path: root/Transport_Phenomena/ch6.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 6 : Turbulent Flow"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.1 - Page No :200\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "'''\n",
      "determine\n",
      "whether the flow is laminar, turbulent, or transitional. At M\u2019F, the viscosity of\n",
      "water is 0.8007 cP, and the density of water is 0.99568 g cmm3.\n",
      "'''\n",
      "\n",
      "import math \n",
      "\n",
      "\n",
      "# Variables\n",
      "# given\n",
      "q = 50.;        \t\t\t    #[gal/min] - volumetric flow rate\n",
      "d = 2.067/12;  \t    \t\t    #[ft] - diameter\n",
      "A = 0.02330;  \t\t             #[ft**2] - flow area\n",
      "p = 0.99568*62.43;  \t\t\t #[lb/ft**3] - density of water at 86degF\n",
      "mu = 0.8007*6.72*10**-4;  \t\t #[lb/ft*sec] - viscosity of water at 86degF\n",
      "u = q/(60.*7.48*A);\n",
      "\n",
      "# Calculations\n",
      "# using the formula Nre = d*u*p/mu;\n",
      "Nre = round((d*u*p)/mu,-2);\n",
      "\n",
      "# Results\n",
      "print \"Nre = \",Nre\n",
      "print \"Hence the flow is turbulent. Note also that Nre is dimensionless\";\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nre =  95100.0\n",
        "Hence the flow is turbulent. Note also that Nre is dimensionless\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.2 - Page No :202\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "'''\n",
      "Calculate the location along a flat plate (Fig. 6.2) where transition\n",
      "would be expected to occur for a free stream velocity of 4.78fts-\u2019 for water at\n",
      "86\u00b0F.\n",
      "'''\n",
      "# Variables\n",
      "# given\n",
      "p = 0.99568*62.43;  \t\t\t #[lb/ft**3] - density of water at 86degF\n",
      "mu = 0.8007*6.72*10**-4;  \t\t #[lb/ft*sec] - viscosity of water at 86degF\n",
      "u = 4.78;  \t\t\t             #[ft/sec] - free stream velocity \n",
      "Nre = 5.*10**5;  \t\t\t     # the lower limit for the transition reynolds number range is substituted\n",
      "\n",
      "# Calculations\n",
      "x = (Nre*mu)/(p*u);\n",
      "\n",
      "# Results\n",
      "print \"x = %.1f\"%x\n",
      "print \"Thus the transition could star at about %.2f ft. \\\n",
      "\\nThe reynolds number at the  upper end of the transition range is %.0e .\\\n",
      "\\nThe value of x at this location is ten times then the value obtained above i.e %.1f ft\"%(x,Nre*10,x*10)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "x = 0.9\n",
        "Thus the transition could star at about 0.91 ft. \n",
        "The reynolds number at the  upper end of the transition range is 5e+06 .\n",
        "The value of x at this location is ten times then the value obtained above i.e 9.1 ft\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.3 - Page No :212\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the mean velocity for the flow data in Table 6.2.\n",
      "\n",
      "# Variables\n",
      "# given\n",
      "t = [0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.11, 0.12];\n",
      "Ux = [3.84, 3.50, 3.80, 3.60, 4.20, 4.00, 3.00, 3.20, 3.40,  3.00, 3.50, 4.30, 3.80];\n",
      "Uy = [0.43, 0.21, 0.18, 0.30, 0.36, 0.28, 0.35, 0.27, 0.21, 0.22, 0.23, 0.36, 0.35];\n",
      "Uz = [0.19, 0.16, 0.17, 0.13, 0.09, 0.10, 0.16, 0.15, 0.13, 0.18, 0.17, 0.18, 0.17];\n",
      "# using the formula AREA = [deltat/2]*[U1+U13+2*[U2+U3+U4+U5+U6+U7+U8+U9+U10+U11+U12]]\n",
      "# for Uxmean\n",
      "deltat = 0.01;\n",
      "T = t[12]-t[0];\n",
      "\n",
      "# Calculation and Results\n",
      "AREA = (deltat/2)*(Ux[0]+Ux[12]+2*(Ux[1]+Ux[2]+Ux[3]+Ux[4]+Ux[5]+Ux[6]+Ux[7]+Ux[8]+Ux[9]+Ux[10]+Ux[11]));\n",
