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+{
+ "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": [
+ "# 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"
+ ],
+ "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": [
+ "# 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"
+ ],
+ "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": [
+ "# 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"
+ ],
+ "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": [
+ "# 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\""
+ ],
+ "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": [
+ "# 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\""
+ ],
+ "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": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 11:50:57 +0000