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| author | kinitrupti | 2017-05-12 18:53:46 +0530 |
|---|---|---|
| committer | kinitrupti | 2017-05-12 18:53:46 +0530 |
| commit | 6279fa19ac6e2a4087df2e6fe985430ecc2c2d5d (patch) | |
| tree | 22789c9dbe468dae6697dcd12d8e97de4bcf94a2 /Fluid_Mechanics_by_Irfan_A._Khan/Chapter7.ipynb | |
| parent | d36fc3b8f88cc3108ffff6151e376b619b9abb01 (diff) | |
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Removed duplicates
Diffstat (limited to 'Fluid_Mechanics_by_Irfan_A._Khan/Chapter7.ipynb')
| -rwxr-xr-x | Fluid_Mechanics_by_Irfan_A._Khan/Chapter7.ipynb | 428 |
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diff --git a/Fluid_Mechanics_by_Irfan_A._Khan/Chapter7.ipynb b/Fluid_Mechanics_by_Irfan_A._Khan/Chapter7.ipynb new file mode 100755 index 00000000..a8fa6c1f --- /dev/null +++ b/Fluid_Mechanics_by_Irfan_A._Khan/Chapter7.ipynb @@ -0,0 +1,428 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Chapter 7 : Fluid Resistance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 7.1 Page no 245" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Reynolds number for water = 7463.0\n", + "R > 2000 the flow is turbulent for water\n", + "\n", + "\n", + "Reynolds number for glycerine = 8.7\n", + "R < 2000 the flow is laminar for glycerine\n" + ] + } + ], + "source": [ + "# Is the flow laminar or turbulent\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "# Given\n", + "\n", + "nu1 = 0.804*10**-6 # viscosity in m**2/s\n", + "\n", + "V = 0.3 # velocity in m/s\n", + "\n", + "D = 0.02 # diameter in m/s\n", + "\n", + "# for water \n", + "\n", + "rho = 995.7 # density in kg/m**3\n", + "\n", + "# for gylcerine\n", + "\n", + "mu = 8620*10**-4 # viscosity in Ns/m**2\n", + "\n", + "S = 1.26 # specific gravity\n", + "\n", + "nu2 = mu/(S*rho) # viscosity of glycerine in Ns/m**2\n", + "\n", + "# Solution\n", + "\n", + "R1 = V*D/nu1\n", + "\n", + "print \"Reynolds number for water =\",round(R1,0)\n", + "\n", + "print \"R > 2000 the flow is turbulent for water\"\n", + "\n", + "print \"\\n\"\n", + "R2 = V*D/nu2\n", + "\n", + "print \"Reynolds number for glycerine =\",round(R2,1)\n", + "\n", + "print \"R < 2000 the flow is laminar for glycerine\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 7.2 Page no 248" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7/y\n", + "Turbulence constant = 0.46\n", + "Mixing length = 13.8 cm\n", + "Eddy viscosity = 44.1 Nm/s**2\n" + ] + } + ], + "source": [ + "# Eddy Viscosity; mixing length ; turbulence constant\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "from scipy import *\n", + "\n", + "import numpy as np\n", + "\n", + "from sympy import *\n", + "\n", + "y = Symbol('y')\n", + "\n", + "d = 0.0175 # diameter in m\n", + "\n", + "s = 0.3 # shear stress at a distance in m\n", + "\n", + "tau = 103 # shear stress in Pa\n", + "\n", + "rho = 1000 # density in kg/m**3\n", + "\n", + "#y = 0.3\n", + "\n", + "# solution\n", + "\n", + "Up = diff(8.5+0.7*log(y),y)\n", + "\n", + "print Up\n", + "\n", + "Up = (0.7/0.3) # for y = 0.3\n", + "\n", + "k = sqrt(tau/(rho*s**2*Up**2))\n", + "\n", + "print \"Turbulence constant = \",round(k,2)\n", + "\n", + "Ml = k*s*100 # mixing length\n", + "\n", + "print \"Mixing length = \",round(Ml,1),\"cm\"\n", + "\n", + "Eta = rho*(Ml/100)**2*Up\n", + "\n", + "print \"Eddy viscosity =\",round(Eta,1),\"Nm/s**2\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 7.3 Page no 256" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x446d2d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# PLot boundary layer distribution and total drag on the plate\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "from pylab