      "Uxmean = AREA/T;\n",
      "print \"Uxmean = %.2f m s**-1\"%Uxmean\n",
      "\n",
      "# for Uymean\n",
      "deltat = 0.01;\n",
      "AREA = (deltat/2)*(Uy[0]+Uy[12]+2*(Uy[1]+Uy[2]+Uy[3]+Uy[4]+Uy[5]+Uy[6]+Uy[7]+Uy[8]+Uy[9]+Uy[10]+Uy[11]));\n",
      "Uymean = AREA/T;\n",
      "print \"Uymean = %.2f m s**-1\"%Uymean\n",
      "\n",
      "# for Uzmean\n",
      "AREA = (deltat/2)*(Uz[0]+Uz[12]+2*(Uz[1]+Uz[2]+Uz[3]+Uz[4]+Uz[5]+Uz[6]+Uz[7]+Uz[8]+Uz[9]+Uz[10]+Uz[11]));\n",
      "Uzmean = AREA/T;\n",
      "print \"Uzmean = %.2f m s**-1\"%Uzmean\n",
      "U = (Uxmean**2+Uymean**2+Uzmean**2)**(1./2);\n",
      "print \"U = %.3f m s**-1\"%U\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Uxmean = 3.61 m s**-1\n",
        "Uymean = 0.28 m s**-1\n",
        "Uzmean = 0.15 m s**-1\n",
        "U = 3.624 m s**-1\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.4 Page no : 218"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Express the cross term as a ratio to the r.m.s. values\n",
      "\n",
      "import math\n",
      "\n",
      "# Variables\n",
      "#Following values are taken from example 6.3\n",
      "U_dash_z2 = 8.917*10**-4   #m**2s**-2  square velocity\n",
      "Uz2 = .02340               #m**2s**-2\n",
      "U_dash_x2 = 8.947 * 10**-4 #m**2s**-2\n",
      "Ux22 = .02409              #m**2s**-2\n",
      "U = 3.634\n",
      "U2x = 3.63                  #m**2s**-2\n",
      "U2x2 = .41                  #m**2s**-2\n",
      "Ix = 11.37                  #percent\n",
      "U2y = .0288                 #m**2s**-2\n",
      "U2y2 = .069                 #m**2s**-2\n",
      "Iy = 1.92                   #percent\n",
      "dt = .01108\n",
      "\n",
      "# Calculation\n",
      "rmsUz = math.sqrt(U_dash_z2)\n",
      "rmsUx = math.sqrt(Uz2)\n",
      "rmsUx2 = math.sqrt(U_dash_x2)\n",
      "rmsUx2 = math.sqrt(Ux22)\n",
      "I = 100*rmsUz/U\n",
      "Ux = 3.84 - 3.61\n",
      "Uy = .43 - .28\n",
      "UxUy = Ux*Uy\n",
      "ratio = dt/(U2x2*U2y2)\n",
      "\n",
      "\n",
      "# Results\n",
      "print \"I = %.2f percent\"%I\n",
      "print \"U'xU'y = %.4f m**2s**-2\"%UxUy\n",
      "print \"The ratio = %.2f \"%ratio"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "I = 0.82 percent\n",
        "U'xU'y = 0.0345 m**2s**-2\n",
        "The ratio = 0.39 \n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.5 - Page No :232\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# prepare a graph of E./v versus (1 - r/To).\n",
      "\n",
      "%pylab inline\n",
      "\n",
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "import math \n",
      "\n",
      "\n",
      "# Variables\n",
      "# given\n",
      "UzmaxbyU = 24.83;\n",
      "roUbyv = 2312.;\n",
      "Re = 100000.;\n",
      "\n",
      "# using the formula Et/v = 95.5*((r/ro)/slope)-1\n",
      "# from fig 6.6 at Re = 100000\n",
      "rbyro = [0, 0.040, 0.100, 0.200, 0.300, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.960, 1]\n",
      "slope = [0, 0.105, 0.112, 0.126, 0.144, 0.168, 0.201, 0.252, 0.336, 0.503, 1.007, 2.517, 94.59]\n",
      "\n",
      "# Calculations\n",
      "Etbyv = zeros(13)\n",
      "for i in range(1,13):\n",
      "    Etbyv[i] = 95.5*((rbyro[i])/slope[i])-1;\n",
      "\n",
      "# Results\n",
      "plot(rbyro,Etbyv);\n",
      "suptitle(\"Eddy viscosity ratio (E,/v) versus dimensionless radius.\")\n",
      "xlabel(\"r/ro\")\n",
      "ylabel(\"Er/v\")\n",
      "\n",
      "show()\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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zhYWHs9O6LHgGQY+4c0d2Ss+fz+JApm35cuDqVTlNOBkGzyDMmBByGo0GDeTK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\nqFRKJyEiczFoEJCYKAe+GDs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sEEREpBULBBERacUCQUREWv0f7H5+wWyWJFYAAAAASUVO\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x392ca50>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.7 page no : 246"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the velocity distribution by the various methods available\n",
