] g/L\n" + "After 12 hours, the final cell density is [ 806.85766419] g/L\n" ] }, { "data": { - "image/png": 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\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -214,103 +218,55 @@ ] }, { - "cell_type": "code", - "execution_count": 31, + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ - "C0 = 500 # g/L\n", - "t = np.linspace(0,100,200) # minutes \n", - "dt= t[1]-t[0]\n", + "## Problem 1: \n", "\n", - "def dcdt(C,t):\n", - " return (600/700-30/700*C)\n", + "A tank of $ 700 L $ contains a solution of $ 50 \\frac{g}{L} $ NaOH. 2 inlet valves and 1 oulet valve are opened. One inlet have inputs a solution of $ 12 \\frac{g}{L} $ at $ 10 \\frac{L}{hr} $. The other inlet stream is pure water running at $ 15 \\frac{L}{hr} $. The outlet stream is set to maintain an equal flow to that of the inlet streams. \n", "\n", - "sol = integrate.odeint(dcdt,C0,t)\n", + "Plot the concentration of the tank as a function of time. What concentration of NaOH will the tank have at 30hrs?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution: \n", "\n", + "Let $ x_1 $ be the concentration of NaOH at the exit stream. Setting up the differential:\n", "\n", - "# print(t)\n", - "plt.plot(t,sol)" + "$$ \\dot m_{out} = 10 + 15 = 25 \\frac{L}{hr} $$ \n", + "\n", + "\n", + "$$ \\frac{d(Vx)}{dt} = (12)*(10) + (0)*(15) - (x_1)(25) $$ \n", + "\n", + "Since V is held constant: \n", + "\n", + "$$ \\frac{d(x)}{dt} = \\frac{(12)*(10)}{V} + \\frac{(0)*(15)}{V} - \\frac{(x_1)(25)}{V} $$ \n", + "\n", + "$$ \\frac{d(x)}{dt} = \\frac{(12)*(10)}{700} + \\frac{(0)*(15)}{700} - \\frac{(x_1)(25)}{700} $$ \n", + "\n", + "Coupled with the initial Concentration $ C_0 = 50 $, the ODE can be solved. " ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "\n" + "[ 4.8]\n" ] - } - ], - "source": [ - "print(type(X))" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "500" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(t2)" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -318,16 +274,30 @@ } ], "source": [ - "def dvdt(V,t):\n", - " return (-20)\n", - "vol = integrate.odeint(dvdt,700,t)\n", - "plt.plot(t,vol)" + "\n", + "\n", + "C0 = 50 # g/L\n", + "t = np.linspace(0,1050,200) # minutes \n", + "dt= t[1]-t[0]\n", + "\n", + "def dcdt(C,t):\n", + " return (120/700-25/700*C)\n", + "\n", + "sol = odeint(dcdt,C0,t)\n", + "\n", + "\n", + "# print(t)\n", + "plt.plot(t,sol)\n", + "\n", + "print(sol[-1])" ] }, { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [] } @@ -348,7 +318,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.4" + "version": "3.6.1" } }, "nbformat": 4,