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authorhardythe12015-06-03 15:27:17 +0530
committerhardythe12015-06-03 15:27:17 +0530
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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:7a83d458ec863729e5567b39b8a122f73ab73bc391e4a0f9cd56c8645c12c28b"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 07: Dimensional Analysis and Modeling"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-4, Page No:290"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable Decleration\n",
+ "g_earth=9.81 #Acceleration due to gravity on earth in m/^2\n",
+ "theta=(pi*5)/180 #Angle above the horizon in radians\n",
+ "v=21 #Speed of the baseball in m/s\n",
+ "zo=2 #Height at wich the ball is left in m\n",
+ "t_star=2.75 #Time required to hit the ground in s\n",
+ "\n",
+ "#Calculations\n",
+ "#Part(a)\n",
+ "g_moon=g_earth/6 #Acceleration due to gravity on the moon in m/s^2\n",
+ "w_o=v*sin(theta) #Vertical component of Speed in m/s\n",
+ "Fr_square=w_o**2/(g_moon*zo) #Value of froude number square \n",
+ "t_a=(t_star*zo)/w_o #Estimated time required to hit the ground in s\n",
+ "#Part(b)\n",
+ "#simplfying the calculations\n",
+ "a=w_o**2+(2*zo*g_moon)\n",
+ "b=a**0.5\n",
+ "t_b=(w_o+b)/g_moon #Exact time required for the ball to hit the ground in s\n",
+ "\n",
+ "#Result\n",
+ "print \"The estimated time required to hit the ground is\",round(t_a,2),\"s\"\n",
+ "print \"The exact time required for the ball to hit the ground is\",round(t_b,2),\"s\"\n",
+ "#Due to the decimal accuracy the answer in textbook differs "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The estimated time required to hit the ground is 3.01 s\n",
+ "The exact time required for the ball to hit the ground is 3.04 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-5, Page No:293"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable Decleration\n",
+ "Vp=50 #Velocity in the prototype in mi/h\n",
+ "um=1.754*10**-5 #Viscosity in the model in kg/m.s\n",
+ "up=1.849*10**-5 #Viscosity in the prototype in kg/m.s\n",
+ "rhop=1.184 #Density of air in prototype in kg/m^3\n",
+ "rhom=1.269 #Density of air in model in kg/m^3\n",
+ "Lp_Lm=5 #ratio of length \n",
+ "\n",
+ "#Calculations\n",
+ "a=um/up\n",
+ "b=rhop/rhom\n",
+ "Vm=Vp*a*b*Lp_Lm #Velocity in the model in mi/h\n",
+ "\n",
+ "#result\n",
+ "print \"The velocity in the wind tunnel required is\",round(Vm),\"mi/h\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The velocity in the wind tunnel required is 221.0 mi/h\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-6, Page No:294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable Decleration\n",
+ "Fd=94.3 #Average Drag force on the model in N\n",
+ "Vp=float(50) #Velocity of the prototype in mi/h\n",
+ "Vm=float(221) #Velocity of the model in mi/h\n",
+ "rhop=1.184 #Density of air in prototype in kg/m^3\n",
+ "rhom=1.269 #Density of air in model in kg/m^3\n",
+ "Lp_Lm=5 #ratio of length \n",
+ "\n",
+ "#Calculations\n",
+ "a=(rhop/rhom)\n",
+ "c=(Lp_Lm**2)\n",
+ "b=Vm/Vp\n",
+ "Fd_p=(Fd*a*c)/(b**2) #Drag Force on the prototype in N\n",
+ "\n",
+ "#Result\n",
+ "print \"The Drag force on the prototype is\",round(Fd_p),\"N\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Drag force on the prototype is 113.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-10, Page No:313"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Variable Decleration\n",
+ "Lm=0.991 #Length of the model truck in m\n",
+ "Hm=0.257 #height of the model truck in m\n",
+ "Wm=0.159 #Width of the model truck in m\n",
+ "rho=1.184 #Density of Air in kg/m^3\n",
+ "u=1.849*10**-5 #Viscosity of air in kg/m.s\n",
+ "FD_m=89.9 #Drag Force in the model in N\n",
+ "V_m=70 #Velocity in the model in m/s\n",
+ "C=16 #Geometric Ratio\n",
+ "Vp=26.8 #Velocity of the prototype in m/s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "V=range(20,75,5) #Velocity array each in m/s\n",
+ "F=[12.4,19,22.1,29,34.3,39.9,47.2,55.5,66,77.6,89.9] #Drag force array in N\n",
+ "X=transpose(F) #Transpose of the matrix in order to mutliply\n",
+ "#Simplfying the calculations by using steps\n",
+ "\n",
+ "CD_m1=(X/V)\n",
+ "CD_m2=CD_m1/V\n",
+ "CD_m=(2*CD_m2)/(rho*Wm*Hm) #Drag Coefficient \n",
+ "\n",
+ "Y=transpose(V)\n",
+ "Re_m=(rho*Y*Wm)/u #Reynolds Number for each set\n",
+ "\n",
+ "#Calculations for prototype\n",
+ "Re_p=(rho*Vp*C*Wm)/u #Reynolds Number for the prototype\n",
+ "\n",
+ "#Aerodynamic Drag Calculations\n",
+ "FD_p=0.5*rho*Vp**2*C**2*Wm*Hm*CD_m[10] #Aerodynamic Drag on the Vehicle in N\n",
+ "\n",
+ "#Result\n",
+ "print \"The Aerodynamic Drag on the Vehicle is\",round(FD_p),\"N\"\n",
+ "\n",
+ "plt.plot(Re_m,CD_m,'ro')\n",
+ "plt.ylabel('Cd')\n",
+ "plt.xlabel('Re')\n",
+ "plt.show()\n",
+ "\n",
+ "#The answer in the textbook has been rounded off to the nearest value"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Aerodynamic Drag on the Vehicle is 3373.0 N\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x10b5b8950>"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-11, Page No:316"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable Decleration\n",
+ "Lm_Lp=10**-2 #Length Scale Factor\n",
+ "vp=1.002*10**-6 #Kinematic viscosity of the prototype in m^2/s\n",
+ "\n",
+ "#Calculations\n",
+ "vm=vp*(Lm_Lp)**1.5 #Required Kinematic Viscosity in m^2/s\n",
+ "\n",
+ "#Result\n",
+ "print \"Looking up in a table we cannot find a fluid of the kinematic viscosity\",vm,\"m^2/s\"\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Looking up in a table we cannot find a fluid of the kinematic viscosity 1.002e-09 m^2/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file