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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 9:Flow over immersed bodies"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.1 Page no.487"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "U=25.0                     #ft/sec\n",
      "p=0                        #gage\n",
      "b=10.0                     #ft\n",
      "t=1.24*(10**-3)            #where t=stress*(x**0.5)\n",
      "a=0.744                    #where a=p/(1-((y**2)/4))\n",
      "p1=-0.893                  #lb/(ft**2)\n",
      "from scipy import integrate\n",
      "def f(x):\n",
      "    return(2*t*b/(x**0.5))\n",
      "drag1=integrate.quad(f,0.0,4.0)\n",
      "print \"The drag when plate is parallel to the upstream flow=\",drag1[0],\"lb\"\n",
      "\n",
      "def f1(y):\n",
      "    return((((a*(1-((y**2)/4))))-p1)*b)\n",
      "drag2=integrate.quad(f1,-2.0,2.0)\n",
      "\n",
      "#result\n",
      "print  \"The drag when plate is perpendicular to the upstream flow=\",drag2[0],\"lb\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The drag when plate is parallel to the upstream flow= 0.0992 lb\n",
        "The drag when plate is perpendicular to the upstream flow= 55.56 lb\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.5 Page no.508"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "U=10.0                        #ft/sec\n",
      "Twater=60.0                #degree F\n",
      "Tglycerin=68.0            #degree F\n",
      "kviswater=1.21*(10**-5)          #(ft**2)/sec\n",
      "kvisair=1.57*(10**-4)               #(ft**2)/sec\n",
      "kvisglycerin=1.28*(10**-2)       #(ft**2)/sec\n",
      "Re=5*(10**5)                         #assumption\n",
      "\n",
      "#calculation\n",
      "xcrwater=kviswater*Re/U          #ft\n",
      "xcrair=kvisair*Re/U                   #ft\n",
      "xcrglycerin=kvisglycerin*Re/U   #ft\n",
      "btwater=5*(kviswater*xcrwater/U)**0.5       #ft where bt=thickness of boundary layer\n",
      "btair=5*(kvisair*xcrair/U)**0.5                             #ft\n",
      "btglycerin=5*(kvisglycerin*xcrglycerin/U)**0.5     #ft\n",
      "\n",
      "#result\n",
      "print \"a)WATER\"\n",
      "print \"location at which boundary layer becomes turbulent=\",round(xcrwater,2),\"ft\"\n",
      "print \"Thickness of the boundary layer=\",round(btwater,5),\"ft\"\n",
      "print \"b)AIR\"\n",
      "print \"location at which boundary layer becomes turbulent=\",round(xcrair,2),\"ft\"\n",
      "print \"Thickness of the boundary layer=\",round(btair,3),\"ft\"\n",
      "print \"c)GLYCERIN\"\n",
      "print \"location at which boundary layer becomes turbulent=\",round(xcrglycerin,2),\"ft\"\n",
      "print \"Thickness of the boundary layer=\",round(btglycerin,2),\"ft\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a)WATER\n",
        "location at which boundary layer becomes turbulent= 0.61 ft\n",
        "Thickness of the boundary layer= 0.00428 ft\n",
        "b)AIR\n",
        "location at which boundary layer becomes turbulent= 7.85 ft\n",
        "Thickness of the boundary layer= 0.056 ft\n",
        "c)GLYCERIN\n",
        "location at which boundary layer becomes turbulent= 640.0 ft\n",
        "Thickness of the boundary layer= 4.53 ft\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.7 Page no.512"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "T=70.0        #degree F\n",
      "U1=0.0        #ft/sec\n",
      "U2=30.0       #ft/sec\n",
      "l=4.0         #ft\n",
      "b=0.5         #ft\n",
      "d=1.94\n",
      "vis=2.04*(10**(-5))\n",
      "x=d*l/vis\n",
      "U=10.0       #ft/s  U1 < U < U2\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "Re=d*l*U/(vis)    #Reynold no.\n",
      "#but we take Re approximately =3800000\n",
      "Re_=3.8*10**6\n",
      "Cd=0.455/((math.log10(Re_))**2.58)-(1700.0/Re_)\n",
