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authorTrupti Kini2016-02-23 23:30:06 +0600
committerTrupti Kini2016-02-23 23:30:06 +0600
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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:50af8d3cf8d660e7f072a797c56082a406513e091b4f2f4b68a912e6ceab549d"
+ },
+ "nbformat": 3,
+ "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": {}
+ }
+ ]
+} \ No newline at end of file