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{
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"name": "",
"signature": "sha256:50af8d3cf8d660e7f072a797c56082a406513e091b4f2f4b68a912e6ceab549d"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER19:TURBULENT BOUNDARY LAYERS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E01 : Pg 612"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"# (a)\n",
"import math \n",
"from math import sqrt\n",
"Re_c = 1.36e7; # as obtained from ex. 18.1a\n",
"rho_inf = 1.22; # freestream air denstiy\n",
"S = 40.; # plate planform area\n",
"# hence, from eq.(19.2)\n",
"Cf = 0.074/Re_c**0.2;\n",
"V_inf = 100.;\n",
"# hence, for one side of the plate\n",
"D_f = 1./2.*rho_inf*V_inf**2.*S*Cf;\n",
"# the total drag on both the surfaces is\n",
"D = 2.*D_f;\n",
"print\"The total frictional drag is: (a)D =\",D,\"N\"\n",
"# (b)\n",
"Re_c = 1.36e8; # as obtained from ex. 18.1b\n",
"# hence, from fig 19.1 we have\n",
"Cf = 1.34*10.**-3.;\n",
"V_inf = 1000.;\n",
"# hence, for one side of the plate\n",
"D_f = 1./2.*rho_inf*V_inf**2.*S*Cf;\n",
"# the total drag on both the surfaces is\n",
"D = 2.*D_f;\n",
"print\"(b) D =\",D,\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total frictional drag is: (a)D = 1351.89748485 N\n",
"(b) D = 65392.0 N\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E02 : Pg 612"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"# from ex 18.2\n",
"import math\n",
"from math import sqrt\n",
"Re_c_star = 3.754e7; # Reynolds number at the trailing edge of the plate\n",
"rho_star = 0.574;\n",
"ue = 1000.; # velocity of the upper plate\n",
"S = 40.; # plate planform area\n",
"# from eq.(19.3) we have\n",
"Cf_star = 0.074/Re_c_star**0.2;\n",
"# hence, for one side of the plate\n",
"D_f = 1./2.*rho_star*ue**2.*S*Cf_star;\n",
"# the total drag on both the surfaces is\n",
"D = 2.*D_f;\n",
"print\"The total frictional drag is:D =\",D,\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total frictional drag is:D = 51916.421508 N\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E03 : Pg 615"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"Me = 2.94; # mach number of the flow over the upper plate\n",
"ue = 1000.;\n",
"Te = 288.; # temperature of the upper plate\n",
"ue = 1000.; # velocity of the upper plate\n",
"S = 40.; # plate planform area\n",
"Pr = 0.71; # Prandlt number of air at standard condition\n",
"gam = 1.4; # ratio of specific heats\n",
"\n",
"# the recovery factor is given as\n",
"r = Pr**(1./3.);\n",
"\n",
"# for M = 2.94\n",
"T_aw = Te*(1.+r*(2.74-1.));\n",
"T_w = T_aw; # since the flat plate has an adiabatic wall\n",
"\n",
"# from the Meador-Smart equation\n",
"T_star = Te*(0.5*(1.+T_w/Te) + 0.16*r*(gam-1.)/2.*Me**2.);\n",
"\n",
"# from the equation of state\n",
"p_star=1.\n",
"R=1.\n",
"rho_star = p_star/R/T_star;\n",
"\n",
"# from eq.(15.3)\n",
"mue0=1.\n",
"T0=1.\n",
"c=1.\n",
"mue_star = mue0*(T_star/T0)**1.5*(T0+110.)/(T_star+110.);\n",
"\n",
"# thus\n",
"Re_c_star = rho_star*ue*c/mue_star;\n",
"\n",
"# from eq.(18.22)\n",
"Cf_star = 0.02667/Re_c_star**0.139;\n",
"\n",
"# hence, the frictional drag on one surface of the plate is\n",
"D_f = 1./2.*rho_star*ue**2.*S*Cf_star;\n",
"\n",
"# thus, the total frictional drag is given by\n",
"D = 2.*D_f;\n",
"\n",
"print\"The total frictional drag is:D =\",D,\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total frictional drag is:D = 4967.70450221 N\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
