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{
"metadata": {
"name": "",
"signature": "sha256:ac94f65c54c89da6d7a90bae31a6309586e55713ceeeb8cf1cb6a41246a395ce"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER18:LAMINAR BOUNDARY LAYERS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E01 : Pg 595"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import sqrt\n",
"p_inf = 101000.; # freestream pressure\n",
"T_inf = 288.; # freestream temperature\n",
"c = 2.; # chord length of the plate\n",
"S = 40.; # planform area of the plate\n",
"mue_inf=1.7894*10.**5.; # coefficient of viscosity at sea level\n",
"gam=1.4; # ratio of specific heats\n",
"R=287.; # specific gas constant\n",
"# the freestream density is\n",
"rho_inf = p_inf/R/T_inf;\n",
"# the speed of sound is\n",
"a_inf = sqrt(gam*R*T_inf);\n",
"# (a)\n",
"V_inf = 100.;\n",
"# thus the mach number can be calculated as\n",
"M_inf = V_inf/a_inf;\n",
"# the Reynolds number at the trailing is given as\n",
"Re_c = rho_inf*V_inf*c/mue_inf;\n",
"# from eq.(18.22)\n",
"Cf = 1.328/sqrt(Re_c);\n",
"# the friction drag on one surface of the plate is given by\n",
"D_f = 1./2.*rho_inf*V_inf**2.*S*Cf;\n",
"# the total drag generated due to both surfaces is\n",
"D = 2.*D_f;\n",
"print\"The total frictional drag is:(a)D =\",D,\"N\"\n",
"# (b)\n",
"V_inf = 1000.;\n",
"# thus the mach number can be calculated as\n",
"M_inf = V_inf/a_inf;\n",
"# the Reynolds number at the trailing is given as\n",
"Re_c = rho_inf*V_inf*c/mue_inf;\n",
"# from eq.(18.22)\n",
"Cf = 1.2/sqrt(Re_c);\n",
"# the friction drag on one surface of the plate is given by\n",
"D_f = 1./2.*rho_inf*V_inf**2.*S*Cf;\n",
"# the total drag generated due to both 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 = 17563872.6566 N\n",
"(b) D = 501884115.614 N\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E02 : Pg 596"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import sqrt\n",
"Pr = 0.71; # Prandlt number of air at standard conditions\n",
"Pr_star = Pr;\n",
"Te = 288.; # temperature of the upper plate\n",
"ue = 1000.; # velocity of the upper plate\n",
"Me = 2.94; # Mach number of flow on the upper plate\n",
"p_star = 101000.;\n",
"R = 287.; # specific gas constant\n",
"T0 = 288.; # reference temperature at sea level\n",
"mue0 = 1.7894*10**-5; # reference viscosity at sea level\n",
"c = 2.; # chord length of the plate\n",
"S = 40.; # plate planform area\n",
"\n",
"# recovery factor for a boundary layer is given by eq.(18.47) as\n",
"r = sqrt(Pr);\n",
"\n",
"# rearranging eq.(16.49), we get for M = 2.94\n",
"T_aw = Te*(1+r*(2.74-1));\n",
"\n",
"# from eq.(18.53)\n",
"T_star = Te*(1 + 0.032*Me**2. + 0.58*(T_aw/Te-1.));\n",
"\n",
"# from the equation of state\n",
"rho_star = p_star/R/T_star;\n",
"\n",
"# from eq.(15.3)\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 = 1.328/sqrt(Re_c_star);\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 = 4978.09594496 N\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E03 : Pg 600"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import sqrt\n",
"Pr = 0.71; # Prandlt number of air at standard conditions\n",
"Pr_star = Pr;\n",
"Te = 288.; # temperature of the upper plate\n",
"ue = 1000.; # velocity of the upper plate\n",
"Me = 2.94; # Mach number of flow on the upper plate\n",
"p_star = 101000.;\n",
"R = 287.; # specific gas constant\n",
"gam = 1.4; # ratio of specific heats\n",
"T0 = 288.; # reference temperature at sea level\n",
"mue0 = 1.7894*10**-5; # reference viscosity at sea level\n",
"c = 2.; # chord length of the plate\n",
"S = 40.; # plate planform area\n",
"\n",
"# recovery factor for a boundary layer is given by eq.(18.47) as\n",
"r = sqrt(Pr);\n",
"\n",
"# from ex.(8.2)\n",
"T_aw = Te*2.467;\n",
"T_w = T_aw;\n",
"\n",
"# from the Meador-Smart equation\n",
"T_star = Te*(0.45 + 0.55*T_w/Te + 0.16*r*(gam-1)/2*Me**2.);\n",
"\n",
"# from the equation of state\n",
"rho_star = p_star/R/T_star;\n",
"\n",
"# from eq.(15.3)\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 = 1.328/sqrt(Re_c_star);\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 = 5014.11379241 N\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
