{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CHAPTER18:LAMINAR BOUNDARY LAYERS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example E01 : Pg 595" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The total frictional drag is:(a)D = 17563872.6566 N\n", "(b) D = 501884115.614 N\n" ] } ], "source": [ "# All the quantities are expressed in SI units\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\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example E02 : Pg 596" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The total frictional drag is: D = 4978.09594496 N\n" ] } ], "source": [ "# All the quantities are expressed in SI units\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\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example E03 : Pg 600" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The total frictional drag is: D = 5014.11379241 N\n" ] } ], "source": [ "# All the quantities are expressed in SI units\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\"" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [Root]", "language": "python", "name": "Python [Root]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }