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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 6:Differential analysis of fluid flow"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.4 Page no.296"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "p1=30                       #kPa\n",
      "d=1000                    #kg/(m**3)\n",
      "r1=1                        #m\n",
      "r2=0.5                     #m\n",
      "#applying energy equation between points (1) and (2) and using the equation V**2=16*(r**2)\n",
      "V1=(16*(r1**2))**0.5          #m/sec\n",
      "V2=(16*(r2**2))**0.5         #m/sec\n",
      "p2=((p1*1000)+(d*((V1**2)-(V2**2)))/2)/1000#kPa\n",
      "\n",
      "#result\n",
      "print \"The pressure at point (2) =\",round(p2,3),\"kpa\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The pressure at point (2) = 36.0 kpa\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.5 Page no.301"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "ang2=math.pi/6                      #radians\n",
      "#vp=-2*math.log(r)\n",
      "\n",
      "#calculation\n",
      "#vr=d(vp)/d'r\n",
      "#vr=(-2)/r\n",
      "#vang=(1/r)*(d(vp)/d(ang))\n",
      "import math\n",
      "from scipy import integrate\n",
      "def f1(dtheta):\n",
      "    R=1\n",
      "    return((-2/R)*R)\n",
      "q=integrate.quad(f1,0.0,(3.14/6))\n",
      "\n",
      "#result\n",
      "print \"Volume rate of flow (per unit length) into the opening = \",round(q[0],2),\"ft**2/s\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Volume rate of flow (per unit length) into the opening =  -1.05 ft**2/s\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.7 Page no.310"
     ]
    },
    {
     "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",
      "h=200                                 #ft\n",
      "U=40                                  #mi/hr\n",
      "d=0.00238                          #slugs/ft**3\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "#V**2= (U**2)*(1 + (2*b*math.cos(ang)/r) + ((b**2)/(r**2)))\n",
      "#at point 2, ang=math.pi/2\n",
      "#r=b*(math.pi-ang)/math.sin(ang)=(math.pi*b/2)\n",
      "V=U*(1+(4/(math.pi**2)))**0.5      #mi/hr\n",
      "y2=h/2                                           #ft\n",
      "#bernoulli equation\n",
      "#p1-p2= d*((V2**2)-(V1**2)) + (sw*(y2-y1))\n",
      "V1=U*(5280/3600)\n",
      "V2=V*(5280/3600)\n",
      "pdiff=((d*((V2**2)-(V1**2))/2) + (d*32.2*(y2)))/144#psi\n",
      "\n",
      "#result\n",
