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diff --git a/Principles_Of_Fluid_Mechanics/ch11.ipynb b/Principles_Of_Fluid_Mechanics/ch11.ipynb new file mode 100644 index 00000000..c955d372 --- /dev/null +++ b/Principles_Of_Fluid_Mechanics/ch11.ipynb @@ -0,0 +1,284 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:bc810be53841861ce90eab0fd4e6714fb575581f40efe36263891984b30579a4" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11 : Forces on Immersed Bodies" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.1 Page No : 413" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "d = 1.2 \t\t \t#diameter - m\n", + "w = 1. \t \t\t #m\n", + "U = 60.*1000/3600 \t\t\t#speed - m/s\n", + "nu = 1.5e-5 \t\t\t#m**2/s\n", + "Cd = 0.4\n", + "rho = 1.22 \t\t \t#kg/m**3\n", + "\t\t\t\n", + "#calculations\n", + "Rn = U*d/nu\n", + "A = d*w\n", + "Fd = Cd*0.5*rho*U**2 *A\n", + "M = 0.5*Fd\n", + "\t\t\t\n", + "#results\n", + "print \"Bending moment = %.2f h**2 N m\"%(M)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Bending moment = 40.67 h**2 N m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.2 Page No : 415" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "d = 0.006 \t\t\t#diameter - m\n", + "U = 0.01 \t\t\t#m/s\n", + "gaml = 8000. \t\t#specific weight - N/m**3\n", + "gams = 7.9*10**3 *9.81\n", + "mu = 13.9 \n", + "\t\t\t\n", + "#calculations\n", + "mu = d**2 /18 *(gams - gaml)/U\n", + "RN = U*d*(gaml/9.81) /mu\n", + "\t\t\t\n", + "#results\n", + "print \"Viscosity of oil = %.1f Ns /m**2\"%(mu)\n", + "print \"Reynolds number of motion is = %.3f\"%RN\n", + "\n", + "# rounding off error. please check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Viscosity of oil = 13.9 Ns /m**2\n", + "Reynolds number of motion is = 0.004\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.3 Page No : 416" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\t\n", + "#Initialization of variables\n", + "s = 2.7\n", + "gamw = 9810. \t\t\t#N/m**3\n", + "mu = 0.001 \t\t\t#Ns/m**2\n", + "d = 0.15*10**-3 \t\t\t#m\n", + "rho = 1000. \t\t\t#kg/m**3\n", + "\t\t\t\n", + "#calculations\n", + "gams = s*gamw\n", + "U = d**2 *(gams-gamw)/(18*mu)\n", + "RN = U*d*rho/mu\n", + "Cd = (1+ 3./16 *RN)**0.5 *(24/RN)\n", + "U22 = 4./3 *d*(gams-gamw) /(Cd*rho)\n", + "U2 = math.sqrt(U22)\n", + "\t\t\t\n", + "#results\n", + "print \"Settling velocity of sand in case 1 = %.2f m/s\"%(U)\n", + "print \" Settling velocity of sand in case 2 = %.4f m/s\"%(U2)\n", + "#The answer is a bit different due to rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Settling velocity of sand in case 1 = 0.02 m/s\n", + " Settling velocity of sand in case 2 = 0.0186 m/s\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.4 Page No : 417" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "A = 2. \t\t\t#area - m**2\n", + "U = 100*1000./3600 \t\t\t#speed-m/s\n", + "Cd = 0.32\n", + "rho = 1.24\n", + "\t\t\t\n", + "#calculations\n", + "Fd = Cd*0.5*rho*U**2 *A\n", + "P = Fd*U\n", + "\t\t\t\n", + "#results\n", + "print \"Power required = %.1f kW\"%(P/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power required = 8.5 kW\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.5 Page No : 417" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "ratio = 0.15\n", + "\t\t\t\n", + "#calculations\n", + "VU = (1/(1-ratio))**(1./3)\n", + "percent = (VU-1)*100\n", + "\t\t\t\n", + "#results\n", + "print \"percent increase in speed = %.1f %%\"%(percent)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "percent increase in speed = 5.6 %\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.6 Page No : 419" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from sympy import Symbol,solve\n", + "\t\t\t\n", + "#Initialization of variables\n", + "U = 50.*1000/3600 \t\t\t#speed - m/s\n", + "cd1 = 0.34\n", + "cd2 = 1.33\n", + "\t\t\t\n", + "#calculations\n", + "print (\"On solving for both convex and concave surfaces,\")\n", + "w = Symbol(\"w\")\n", + "ans = solve(1.98*(13.98 - 0.25*w) - (13.88 + 0.25*w))\n", + "w = ans[0]\n", + "N = w/(2*math.pi) *60\n", + "\n", + "#results\n", + "print \"rotational speed = %.1f rpm\"%(N)\n", + "\n", + "# note : value of w is slightly different because of sympy inbuilt method solve. but it is very accurate." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "On solving for both convex and concave surfaces,\n", + "rotational speed = 176.9 rpm\n" + ] + } + ], + "prompt_number": 4 + } + ], + "metadata": {} + } + ] +}
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