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-{
- "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": [
- "\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": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-09 13:23:06 +0000