diff options
Diffstat (limited to 'Fluid_Mechanics/Chapter_7.ipynb')
| -rwxr-xr-x | Fluid_Mechanics/Chapter_7.ipynb | 221 |
1 files changed, 221 insertions, 0 deletions
diff --git a/Fluid_Mechanics/Chapter_7.ipynb b/Fluid_Mechanics/Chapter_7.ipynb new file mode 100755 index 00000000..95848de2 --- /dev/null +++ b/Fluid_Mechanics/Chapter_7.ipynb @@ -0,0 +1,221 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:58b7373e6785b57ec4db0eaf49754884e3dad15de9e9489fc1c2bb500d413f82" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7: Two-Dimentional Idea Flow" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.2, Page 235" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "x = 120; #Theta\n", + "r = 1;\n", + "v0 = 0.5;\n", + "q = 2;\n", + "theta =120;\n", + "\n", + " #Calculations\n", + "Vr = v0*r*math.cos(math.radians(theta)) +q/(2*math.pi)\n", + "Vth = -v0*math.sin(math.radians(theta))\n", + "V = (Vr**2+Vth**2)**0.5;\n", + "alpha = math.atan(abs(Vth/Vr));\n", + "bet = x-alpha*180/math.pi;\n", + "\n", + "\n", + "print \"Fluid Velocity(m/s) :\",round(V,3)\n", + "print \"Beta (Degree) :\",round(bet,2)\n", + "print \"Alpha (Degree) :\",round(alpha*180/math.pi,2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fluid Velocity(m/s) : 0.438\n", + "Beta (Degree) : 38.96\n", + "Alpha (Degree) : 81.04\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.3, Page 239" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "from scipy.optimize import fsolve\n", + "import sympy\n", + "from sympy import RootOf, I, Symbol\n", + " #Initializing the variables \n", + "q = 10;\n", + "def shi(x,y):\n", + " Z = (q/2/math.pi)*(math.atan(y/(x-1))-math.atan(y/(x+1))) - 25*y;\n", + " return Z\n", + "h = 0.0000001;\n", + "Vinf = 25;\n", + "x=Symbol('x')\n", + " #Calculations\n", + "#f = lambda x : x**2 - 2/(5*math.pi) -1\n", + "result = [RootOf(x**2- 2/(5*math.pi) -1,i) for i in (0,1)] \n", + "\n", + "root1=round(result[0],3)\n", + "root2=round(result[1],3)\n", + "l = abs(abs(root1)+abs(root2));\n", + "Ymax = 0.047;\n", + "width = 2*Ymax;\n", + "Vx = (shi(1-h,1)-shi(1-h,1-h))/h; # At x=1 the function atan is not defined hence taking x a little smaller.\n", + "Vy = -1*(shi(1-2*h,1)-shi(1-h,1))/h; # At x=1 the function atan is not defined hence taking x a little smaller.\n", + "\n", + "V = (Vx**2+Vy**2)**0.5;\n", + "rho = Symbol('rho')\n", + "dP = rho/2*round((V**2 - Vinf**2),2); #difference in pressure\n", + "\n", + "print \"Pressure Difference (N/m2) :\",dP\n", + "print \"Velocity (m/s) :\",round(V,2)\n", + "print \"Length of Rankine Body(m) :\",l\n", + "print \"Width of Rankine Body (m) :\",width" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure Difference (N/m2) : 16.93*rho\n", + "Velocity (m/s) : 25.67\n", + "Length of Rankine Body(m) : 2.124\n", + "Width of Rankine Body (m) : 0.094\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.4, Page 242" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math #Example 7.4\n", + "\n", + " #Initializing the variables\n", + "a = 0.02;\n", + "r = 0.05;\n", + "V0 = 1;\n", + "x = 135; # Theta\n", + "def shi(r,x):\n", + " Z = V0*math.sin(math.radians(x))*(r-((a**2)/r));\n", + " return Z\n", + "h = 0.0001;\n", + "\n", + " #Calculations\n", + "Vr = 57*(shi(r,x+h)-shi(r,x))/(r*h);\n", + "Vx = -1*(shi(r+h,x)-shi(r,x))/h;\n", + "\n", + "print \"Radial Velocity (m/s) :\",round(Vr,3)\n", + "print \"Normal component of velocity (m/s):\",round(Vx,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radial Velocity (m/s) : -0.591\n", + "Normal component of velocity (m/s): -0.82\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5, Page 246" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables\n", + "rho = 1000;\n", + "r = 2;\n", + "psi = 2*math.log(r);\n", + "\n", + " #Calculations\n", + "y = psi/math.log(r); # y = GammaC / 2*pi\n", + "v = y/r;\n", + "dPbydr = rho*v**2/r;\n", + "print \"Pressuer Gradient (N/m3 ) :\",dPbydr" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressuer Gradient (N/m3 ) : 500.0\n" + ] + } + ], + "prompt_number": 5 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |