path: root/Mechanics_Of_Fluids/ch8.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8 : Behaviour of Ideal and Viscous Fluids"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.2.1 page no : 190"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#initialisation of variables\n",
      "\n",
      "v= 5.*10**-6 \t\t\t#gmsec/m**2\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "g1= 981. \t\t\t#gm/cm**2\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "v1= v*2.2*30.5**2/1000.\n",
      "v2= v1*g\n",
      "v3= v*g1*100\n",
      "\t\t\t\n",
      "#RESULTS\n",
      "print  'viscosity = %.2e lbf sec/ft**2 '%(v1)\n",
      "print  'viscosity = %.2e lb/ft sec '%(v2)\n",
      "print  'viscosity = %.3f centi-poise '%(v3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "viscosity = 1.02e-05 lbf sec/ft**2 \n",
        "viscosity = 3.29e-04 lb/ft sec \n",
        "viscosity = 0.490 centi-poise \n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.3.1 page no : 192"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "\n",
      "v= 3.732*10**-7 \t\t\t#slug/ft sec\n",
      "y= 0.\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "vbyy= 40000.*(1.-50*y)\n",
      "q= v*vbyy\n",
      "\t\t\t\n",
      "#RESULTS\n",
      "print  ' viscous shear stress= %.4f lbf/ft**2 '%(q)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " viscous shear stress= 0.0149 lbf/ft**2 \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.3.2 page no : 193"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "import math \n",
      "\n",
      "T= 2.95 \t\t\t#lbf ft\n",
      "y= 0.025 \t\t\t#in\n",
      "d= 3. \t\t\t    #in\n",
      "w= 450. \t\t\t#r.p.m\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "R = 1.5\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "A = math.pi*d*(2./3.)\n",
      "u = (T*y*144*60*32.2)/(A*R**2*w*2*math.pi)\t\t\n",
      "\n",
      "#RESULTS\n",
      "print  ' coefficient of viscocity of oil= %.3f lb/ft sec '%(u)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " coefficient of viscocity of oil= 0.513 lb/ft sec \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.3.3 page no : 194"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "import math \n",
      "\n",
      "v= 0.02 \t\t\t#lb/ft sec\n",
      "L= 5. \t\t\t#in\n",
      "D= 2.5 \t\t\t#in\n",
      "M= 26. \t\t\t#lbf in\n",
      "w= 1200. \t\t\t#rev/min\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "C= math.pi*v*w*2*math.pi*D**3*L/(2*M*g*60*144.)\n",
      "\t\t\t\n",
      "#RESULTS\n",
      "print  ' coefficient= %.4f in '%(C)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " coefficient= 0.0026 in \n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.3.4 page no : 195"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "import math \n",
      "\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "l= 2.54 \t\t\t#cm\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "v= 3.22 \t\t\t#centi-poise\n",
      "f= 0.01\n",
      "p= 1.74 \t\t\t#lbf/in**2\n",
      "w= 100. \t\t\t#rev\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "V= v*l/(453.6*g*12)\n",
      "R= f*p*60/(math.pi*2*math.pi*w*V)\n",
      "\n",
      "\t\t\t\n",
      "#RESULTS\n",
      "print ' relevant ratio of diameter to clearance= %.1f '%(R)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " relevant ratio of diameter to clearance= 11.3 \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.4.1 page no : 196"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "g= 981. \t\t\t#cm/sec**2\n",
      "d= 0.1 \t\t\t#mm\n",
      "v= 35. \t\t\t#centi-stokes\n",
      "d1= 10. \t\t\t#mm\n",
      "d2= 1. \t\t\t#mm\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "u= g*d**2.*100/(18*v*d1**2)\n",
      "ub= (d2/d)**2*u\n",
      "\t\t\t\n",
      "#RESULTS\n",
      "print  ' rate for diameter 0.1 mm= %.4f cm/sec'%(u) \n",
      "print  '  rate for diameter 1 mm= %.2f cm/sec'%(ub) \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " rate for diameter 0.1 mm= 0.0156 cm/sec\n",
        "  rate for diameter 1 mm= 1.56 cm/sec\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.5.1 page no : 201"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "import math\n",
      "a= 0.25 \t\t\t#ft\n",
      "v= 1.2 \t\t\t#poises\n",
      "u= 10. \t\t\t#ft/sec\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "s= 0.9\n",
      "d= 6. \t\t\t#in\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "q= -2.*u*v*30.5/(a*454*g)\n",
      "Q= math.pi*u*(d/24)**2/2\n",
      "R= 2.5*30.5**2/(v)\n",
      "\t\t\n",
      "#RESULTS\n",
      "print  ' quantity flow = %.2f ft**3/sec'%(q) \n",
      "print  '  shear stress in the oil = %.2f lbf/ft**2'%(Q) \n",
      "print  '  Reynolds number = %.f '%(R)\n",
      "print 'Which is less than 2300 .Hence flow is laminar.'\n",
      "# Note : Answer in book is wrong for R. Please check it manually."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " quantity flow = -0.20 ft**3/sec\n",
        "  shear stress in the oil = 0.98 lbf/ft**2\n",
        "  Reynolds number = 1938 \n",
        "Which is less than 2300 .Hence flow is laminar.\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.5.2 page no : 202"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "import math\n",
      "\n",
      "s= 0.9          #relative density\n",
      "v= 5. \t\t\t#ft/sec\n",
      "l= 10. \t\t\t#ft\n",
      "di= 0.5 \t\t\t#in\n",
      "n= 100.\n",
      "u= 0.002 \t\t\t#lbfsec/ft**2\n",
      "w= 62.3 \t\t\t#lbf/ft**3\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "dp= 8.*u*v*l/(di/2)**2\n",
      "hf= dp*144./(s*w)\n",
      "hk= v**2/(2.*g)\n",
      "ht=hf+hk\n",
      "P= s*w*n*v*math.pi*ht*di**2/(144.*4*550)\n",
      "\n",
      "#RESULTS\n",
      "print  ' horse-power required = %.1f h.p'%(P)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " horse-power required = 2.3 h.p\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.6.2 pageno : 206"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialisation of variables\n",
      "import math \n",
      "\n",
      "W= 50. \t\t\t#tonf\n",
      "u= 0.1 \t\t\t#lb/ft sec\n",
      "d= 8. \t\t\t#in\n",
      "g= 32.2 \t\t\t#ft/sec**2\n",
      "r= 0.01\n",
      "\t\t\t\n",
      "#CALCULATIONS\n",
      "P = (4*W**2)/(3*math.pi*u) * ((1./800)**3)*(12./8)*(g/550)*2240**2\n",
      "Q= 4*W*2240*g*12*(r/d)**3/(3*math.pi*u*(d/12))\n",
      "\t\t\t\n",
      "#RESULTS\n",
      "print ' power required = %.2f'%P\n",
      "print  ' rate = %.3f in/sec'%(Q)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " power required = 9.13\n",
        " rate = 0.538 in/sec\n"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}