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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 17 : The boundary layer"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 17.1 page no : 519\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the boundary layer thickness\n",
"#for the aeroplane\n",
"\n",
"# variables\n",
"v=1.61*10**(-4) #ft**2/s\n",
"x=2. #ft\n",
"V=200. #miles/hr\n",
"\n",
"# calculation\n",
"#1 mile = 5280 ft\n",
"#1 hr = 3600 sec\n",
"delta_aeroplane=5*(v*x/(V*5280/3600.0))**0.5\n",
"\n",
"# result\n",
"print \"The boundary layer thickness for the aeroplane is %f ft\\n\"%delta_aeroplane\n",
"#for the boat\n",
"v1=1.08*10**(-5) #ft**2/s\n",
"x1=2. #ft\n",
"V1=10. #miles/hr\n",
"#1 mile = 5280 ft\n",
"#1 hr = 3600 sec\n",
"delta_boat=5*(v1*x1/(V1*5280/3600.0))**0.5\n",
"print \"The boundary layer thickness for the boat is %f ft\"%delta_boat"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The boundary layer thickness for the aeroplane is 0.005239 ft\n",
"\n",
"The boundary layer thickness for the boat is 0.006068 ft\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 17.2 page no : 521\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the force required to tow a square metal plate by a boat\n",
"\n",
"# variables\n",
"rho_water=998.2 #Kg/m**3\n",
"V=15. #km/hr\n",
"v=1.004*10**(-6) #m**2/s\n",
"l=1. #m length of plate\n",
"\n",
"#Calculations\n",
"#1 km = 1000 m\n",
"#1 hr = 3600 s\n",
"Rx=(V*1000/3600.)*l/v #dimentionless (reynold's number)\n",
"Cf=1.328/Rx**0.5 #dimentionless\n",
"F=Cf*rho_water*(V*1000/3600.0)**2 #N\n",
"\n",
"#Result\n",
"print \"The force required to tow the square plate is %f N\"%F"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The force required to tow the square plate is 11.297065 N\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 17.3 page no : 528\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the distance between the wall and edge of the laminar sublayer and buffer layer\n",
"\n",
"#Variables\n",
"V=10. #ft/s\n",
"l=0.25 #ft\n",
"v=1.08*10**(-5) #ft**2/s\n",
"f=0.0037 #dimentionless (fanning friction factor)\n",
"u01=5. #dimentionless\n",
"y01=5. #dimentionless\n",
"\n",
"#Calculations\n",
"R=V*l/v #dimentionless (reynold's number)\n",
"u1=V*(f/2.0)**0.5 #ft/s\n",
"r1=y01*v/u1 #ft\n",
"\n",
"#for buffer layer\n",
"u02=12. #dimentionless\n",
"y02=26. #dimentionless\n",
"r2=y02*v/u1 #ft\n",
"\n",
"#Results\n",
"print \"the distance between the wall and edge of the laminar sublayer is %f ft\\n\"%r1\n",
"print \"the distance between the wall and edge of the buffer layer is %f ft\"%r2\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the distance between the wall and edge of the laminar sublayer is 0.000126 ft\n",
"\n",
"the distance between the wall and edge of the buffer layer is 0.000653 ft\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 17.4 page no : 530\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the boundary layer thickness and the drag on the plate\n",
"\n",
"# variables\n",
"V=50. #ft/s\n",
"l=20. #ft\n",
"b=1. #ft\n",
"v=1.08*10**(-5) #ft**2/s\n",
"\n",
"# calculation and result\n",
"R=V*l/v #dimentionless (reynold's number)\n",
"delta=0.37*l/R**0.2 #ft\n",
"print \"The boundary layer thichness at the end of the plate is %f ft\\n\"%delta\n",
"Cf=0.072/R**0.2 #dimentionless\n",
"rho_water=62.3 #lbm/ft**3\n",
"V=50. #ft/s\n",
"#let A be the area of contact\n",
"A=2*l*b #ft**2\n",
"#1 lbf.s**2 = 32.2 lbm.ft\n",
"F=(1/2.0)*Cf*rho_water*V**2*A/32.2 #lbf\n",
"print \"The drag on the plate is %f lbf\"%F"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The boundary layer thichness at the end of the plate is 0.188763 ft\n",
"\n",
"The drag on the plate is 177.672178 lbf\n"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}
|
