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"name": "",
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"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",
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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": {}
}
]
}
|