      "print \"elevation of point above the plane\",round(y2,2),\"ft\"\n",
      "print \"The magnitude of velocity at (2) for a 40 mi/hr approaching wind =\",round(V,1),\"mi/hr\"\n",
      "print \"The pressure difference between points (1) and (2)=\",round(pdiff,2),\"psi\"\n",
      "\n",
      "#Plot\n",
      "import matplotlib.pyplot as plt\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "u=[0,20,40,60,80,100]\n",
      "p=[0.05,0.055,0.0647,0.08,0.10,0.12]\n",
      "xlabel(\"U  (mph)\") \n",
      "ylabel(\"p1-p2  (psi)\") \n",
      "plt.xlim((0,100))\n",
      "plt.ylim((0,0.14))\n",
      "ax.plot([40], [0.0647], 'o')\n",
      "ax.annotate('(40mph,0.0647psi)', xy=(40,0.06))\n",
      "\n",
      "a=plot(u,p)\n",
      "show(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "elevation of point above the plane 100.0 ft\n",
        "The magnitude of velocity at (2) for a 40 mi/hr approaching wind = 47.4 mi/hr\n",
        "The pressure difference between points (1) and (2)= 0.06 psi\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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IjBs3rtXXLl682HHDbYzZ9uR4LXXNzfqbyLmQY7pgfdJwErbWtghyujXUtPb+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\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 6.10 Page no.331"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "d=1.18*1000                                          #kg/m**3\n",
      "vis=0.0045                                             #Ns/m**2, viscosity\n",
      "Q=12.0                                                     #ml/sec\n",
      "dia1=4.0                                                   #mm\n",
      "l=1.0                                                         #m\n",
      "dia2=2.0                                                   #mm\n",
      "\n",
      "#calculation\n",
      "import math\n",
      "V=Q/(1000000*math.pi*((dia1/1000)**2)/4)       #mean velocity, m/sec\n",
      "Re=(d*V*dia1/1000)/vis\n",
      "\n",
      "#result\n",
      "print \"  The Reynolds number is \",round(Re,0),\"is well below critical value of 2100 so flow is laminar.\"\n",
      "pdiff=(8*vis*(l)*(12*10**-6)/(math.pi*(dia1/2000)**4))*10**-3        #kPa\n",
      "print \"a)The pressure drop along a 1 m length of the tube which is far from the tube entrance \",round(pdiff,),\"kpa\"\n",
      "\n",
      "#for flow in the annulus\n",
      "V1=Q/(1000000*math.pi*(((dia1/1000)**2)-((dia2/1000)**2))/4)     #mean velocity, m/sec\n",
      "Re1=d*((dia1-dia2)/1000)*V1/vis\n",
      "\n",
      "#Result\n",
      "print \"b) The Reynolds number is \",round(Re1),\" is well below critical value of 2100 so flow is laminar.\"\n",
      "r1=dia1/2000\n",
      "r2=dia2/2000\n",
      "pdiff1=((8*vis*(l)*(12*10**-6)/(math.pi))*((r1**4)-(r2**4)-((((r1**2)-(r2**2))**2)/(math.log(r1/r2))))**(-1))*10**-3  #kPa\n",
      "\n",
      "#result\n",
      "print \"The pressure drop along a 1 m length of the symmetric annulus =\",round(pdiff1,1),\"kpa\"\n",
      "\n",
      "#plot\n",
      "import matplotlib.pyplot as plt\n",
      "fig = plt.figure()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "T=[0,0.001,0.005,0.01,0.2,0.35,0.5]\n",
      "K=[1.1,1.17,1.22,1.28,2.2,3.8,7.94]\n",
      "xlabel(\"Ri/Ro\") \n",
      "ylabel(\"Pannulus/Ptube\") \n",
      "plt.xlim((0,0.5))\n",
      "plt.ylim((1,8))\n",
      "ax.plot([0.5], [7.94], 'o')\n",
      "ax.annotate('(0.5,7.94)', xy=(0.5,7.9))\n",
      "a=plot(T,K)\n",
      "show(a)\n",
      "\n",
      "T1=[0,0.001,0.005,0.01]\n",
      "K1=[1.1,1.14,1.20,1.28]\n",
      "xlabel(\"Ri/Ro\") \n",
      "ylabel(\"Pannulus/Ptube\") \n",
      "plt.xlim((0,0.01))\n",
      "plt.ylim((1,1.3))\n",
      "a1=plot(T1,K1)\n",
      "show(a1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  The Reynolds number is  1002.0 is well below critical value of 2100 so flow is laminar.\n",
        "a)The pressure drop along a 1 m length of the tube which is far from the tube entrance  9.0 kpa\n",
        "b) The Reynolds number is  668.0  is well below critical value of 2100 so flow is laminar.\n",
        "The pressure drop along a 1 m length of the symmetric annulus = 68.2 kpa\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8+nE42DpIHYtIcqIVpPLycvTt2xf37t1DRUUFhg8fjkWLFok1HJHBu1V2C18l\nf4Xl6csR1CkIR/55BM52zlLHIjIYohWkxo0bY9++fbCyskJVVRX8/PyQkJAAPz8/sYYkMkh3yu/g\nm5RvsCx1GUa4jUBGWAZcmrpIHYvI4IjasvvrPKaKigpUV1ejefPmYg5HZFCK7xUj6lAUvjn0DQZ3\nHIxDUw/Btbmr1LGIDJao9y9Wq9Xo2rUrnnvuOQQEBKBTp05iDkdkEEoqSvBlwpdwjXLFqRunkDg5\nET+P+JnFiEgLUbeQTExMcOTIEdy5cwevvvoqVCoV/P39Nc9HRERoHvv7+9d4jqihuVt5F8vTlmNx\n0mL4u/hDNUmFTvb8I4zqR6VSQaVSSR1DL7TeMfZZWbBgASwtLfHBBx/cH1jGl78g41JWWYYVGSvw\nZeKX6OXUC+F9w+HxnIfUsUim5Lx2itayu3HjBgoLCwHcvw7enj17oFQqxRqOSO/uVd3Dd6nfoeOy\njtiXuw87xu3A5jGbWYyInpJoLburV69i4sSJUKvVUKvVGD9+PF5++WWxhiPSm4rqCqw+vBqfH/wc\nns95YusbW+HT1kfqWEQNnt5ado8MLOPNTpKnyupKrD26FgsOLIBbSzfM85+HFx1flDoWGRk5r528\nUgORFlXqKqw7tg7zD8xHu6btsG7UOvR27i11LCLZYUEiqkW1uhobT2zEvP3z0KZJG6watgp9XfpK\nHYtItliQiP5GLagRfTIaEfsj0NyyOZYPXo5+7fpBoVBIHY1I1liQiP5HLajx26nfELE/AlbmVvjm\n1W/wiusrLEREesKCREZPEATEZcchXBUOUxNTfPHyFxjUcRALEZGesSCR0RIEATvO7kC4KhxV6irM\n85+HYS8MYyEikggLEhkdQRCw+9xuzFXNRWlFKeb5z8NI95EwUYh6aUci0oIFiYyGIAj4I+cPzFXN\nxa2yW4joG4GgzkEsREQGggWJjML+3P2Yq5qLq8VXEd43HG90eQOmJqZSxyKih7AgkawlXkxEuCoc\nOYU5mPvSXIzzHAczE/7aExki/p9JsnTo0iGEq8Jx+sZpzHlpDiZ4TYC5qbnUsYjoCViQSFYyrmQg\nXBWOY9eOYXaf2QhRhsDC1ELqWESkAxYkkoUj+UcQoYpA2pU0fOr3KWLGxKCRWSOpYxFRHbAgUYN2\nouAEIlQRSMxLxMe9P8aG1zbA0txS6lhE9BRYkKhBOnX9FObtnwdVrgof9voQa0euhZW5ldSxiKge\nWJCoQTk17LFKAAAMrElEQVRz8wzm75+P3ed2Y1bPWfhx2I+wsbCROhYRPQM8I5AahHO3zmHS1kno\nvao33Fu6488Zf+Ijv49YjIhkhFtIZNByC3Px2YHP8Nvp3/BO93dw9p2zaNq4qdSxiEgELEhkkPLu\n5OHzg58jOisa032m4+w7Z9HcsrnUsYhIRCxIZFAuF13GooRFWH98PcK8w5D9djZaWrWUOhYR6QEL\nEknqeul1JOUlITEvEYl5iThZcBJTu03F6bdPo5V1K6njEZEeKQRBECQZWKGAREOTRARBQPbNbCRe\nTNQUoPySfPRw7IHeTr3R26k3XnR8kQcqED2BnNdOFiQSTXlVOdKvpGsKUFJeEmwsbNDbubemAHVp\n1YVX3SaqAzmvnaIVpLy8PEyYMAEFBQVQKBQICwvDjBkzHgws40k1VtdLr2u2fBIvJuLotaNwb+le\nowA52DpIHZOoQZPz2ilaQcrPz0d+fj66du2KkpISeHt7Y+vWrXB3d78/sIwn1Rj8vf2WcDEBBaUF\nD9pvzr3R3aE7229Ez5ic107RDmpo3bo1WrduDQCwsbGBu7s7rly5oilI1LA8rv3WpFETzZbPzB4z\n0dm+M9tvRPTU9LIPKTc3F3379sXJkydhY3P/L2Y5V3k5eFz7rZN9J00B6u3cG22btJU6JpHRkfPa\nKfph3yUlJRg9ejQiIyM1xegvERERmsf+/v7w9/cXOw49hiAIOH3jdI0CVFBagJ5OPdHbqTc+7/c5\nujt0h7WFtdRRiYyOSqWCSqWSOoZeiLqFVFlZiSFDhmDgwIGYOXNmzYFlXOUNXXlVOdIup2kKUFJe\nEmwb2cLP2U+zBdTJvhPbb0QGSM5rp2gFSRAETJw4ES1atMDXX3/96MAynlRDU1BaUOPcn2PXjrH9\nRtRAyXntFK0gJSQk4KWXXoKnpycUCgUAYNGiRRgwYMD9gWU8qVJSC+r77beHCtD10uua9ltvp95s\nvxE1YHJeO3libANXVll2/+i3h9pvdo3sapz707lVZ5goeKcRIjmQ89rJgtTAPK791tm+c40C1KZJ\nG6ljEpFI5Lx2siAZsMe1327cvYGejj01+3582/qy/UZkROS8drIgGZCyyjKkXUnTFKDkS8lo2rhp\njYMPOtl3YvuNyIjJee1kQZLQtZJrNc79OV5wXNN+83PyQy+nXmy/EVENcl47WZD0RC2ocer6qRoF\n6GbZzRrtt+4O3WFlbiV1VCIyYHJeO1mQRFJWWYbUy6maApScl4xmls3YfiOiepHz2smC9Iw8rv3W\npVUXTQFi+42IngW5rZ0PY0F6Co9rv90qu1Xj5FNfB1+234jomWvIa6c2LEg6uFt5t8a135LzktHc\nsnmNc3/c7d3ZfiMi0TWktbOuWJAeI78kv8a5PycKTsCjlYemAPVy6oXWNq2ljklERsiQ1876MvqC\npBbUyLqeVaMA3S67rWm/+Tn7wbetLyzNLaWOSkRkMGunGIyuIP3Vfku4mKA5+bSFZQu234ioQWBB\nEmNgPU0q229EJCcsSGIMLMKk1tZ+6+XUq8a139h+I6KGigVJjIGfwaTerbx7/+TTh6791tKqZY2T\nT91aurH9RkSywYIkxsBPMalXi6/WOPfn5PWT8HzOs8bJp8/ZPCdSYiIi6bEgiTGwlklVC2qcLDhZ\nowDduXfnQfvNqTd82vqw/UZERoUFSYyBHzOpgiAgNjsWKzJWPNJ+83P2wwstX2D7jYiMGguSGAP/\nbVKPXTuGmfEzca30Gua+NBf+Lv5svxER/Y2cC5KZ1AFu3r2J2X/MxpZTWxDeNxzTfKbBzETyWERE\npGeS9r++T/8e7t+5w8LUAtlvZ+Ot7m+xGBERGSlJW3Ye//bAf0b+B16tvaSIQETU4Mi5ZSfpFtLH\nfh+zGBEREQARC9LkyZPx3HPPwcPDo9bXDOgwQKzhGxSVSiV1BIPBuXiAc/EA58I4iFaQQkJCEB8f\n/8TXNLdsLtbwDQr/Z3uAc/EA5+IBzoVxEK0g9enTB82aNRPr44mISGZ4likRERkEUY+yy83NxdCh\nQ3H8+PFHB1YoxBqWiEjW5HqUnWQn/ch1QomI6OmwZUdERAZBtIIUHByMXr164cyZM3BycsLq1avF\nGoqIiGRAtIK0YcMGXLlyBbGxsbC2tsbChQvx5ZdfPva1M2bMQMeOHeHl5YXDhw+LFUly8fHxcHNz\nQ8eOHR87F6dPn0bPnj3RuHFjLF26VIKE+qNtLtatWwcvLy94enqid+/eOHbsmAQp9UPbXMTGxsLL\nywtKpRLe3t74448/JEipH9rm4i9paWkwMzPDli1b9JhOv7TNhUqlgp2dHZRKJZRKJT777DMJUj5j\ngoiqqqoEV1dXIScnR6ioqBC8vLyErKysGq/5/fffhYEDBwqCIAgpKSnCiy++KGYkyegyFwUFBUJa\nWpowe/ZsYcmSJRIlFZ8uc5GUlCQUFhYKgiAIO3fuNOrfi5KSEs3jY8eOCa6urvqOqRe6zMVfrwsI\nCBAGDx4sbN68WYKk4tNlLvbt2ycMHTpUooTiEHUfUmpqKjp06AAXFxeYm5vjjTfeQGxsbI3XxMXF\nYeLEiQCAF198EYWFhbh27ZqYsSShy1zY29vDx8cH5ubmEqXUD13momfPnrCzswNw//fi0qVLUkQV\nnS5zYW1trXlcUlKCli1b6jumXugyFwCwbNkyjB49Gvb29hKk1A9d50KQ2cFhohaky5cvw8nJSfO9\no6MjLl++rPU1clx8dJkLY1HXufjpp58waNAgfUTTO13nYuvWrXB3d8fAgQMRFRWlz4h6o+t6ERsb\ni+nTpwOQ7+kjusyFQqFAUlISvLy8MGjQIGRlZek75jMn6mHfuv6y/L3Ky/GXTI7/pqdVl7nYt28f\nVq1ahcTERBETSUfXuRgxYgRGjBiBgwcPYvz48cjOzhY5mf7pMhczZ87EF198obnitdy2EP6iy1x0\n69YNeXl5sLKyws6dOzFixAicOXNGD+nEI2pBcnBwQF5enub7vLw8ODo6PvE1ly5dgoODg5ixJKHL\nXBgLXefi2LFjCA0NRXx8vGwvQ1XX34s+ffqgqqoKN2/eRIsWLfQRUW90mYuMjAy88cYbAIAbN25g\n586dMDc3x7Bhw/SaVWy6zEWTJk00jwcOHIg333wTt27dQvPmDfgaoWLuoKqsrBTat28v5OTkCPfu\n3dN6UENycrJsd17rMhd/CQ8Pl/VBDbrMxYULFwRXV1chOTlZopT6octc/Pnnn4JarRYEQRAyMjKE\n9u3bSxFVdHX5f0QQBGHSpElCTEyMHhPqjy5zkZ+fr/m9OHTokPCPf/xDgqTPlqhbSGZmZvj222/x\n6quvorq6GlOmTIG7uzt++OEHAMC0adMwaNAg7NixAx06dIC1tbVsz1fSZS7y8/Ph6+uLoqIimJiY\nIDIyEllZWbCxsZE4/bOly1zMnz8ft2/f1uwrMDc3R2pqqpSxRaHLXMTExGDt2rUwNzeHjY0NNm7c\nKHFqcegyF8ZCl7nYvHkzli9fDjMzM1hZWcni90KyO8YSERE9jJcOIiIig8CCREREBoEFiYiIDAIL\nEhERGQQWJDIKpqamUCqV8PT0xKhRo1BSUgIAuHLlCoKCgmq81sfHBxUVFXBxcYGnpye6du2K/v37\n48qVK1JEJzIaLEhkFKysrHD48GEcO3YMtra2msNn27Zti+joaM3rcnJy4OjoCAsLCygUCqhUKhw5\ncgR+fn5YtGiRVPGJjAILEhmdnj174ty5cwCA3NxceHh4aJ6Lj4/HgAEDHnlPjx49arynX79+8PLy\nQv/+/WucUU9ET48FiYxKdXU1du/ejS5dujz2+V27dtUoSH+dphcfH695zzvvvIOQkBAcPXoU48aN\nw4wZM8QPTmQEeGIsGQUzMzN4eHjg8uXLcHFxQUpKCkxMTJCbm4uhQ4fi+PHjqKioQK9evZCeng4A\naNeuHZo0aYJbt27BzMwMJ06cgI2NDezt7ZGfnw9TU1NUVlaibdu2uH79usT/QqKGj1tIZBQsLS1x\n+PBhXLhwAY0bN37svWUOHjwIPz+/Gj9TqVS4cOECevTogZUrV2p+zr/jiJ49FiQyKpaWloiKisLs\n2bMfKSrx8fGPve+SqakpvvnmGyxduhQlJSXo1auX5rph69atw0svvaSX7ERyx4JERuHh+8t07doV\nHTp0wKZNm6BQKDTP7d+/H3379n3se1q3bo1Ro0bhu+++w7Jly7B69Wp4eXlh3bp1iIyM1N8/hEjG\nuA+JCPfvwzVt2jT8/vvvUkchMlosSEREZBDYsiMiIoPAgkRERAaBBYmIiAwCCxIRERkEFiQiIjII\nLEhERGQQ/j8y2WFyYO5hqwAAAABJRU5ErkJggg==\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}