{
 "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": {}
  }
 ]
}