      "D=d*U**2*Cd\n",
      "print \"The Drag is \",round(D,3),\"lb\"\n",
      "\n",
      "#Plot\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "U=[0,3,8,20,30]\n",
      "Df=[0,0.1,0.598,2.4,5]\n",
      "xlabel(\"U  (ft/s)\") \n",
      "ylabel(\"Df  (lb)\") \n",
      "plt.xlim((0,30))\n",
      "plt.ylim((0,5))\n",
      "a=plot(U,Df)\n",
      "\n",
      "U1=[0,1,1.5,3,5,8,15,30]\n",
      "Df1=[4,4,3,1.5,1,0.598,0.4,0.3]\n",
      "ax.annotate('Entire boundary layer laminar', xy=(0.5, 4), xytext=(3,4.2),\n",
      "            arrowprops=dict(facecolor='black', shrink=0.001),\n",
      "            )\n",
      "xlabel(\"U  (ft/s)\") \n",
      "ylabel(\"Df  (lb)\") \n",
      "plt.xlim((0,30))\n",
      "plt.ylim((0,5))\n",
      "\n",
      "a=plot(U1,Df1,linestyle='--')\n",
      "plt.text(20,2.8,'Df')\n",
      "plt.text(3,2.5,'Xcf')\n",
      "\n",
      "show(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Drag is  0.597 lb\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LS+vNS8lGmIJZ//kkJibSq1cv2rVrh7e3N/PnzzdncyWSeXKEtYiNhcce0+rz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\nRK5CYII=\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.10 Page no.525"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=0.1                      #mm\n",
      "sg=2.3\n",
      "vis=1.12*(10**(-3))    #N*s/(m**2)\n",
      "#by free body diagram and assuming CD=24/Re\n",
      "U=(sg-1)*999*9.81*((D/1000)**2)/(18*vis)\n",
      "\n",
      "#Result\n",
      "print \"The velocity of the particle through still water =\",round(U,3),\"m/s\"\n",
      "\n",
      "#Plot\n",
      "import matplotlib.pyplot as plt\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "D=[0,0.01,0.02,0.04,0.06,0.1]\n",
      "U=[0,0,0.0002,0.001,0.0024,0.00632]\n",
      "xlabel(\"D  (mm)\") \n",
      "ylabel(\"U  (m/s)\") \n",
      "plt.xlim((0,0.1))\n",
      "plt.ylim((0,0.007))\n",
      "\n",
      "ax.plot([0.1], [0.00632], 'o')\n",
      "ax.annotate('(0.1mm,0.00632m/s)', xy=(0.06,0.006))\n",
      "a=plot(D,U)\n",
      "show(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The velocity of the particle through still water = 0.006 m/s\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8u+VZzPxqJlapV2HliJX8PHpyKpIGFqPRiNmzZyM/Px/Hjx9HdnY2Tpw40aiN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\n+n+kDMLwirooewAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.11 Page no.528"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "D=1.5                     #in\n",
      "\n",
      "CD=0.5\n",
      "dice=1.84                  #slugs/(ft**3) density of ice\n",
      "dair=2.38*(10**(-3))  #slugs/(ft**3)\n",
      "U=(4*dice*32.2*(D/12)/(3*dair*CD))**0.5     #ft/sec\n",
      "\n",
      "#Result\n",
      "print \"The velocity of the updraft needed=\",round(U*3600/5275,1),\"mph\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The velocity of the updraft needed= 62.2 mph\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.12 Page no.531"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "Dg=1.69                    #in.\n",
      "Wg=0.0992               #lb\n",
      "Ug=200                     #ft/sec\n",
      "Dt=1.5                       #in.\n",
      "Wt=0.00551               #lb\n",
      "Ut=60                            #ft/sec\n",
      "kvis=(1.57*(10**(-4)))    #(ft**2)/sec\n",
      "\n",
      "#Calculation\n",
      "import math\n",
      "Reg=Ug*Dg/kvis\n",
      "Ret=Ut*Dt/kvis\n",
      "#the corresponding drag coefficients are calculated as\n",
      "CDgs=0.25                   #standard golf ball\n",
      "CDgsm=0.51                #smooth golf ball\n",
      "CDt=0.5                       #table tennis ball\n",
      "Dgs=0.5*0.00238*(Ug**2)*math.pi*((Dg/12)**2)*CDgs/4          #lb\n",
      "Dgsm=0.5*0.00238*(Ug**2)*math.pi*((Dg/12)**2)*CDgsm/4     #lb\n",
