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diff --git a/Fluid_Mechanics/Chapter7.ipynb b/Fluid_Mechanics/Chapter7.ipynb new file mode 100755 index 00000000..baafd643 --- /dev/null +++ b/Fluid_Mechanics/Chapter7.ipynb @@ -0,0 +1,367 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:efc6f8f4cd32e5126c4de163e157356596c0806f949ff4295acc9cf31cf6d207" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Chapter 7 : Fluid Resistance" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.1 Page no 245" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\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", + "\n", + "rho = 995.7 # density in kg/m**3\n", + "\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", + "\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" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "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" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.2 Page no 248" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\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", + "\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" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.7/y\n", + "Turbulence constant = 0.46\n", + "Mixing length = 13.8 cm\n", + "Eddy viscosity = 44.1 Nm/s**2\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.3 Page no 256" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\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", + "\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", + "\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.plot(x, d, 'r')\n", + "plt.xlabel('x(m)')\n", + "plt.ylabel('delta(cm),tauo(N/m**2)')\n", + "\n", + "plt.plot(x, tauo, 'b')\n", + "plt.xlabel('x')\n", + "plt.legend('d''t')\n", + "plt.show()\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.4 page no 260" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\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", + "\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", + "\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\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total Drag = 0.595 N\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.5 Page no 270" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import *\n", + "\n", + "from pylab import plt\n", + "\n", + "from __future__ import division\n", + "\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", + "\n", + "R = rho*v*d/mu\n", + "\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\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Drag on the sphere = 0.0043 N\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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