import plt\n", + "\n", + "from numpy import *\n", + "\n", + "from scipy import *\n", + "\n", + "from sympy import *\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Given\n", + "\n", + "# for glycerine\n", + "\n", + "S = 1.26 # specific gravity \n", + "\n", + "mu = 0.862 # dynamic viscosity in Ns/m**2\n", + "\n", + "rho = S *1000 # density in kg/m**3\n", + "\n", + "K2 = 0.332\n", + "\n", + "V=1 # velocity in m/s\n", + "\n", + "# Solution\n", + "\n", + "# from blasius equation\n", + "\n", + "x = [0,0.1,0.5,1.0,2.0];\n", + "\n", + "d = 0.1307*np.sqrt(x)*100\n", + "\n", + "tauo = K2*rho*V**2/(sqrt(1462)*np.sqrt(x))\n", + "\n", + "#plt.figure()\n", + "plt.plot(x, d, 'r')\n", + "plt.xlabel('x(m)')\n", + "plt.ylabel('delta(cm),tauo(N/m**2)')\n", + "#plt.title('delta v/s x')\n", + "#plt.legend('d')\n", + "\n", + "plt.plot(x, tauo, 'b')\n", + "plt.xlabel('x')\n", + "#plt.ylabel('tauo(N/m**2)')\n", + "#plt.title('tauo v/s x(m)')\n", + "plt.legend('d''t')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 7.4 page no 260" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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2cRucf3ZGu4btcNbvLIsAUTUh2XUEpD1Ss1MxMXQirqRdQahPKNwaukkdiYhe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\nsRAQEWk5FgIiIi33f5w+Vkc37U5LAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x4e36b10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total Drag = 0.595 N\n" + ] + } + ], + "source": [ + "# Sketch the boundary layer and drag on the plate\n", + "\n", + "import numpy as np\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from numpy import sqrt\n", + "\n", + "# Given\n", + "\n", + "rho = 1.197 # air density in kg/m**3\n", + "\n", + "mu = 18.22*10**-6 # viscosity in Ns/m**2\n", + "\n", + "l = 5 # length of the plate\n", + "\n", + "V = 8 # velocity in m/s\n", + "\n", + "Rec = 5*10**5 # crictical reynolds number\n", + "\n", + "l1 = 0.951 # length from 0 to 0.951\n", + "\n", + "l2 = 5.0 # length from 0 to 5\n", + "\n", + "l3 = 0.951 # length from 0 to 0.951\n", + "\n", + "# Solution\n", + "\n", + "X = Rec/525576\n", + "\n", + "x = [0,0.1,0.3,0.6,0.951];\n", + "\n", + "d = 0.0069*np.sqrt(x)*100\n", + "\n", + "plt.figure()\n", + "plt.plot(x, d, 'r')\n", + "plt.xlabel('x(m)')\n", + "plt.ylabel('delta(cm)')\n", + "plt.title('delta v/s x')\n", + "plt.legend('L')\n", + "plt.show()\n", + "\n", + "X1 = [0.951,1.5,2.0,2.5,3.0,4.0,5.0]\n", + "\n", + "Dt = 0.0265*np.power(X1,(4/5))*100\n", + "\n", + "plt.figure()\n", + "plt.plot(X1, Dt, 'g')\n", + "plt.xlabel('x(m)')\n", + "plt.ylabel('delta(cm)')\n", + "plt.title('delta v/s x')\n", + "plt.legend('T')\n", + "plt.show()\n", + "\n", + "Td = 0.664*sqrt(mu*rho*V**3*l1)+0.036*rho*V**2*l2*(mu/(rho*V*l2))**0.2-0.036*rho*V**2*l3*(mu/(rho*V*l3))**0.2\n", + "\n", + "print \"Total Drag = \",round(Td,3),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 7.5 Page no 270" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Drag on the sphere = 0.0043 N\n" + ] + } + ], + "source": [ + "# Determine drag on the sphere\n", + "\n", + "from math import *\n", + "\n", + "from pylab import plt\n", + "\n", + "from __future__ import division\n", + "\n", + "# Given\n", + "\n", + "d = 0.01 # doameter of sphere in m\n", + "\n", + "v = 0.05 # velocity in m/s\n", + "\n", + "S = 1.26 # specific gravity\n", + "\n", + "mu = 0.826 # kinematic viscosity in Ns/m**2\n", + "\n", + "rho = S*1000 # density\n", + "\n", + "# Solution\n", + "\n", + "R = rho*v*d/mu\n", + "\n", + "# for the above rho\n", + "\n", + "Cd = 35\n", + "\n", + "Fd = 0.5*Cd*rho*v**2*pi*d**2/4\n", + "\n", + "print \"Drag on the sphere = \",round(Fd,4),\"N\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |