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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Chapter : Fluid Kinematics"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.1 Page no 117"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from math import *\n",
      "\n",
      "\n",
      "\n",
      "x=1 # x co-ordinate\n",
      "\n",
      "y=2 # y co-ordinate\n",
      "\n",
      "\n",
      "print \"(a) u = 4*X; v = -4*Y \"\n",
      "\n",
      "u = 4*x\n",
      "\n",
      "v=- 4*y\n",
      "\n",
      "print \"(b) u=\",round(u,0),\"m/s and v=\",round(v,0),\"m/s\"\n",
      "\n",
      "R =sqrt(u**2+v**2)\n",
      "\n",
      "ang = atan(v/u)*180/pi\n",
      "\n",
      "print \"(c) Magnitude of velocity =\",round(R,2),\"m/s and angle of resultant velocity = \",round(ang,1),\"deg\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) u = 4*X; v = -4*Y \n",
        "(b) u= 4.0 m/s and v= -8.0 m/s\n",
        "(c) Magnitude of velocity = 8.94 m/s and angle of resultant velocity =  -63.4 deg\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.2 Page no 119"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from math import *\n",
      "\n",
      "from __future__ import division\n",
      "\n",
      "\n",
      "d = 0.3                  # diameter of pipe in m\n",
      "\n",
      "v = 15                   # velocity in m/s\n",
      "\n",
      "rho = 997.1              # density in kg/m**3\n",
      "\n",
      "A = pi*d**2/4\n",
      "\n",
      "\n",
      "Q=A*v\n",
      "\n",
      "print \"(a) Discharge =\",round(Q,2),\"m**3/s\"\n",
      "\n",
      "mdot = rho*Q\n",
      "\n",
      "print \"(b) Mass flow rate = \",round(mdot,2),\"kg/s\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Discharge = 1.06 m**3/s\n",
        "(b) Mass flow rate =  1057.21 kg/s\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.3 Page no 120 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from math import *\n",
      "\n",
      "from __future__ import division\n",
      "\n",
      "from scipy import integrate\n",
      "\n",
      "\n",
      "Vo = 10                  # velocity in m/s\n",
      "\n",
      "r1 = 0\n",
      "\n",
      "ro = 0.1                 # radius in m\n",
      "\n",
      "N = 1\n",
      "\n",
      "\n",
      "R = lambda r: (10*r-1000*r**3)\n",
      "\n",
      "R1,err=integrate.quad(R,r1,ro)\n",
      "\n",
      "Q =  R1*2*pi\n",
      "\n",
      "A = pi*(0.1)**2\n",
      "\n",
      "V = Q/A\n",
      "\n",
      "print \"Mean velocity of the flow =\",round(V,0),\"m/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mean velocity of the flow = 5.0 m/s\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.4 Page no 126"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "from math import *\n",
      "\n",
      "from scipy import integrate\n",
      "\n",
      "import numpy as np\n",
      "\n",
      "from sympy import *\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "x = Symbol('x')\n",
      "U = integrate(2,x)\n",
      "\n",
      "\n",
      "y = Symbol('y')\n",
      "\n",
      "V = integrate(-4*y,y)\n",
      "\n",
      "\n",
      "Zhi = U + V\n",
      "\n",
      "print Zhi           # for x and y =0 we get C = 0\n",
      "\n",
      "X = [5,6,7,8,9,10,11,12,13,14,15,16,17]\n",
      "Y = [0,1.414,2,2.449,2.828,3.16,3.46,3.741,4,4.242,4.472,4.69,4.898]\n",
      "\n",
      "b1=plt.plot(X,Y)\n",
      "\n",
      "\n",
      "X1 = [2.5,3,4,5,6,7,8,9,10,11,12,13,14,15]\n",
      "Y1 = [0,1,1.732,2.23,2.645,3,3.31,3.60,3.87,4.123,4.35889,4.5825,4.795,5]\n",
      "\n",
      "b2=plt.plot(X1,Y1)\n",
      "\n",
      "\n",
      "X2 = [0.5,1.5,2.5,3.5,4.5,5.5,6.5,7.5,8.5,9.5,10.5,11.5,12.5,13.5,14.5,15.5]\n",
      "Y2 = [0,1.414,2,2.449,2.828,3.162,3.462,3.741,4,4.242,4.472,4.69,4.898,5.099,5.29,5.4772]\n",
      "\n",
      "b3=plt.plot(X2,Y2)\n",
      "\n",
      "plt.xlabel(\"x\")\n",
      "\n",
      "plt.ylabel(\"y\")\n",
      "\n",
      "plt.title(\"Streamline plot\")\n",
      "\n",
      "plt.legend([\"zhi=10\",\"zhi=5\",\"zhi=1\"])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2*x - 2*y**2\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.5 PAge no 127"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from math import *\n",
      "\n",
      "from sympy import *\n",
      "\n",
      "import numpy as np\n",
      "\n",
      "\n",
      "x = 2             # X co-ordinate\n",
      "\n",
      "Y = 4             # Y co-ordiante\n",
      "\n",
      "y = Symbol('y')\n",
      "\n",
      "zhi = 4*x*y\n",
      "\n",
      "zhiprime = zhi.diff(y)\n",
      "\n",
      "u = zhiprime\n",
      "\n",
      "x = Symbol('x')\n",
      "\n",
      "zhi = 4*x*Y\n",
      "\n",
      "zhiprime = zhi.diff(x)\n",
      "\n",
      "v = zhiprime\n",
      "\n",
      "R=sqrt(u**2+v**2)\n",
      "\n",
      "theta = atan(v/u)*180/pi\n",
      "\n",
      "print \"Resutant velocity magnitude = \",round(R,2),\"m/s\"\n",
      "\n",
      "print \"Angle =\",round(theta,1),\"deg with the X-axis in the 4th quadrant\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Resutant velocity magnitude =  "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "17.89 m/s\n",
        "Angle = 63.4 deg with the X-axis in the 4th quadrant\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.6 Page no 130"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from math import *\n",
      "\n",
      "from __future__ import division\n",
      "\n",
      "from sympy import *\n",
      "\n",
      "import numpy as np\n",
      "\n",
      "from scipy import integrate\n",
      "\n",
      "\n",
      "d1 = 0.09       # diameter in cm\n",
      "\n",
      "d2 = 0.025     # diameter in cm\n",
      "\n",
      "rho = 1000   # density in kg/m**3\n",
      "\n",
      "mdot = 25    # mass flow rate in kg/s\n",
      "\n",
      "\n",
      "x = Symbol('x')\n",
      "\n",
      "A1 = pi*d1**2/4\n",
      "\n",
      "A2 = pi*d2**2/4\n",
      "\n",
      "AA = A1 - ((A1-A2)/40)*10       # from figure\n",
      "\n",
      "V = mdot/(rho*AA)\n",
      "\n",
      "print \"(a) Velocity =\",round(V,1),\"m/s\"\n",
      "\n",
      "AX = (A1 - ((A1-AA)/40)*x)\n",
      "\n",
      "v = 25*10**4/(rho*AX)\n",
      "\n",
      "vprime = v.diff(x)\n",
      "\n",
      "V1 = vprime\n",
      "\n",
      "\n",
      "VPrime = 0.09\n",
      "\n",
      "Acx = V*VPrime\n",
      "\n",
      "print \"(b) Convective acceleration =\",round(Acx,3),\"m**2/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Velocity = 5.1 m/s\n",
        "(b) Convective acceleration = 0.46 m**2/s\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.8 Page no 143 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from math import *\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "y = Symbol('y')\n",
      "\n",
      "U = 16*y-12*x\n",
      "\n",
      "zhiprime = U.diff(y)\n",
      "\n",
      "u = zhiprime\n",
      "\n",
      "\n",
      "x = Symbol('x')\n",
      "\n",
      "V = 12*y-9*x\n",
      "\n",
      "zhiprime1 = V.diff(x)\n",
      "\n",
      "v = zhiprime1\n",
      "\n",
      "\n",
      "\n",
      "z = v-u\n",
      "\n",
      "print \"z = \",round(z,0)\n",
      "\n",
      "print \"Hence the flow is rotational\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "z =  -25.0\n",
        "Hence the flow is rotational\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.10 Page no 148"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from math import *\n",
      "\n",
      "\n",
      "d1 = 0.1              # diameter in m\n",
      "\n",
      "d2 = 0.3              # diameter in m\n",
      "\n",
      "V1 = 30               # velocity in m/s\n",
      "\n",
      "\n",
      "V2 = (d1**2/d2**2)*V1\n",
      "\n",
      "print \"Velocity at the larger cross section = \",round(V2,2),\"m/s\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Velocity at the larger cross section =  3.33 m/s\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}