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diff --git a/Fluid_Mechanics_/Chapter3.ipynb b/Fluid_Mechanics_/Chapter3.ipynb new file mode 100644 index 00000000..e702596e --- /dev/null +++ b/Fluid_Mechanics_/Chapter3.ipynb @@ -0,0 +1,536 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:f598cdc0d1e1209f88ec87b2a9e5b6a08368d8e1e45eff28590bd3252c8de961" + }, + "nbformat": 3, + "nbformat_minor": 0, + "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": [ + "# Dimension of flow field ; velocity components at (1,2) ; magnitude and direction of velocity \n", + "\n", + "from math import *\n", + "\n", + "# Given\n", + "\n", + "# V = 4*Xi-4Yj\n", + "\n", + "x=1 # x co-ordinate\n", + "\n", + "y=2 # y co-ordinate\n", + "\n", + "# Solution\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": [ + "# Discharge and mass flow rate\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "# Given\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", + "# Solution\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": [ + "# Mean Velocity\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "from scipy import integrate\n", + "\n", + "# Given\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", + "# Solution\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": [ + "# Sketch the stream lines in the first quadrant\n", + "\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", + "#init_printing(use_unicode=False, warp_line=False, no_global=True)\n", + "\n", + "# Given\n", + "\n", + "# V = 4*y(m)i+2(m)j\n", + "\n", + "x = Symbol('x')\n", + "U = integrate(2,x)\n", + "\n", + "#print u\n", + "\n", + "y = Symbol('y')\n", + "\n", + "V = integrate(-4*y,y)\n", + "\n", + "#print V\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": [ + "# magnitude and direction of flow field\n", + "\n", + "from math import *\n", + "\n", + "from sympy import *\n", + "\n", + "import numpy as np\n", + "\n", + "# Given\n", + "\n", + "x = 2 # X co-ordinate\n", + "\n", + "Y = 4 # Y co-ordiante\n", + "\n", + "# Solution\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": [ + "# Determine velocity ; convective accleration\n", + "\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", + "# Given\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", + "# Solution\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", + "# at x = 0.1 m we get dv/dx = 0..09\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": [ + "# Is the flow irrotational\n", + "\n", + "from math import *\n", + "\n", + "# Given\n", + "\n", + "# w = (16y-12x)i +(12y-9x)j\n", + "\n", + "# Solution\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", + "#Vx = -9 # differentiate V wrt x\n", + "\n", + "#Vx = -9 # differentiate V wrt x\n", + "#Uy = 16 # differentiate U wrt y\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": [ + "# Velocity in larger section\n", + "\n", + "from math import *\n", + "\n", + "# Given\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", + "# Solution\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": {} + } + ] +}
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