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diff --git a/Fluid_Mechanics-Fundamentals_&_Applications/Chapter10_2.ipynb b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter10_2.ipynb new file mode 100755 index 00000000..505f66cb --- /dev/null +++ b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter10_2.ipynb @@ -0,0 +1,396 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:e9f209a2bf5415ddf06809cb9961528b86fd396a12cb639b1f2552ce5098ec2f" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 10:Approximate Solutions of the Navier-Stokes Equation" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10-2, Page No:499" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "rho_air=0.8588 #Density of the surrounding air by gas law in kg/m^3\n", + "u=1.474*10**-5 #Dynamic Viscosity in kg/m.s\n", + "rho_particle=1240 #Density of the particle in kg/m^3\n", + "D=50*10**-6 #Diameter of the particles in m\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "\n", + "#Calculations\n", + "#Applying Newtons Third Law and solving for V we get\n", + "V=(D**2/(18*u))*(rho_particle-rho_air)*g #Terminal Velocity of the particle in m/s\n", + "\n", + "#Verification of Reynolds Number \n", + "Re=(rho_air*V*D)/u #Reynolds Number\n", + "\n", + "#Result\n", + "print \"The Terminal Velocity of the particles is\",round(V,3),\"m/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Terminal Velocity of the particles is 0.115 m/s\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10-6,Page No:519" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V_dot_by_L1=2 #Strength of source in line 1 in m^2/s at (0,-1)m\n", + "V_dot_by_L2=-1 #Strength of source in line 2 in m^2/s at (1,-1)m\n", + "T=1.5 #Vortex Strength in m^2/s a (1,1) m\n", + "r_vortex=1 #distance in m\n", + "r_source1=1.414 #Distance in m\n", + "r_source2=1 #Distance in m\n", + "\n", + "#Calculations\n", + "V_vortex=T/(2*pi*r_vortex) #Velocity Induced by the Vortex in m/s\n", + "V_source1=V_dot_by_L1/(2*pi*r_source1) #Velocity induced by the source1 in m/s\n", + "V_source2=V_dot_by_L2/(2*pi*r_source2) #Velocity induced by the source2 in m/s\n", + "V=V_vortex+(V_source1/2**0.5)+V_source2+(V_source1/2**0.5) #Vectorial addition of the velocities in m/s\n", + "\n", + "#Result\n", + "print \"The superposed velocity at point (1,0) is\",round(V,3),\"m/s to the right\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The superposed velocity at point (1,0) is 0.398 m/s to the right\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10-8, Page No:526" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V_dot=0.11 #Volumetric flow rate in m^3/s\n", + "L=0.35 #Length of flow in m\n", + "b=0.02 #m\n", + "u_star_max=0.159 #m/s\n", + "\n", + "#Calculations\n", + "V_dot_by_L=-V_dot/L #Strength of the line source in m^2/s\n", + "u_max=(-u_star_max*V_dot_by_L)/b #Umax in m/s\n", + "\n", + "#Result\n", + "print \"The strength of the line source is\",round(V_dot_by_L,3),\"m^2/s\"\n", + "print \"The maximum velocity is\",round(u_max,2),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The strength of the line source is -0.314 m^2/s\n", + "The maximum velocity is 2.5 m/s\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10-9,Page No:535" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V=10 #Velocity of fluid Flow in kh/hr\n", + "rho=999.9 #Density of water at 5\u02daC in kg/m^3\n", + "v=1.519*10**-6 #Kinematic Viscosity in m^2/s\n", + "#Conversion Factors\n", + "C1=1000\n", + "C2=3600\n", + "\n", + "#Calculations\n", + "Rex=(V*0.5*C1)/(v*C2) #Reynolds Number\n", + "\n", + "#Result\n", + "print \"The Reynolds Number is\",round(Rex)\n", + "print \"As a result the boundary layer is Transitional\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Reynolds Number is 914344.0\n", + "As a result the boundary layer is Transitional\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10-10,Page No:541" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V=32 #Velocity of the fluid in m/s\n", + "x=1.1 #Distance in m\n", + "v=1.7*10**-5 #Kinematic Viscosity in m^2/s\n", + "#Conversion factor\n", + "C1=1000 \n", + "C2=3600\n", + "C3=100\n", + "\n", + "#Calculations\n", + "Rex=(V*x*C1)/(v*C2) #Reynolds Number\n", + "delta=4.91*x*C3/Rex**0.5 #Thickness of boundary Layer in cm\n", + "\n", + "#Result\n", + "print \"The Thickness of the boundary Layer is\",round(delta,2),\"cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Thickness of the boundary Layer is 0.71 cm\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10-11, Page No:546" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable decleration\n", + "x=0.3 #Length of the tunnel in m\n", + "V=4 #Optimised speed in m/s\n", + "R=0.15 #Radius of the tunnel in m\n", + "v=1.507*10**-5 #Kinematic Viscosity in m^2/s\n", + "\n", + "#Calculations\n", + "Rex=(V*x)/v #Reynolds Number\n", + "#Using the diplacement thickness formula\n", + "delta_star=(1.72*x)/Rex**0.5 #Displacement Thickness in m\n", + "#Applying the Continuity Equation\n", + "V_end=(V*R**2)/(R-delta_star)**2 #Velocity at the end in m/s\n", + "\n", + "#Result\n", + "print \"The end velocity should be\",round(V_end,2),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The end velocity should be 4.1 m/s\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10-12, Page No:550" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "#NOTE:The Notation has been changed here\n", + "\n", + "#Decleration of variables\n", + "V=10 #Velocity in m/s\n", + "x=1.52 #Length in m\n", + "v=1.516*10**-5 #Kinematic viscosity in m^2/s\n", + "u=[0,0.]\n", + "#Calculations\n", + "#Part(a)\n", + "\n", + "length=range(0,1500,20) #Array of length in mm\n", + "Re=(V*x)/v #Reynolds Number\n", + "y=transpose(length) #Transpose of the length matrix\n", + "#Laminar Boundary Layer\n", + "d_lam=(4.918*y)/((Re)**0.5)\n", + "#Turbulent Boundary Layer\n", + "d_tur=(0.16*y)/((Re)**(0.14285))\n", + "\n", + "#Part(b)\n", + "C_lam=0.664/((Re)**0.5) #Local Skin Friction coefficient for laminar boundary layer\n", + "C_tur=0.027/((Re)**0.14285) #Local Skin Friction coefficient for turbulent boundary Layer\n", + "\n", + "#Result\n", + "print \"The Reynolds Number is\",round(Re)\n", + "print \"The Local skin friction coefficient is\",round(C_lam,4),\"for laminar boundary layer\"\n", + "print \"The Local Skin friction coefficient is\",round(C_tur,4),\"for turbulent boundary layer\"\n", + "\n", + "plt.plot(y,d_tur,y,d_lam)\n", + "plt.xlabel('x,mm')\n", + "plt.ylabel('delta,mm')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Reynolds Number is 1002639.0\n", + "The Local skin friction coefficient is 0.0007 for laminar boundary layer\n", + "The Local Skin friction coefficient is 0.0038 for turbulent boundary layer\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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So0XJwcy+CnySsBucA7j71RHGJRKrykqYMgUefhimTtVeztL+fGyfg5lNBb4NXJw89W1g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\nS0QP6TVEzUCSE1Q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+ "text": [ + "<matplotlib.figure.Figure at 0x10b5b5f90>" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Examples 10.10-15,Page No:563" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "rho=1.204 #Density of the fluid in kg/m^3\n", + "w=0.5 #Width of the test object in m\n", + "U=10 #Velocity of the flow in m/s\n", + "delta1=0.042 #Boundary Layer thickness at 1 in m\n", + "delta2=0.077 #Boundary Layer thickness at 2 in m\n", + "\n", + "#Calculations\n", + "a=(delta2-delta1) \n", + "b=w*rho\n", + "c=U**2\n", + "Fd=(b*c*a*4)/45#Skin friction drag in N\n", + "\n", + "#Result\n", + "print \"The Skin Friction Drag is\",round(Fd,2),\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Skin Friction Drag is 0.19 N\n" + ] + } + ], + "prompt_number": 15 + } + ], + "metadata": {} + } + ] +}
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