      "Dt=0.5*0.00238*(Ut**2)*math.pi*((Dt/12)**2)*CDt/4                 #lb\n",
      "#the  corresponding decelerations are a=D/s=g*D/W\n",
      "#deceleration relative to g=D/W\n",
      "decgs=Dgs/Wg\n",
      "decgsm=Dgsm/Wg\n",
      "dect=Dt/Wt\n",
      "\n",
      "#result\n",
      "print\"STANDARD GOLF BALL:\"\n",
      "print \"The drag coefficient=\",round(Dgs,3),\"lb\"\n",
      "print \"The deceleration relative to g=\",round(decgs,2)\n",
      "print\"SMOOTH GOLF BALL:\"\n",
      "print \"The drag coefficient=\",round(Dgsm,3),\"lb\"\n",
      "print\"The deceleration relative to g=\",round(decgsm,2)\n",
      "print\"TABLE TENNIS BALL:\"\n",
      "print \"The drag coefficient=\",round(Dt,3),\"lb\"\n",
      "print \"The deceleration relative to g=\",round(dect,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "STANDARD GOLF BALL:\n",
        "The drag coefficient= 0.185 lb\n",
        "The deceleration relative to g= 1.87\n",
        "SMOOTH GOLF BALL:\n",
        "The drag coefficient= 0.378 lb\n",
        "The deceleration relative to g= 3.81\n",
        "TABLE TENNIS BALL:\n",
        "The drag coefficient= 0.026 lb\n",
        "The deceleration relative to g= 4.77\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.13 Page no.533"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "U=88                   #fps\n",
      "Ds=40.0                #ft\n",
      "Dc=15.0                #ft\n",
      "b=50#ft\n",
      "Res=U*Ds/(1.57*(10**(-4)))\n",
      "Rec=U*Dc/(1.57*(10**(-4)))\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "#from these values of Re drag coefficients are found as\n",
      "CDs=0.3\n",
      "CDc=0.7\n",
      "#by summing moments about the base of the tower\n",
      "Drs=0.5*0.00238*(U**2)*math.pi*(Ds**2)*CDs/4     #lb\n",
      "Drc=0.5*0.00238*(U**2)*b*Dc*CDc                   #lb\n",
      "M=(Drs*(b+(Ds/2)))+(Drc*(b/2))                          #ft*lb\n",
      "\n",
      "#Result\n",
      "print \"The moment needed to prevent the tower from tripping=\",round(M,3),\"lb*ft\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The moment needed to prevent the tower from tripping= 364139.221 lb*ft\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.15 Page no.544"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "U=15                   #ft/sec\n",
      "b=96                    #ft\n",
      "c=7.5                    #ft\n",
      "W=210                 #lb\n",
      "CD=0.046\n",
      "eff=0.8                  #power train efficiency\n",
      "d=2.38*(10**(-3))       #slugs/(ft**3)\n",
      "#W=L\n",
      "CL=2*W/(d*(U**2)*b*c)\n",
      "D=0.5*d*(U**2)*b*c*CD\n",
      "P=D*U/(eff*550)       #hp\n",
      "\n",
      "#Result\n",
      "print \"The lift coefficient=\",round(CL,3)\n",
      "print \"The power required by the pilot=\",round(P,3),\"hp\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lift coefficient= 1.089\n",
        "The power required by the pilot= 0.302 hp\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.16 Page no.548"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "W=2.45*(10**(-2))               #N\n",
      "D=3.8*(10**(-2))                  #m\n",
      "U=12                                    #m/s\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "#W=L\n",
      "d=1.23                                 #kg/(m**3)\n",
      "W=0.5*d*(U**2)*(D**2)*math.pi*CL/4\n",
      "CL=2*W/(d*(U**2)*math.pi*(D**2)/4)\n",
      "#using this value of CL, omega*D/(2*U)=x is found as \n",
      "x=0.9\n",
      "omega=2*U*x/D                  #rad/sec\n",
      "angvel=omega*60/(2*math.pi)     #rpm where angvel is angular velocity\n",
      "\n",
      "#Result\n",
      "print \"The angular velocity=\",round(angvel,3),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The angular velocity= 5428.021 rpm\n"
       ]
      }
     ],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}