      "# for the flow of cyclohexane at 2.778 ft s- \u2019 (0.8467 m s-\u2018) and 25\u00b0C in a 2-inch I.D.\n",
      "\n",
      "import math\n",
      "\n",
      "# variables\n",
      "do = .0508\n",
      "Uz = .8467                 # cyclohexane\n",
      "aveP = 774.9               # the density of cyclohexane\n",
      "u = 8.892*10**-4           # the viscosity\n",
      "aveF = .00570\n",
      "\n",
      "# Calculation\n",
      "Nre = do*Uz*aveP/u\n",
      "rw = (1./2)*aveP*(Uz**2)*aveF\n",
      "U = math.sqrt(rw/aveP)\n",
      "\n",
      "# for y = .001\n",
      "y001 = (2.54*10**-5)*U*aveP/u\n",
      "ratio = 1 + (U)*(-0.1775)/(1.029)\n",
      "\n",
      "Uz = U*22.77\n",
      "# Results\n",
      "print \"Nre = %.2e \"%Nre\n",
      "print \"The wall shear stress rw = %.3f N m**-2\"%rw\n",
      "print \"The friction velocity U* = %.5f m s*-1\"%U\n",
      "print \"Universal velocity Distribution :\" \n",
      "print \"for y = 0.001 = %d \"%y001\n",
      "print \"Velocity ratio = %.3f\"%ratio\n",
      "print \"Uz = %.3f m s**-1\"%Uz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nre = 3.75e+04 \n",
        "The wall shear stress rw = 1.583 N m**-2\n",
        "The friction velocity U* = 0.04520 m s*-1\n",
        "Universal velocity Distribution :\n",
        "for y = 0.001 = 1 \n",
        "Velocity ratio = 0.992\n",
        "Uz = 1.029 m s**-1\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.8 Pageno :250"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Estimate the temperature distribution in water\n",
      "\n",
      "import math\n",
      "\n",
      "# variables\n",
      "Cp = 4184.           # lg-K-=4184Jkg-K-*\n",
      "P = 1000.            # g cm**-3\n",
      "k = 0.628            # wm**-1\n",
      "Nre = 1.2*10**5\n",
      "v = 1*10**-6\n",
      "do = 2*0.05\n",
      "\n",
      "# calculation\n",
      "alpha = k/(P*Cp)\n",
      "qa = (1.7*10**4)/(P*Cp)\n",
      "Uz = Nre*v/(do)\n",
      "U = Uz*math.sqrt(.0045/2)\n",
      "y = (5*v)/U\n",
      "\n",
      "# Results\n",
      "print \"A = %.3e m**2s**-2\"%alpha\n",
      "print \"The average velocity = %.2f m s**-1\"%Uz\n",
      "print \"U* = %.5f m s**-1\"%U\n",
      "print \"the value of y = %.3e cm\"%y\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A = 1.501e-07 m**2s**-2\n",
        "The average velocity = 1.20 m s**-1\n",
        "U* = 0.05692 m s**-1\n",
        "the value of y = 8.784e-05 cm\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.9 - Page No :258\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compute the Fanning friction factor.\n",
      "\n",
      "# Variables\n",
      "p = 0.84*62.4;  \t\t\t #[lbf/ft**3] - density\n",
      "dP = 80.*144;  \t\t\t #[lbf/ft**2] - pressure\n",
      "dz = 2000.;  \t\t\t #[ft] - length of pipe\n",
      "gc = 32.174;  \t\t\t #[(lbm*ft)/(lbf*sec**2)] - gravitational conversion consmath.tant\n",
      "dpbydz = -dP/dz;\n",
      "do = 2.067/12;  \t\t\t #[ft]\n",
      "\n",
      "# Calculations\n",
      "U = 2000*(1./24)*(1./3600)*(42)*(1./7.48)*(1./0.02330);\n",
      "# using the formula f = ((do/2)*(-dp/dz)*gc)/(p*(U)**2)\n",
      "f = ((do/2)*(-dpbydz)*gc)/(p*(U)**2)\n",
      "\n",
      "# Results\n",
      "print \"f = %.5f (dimensionless)\"%f\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "f = 0.00979 (dimensionless)\n"
       ]
      }
     ],
     "prompt_number": 19
    }
   ],
   "metadata": {}
  }
 ]
}