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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "# Chapter 06:Incompressible viscous flow: A brief review"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex6.1:pg-226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 6, Example 1\n",
+ "Umax in m/s is\n",
+ "Umax= 1.6\n",
+ "The shear stress T in N/m**2\n",
+ "T= 64.0\n",
+ "(dp/dx) in N/m**3 is\n",
+ "X= -19200.0\n",
+ "The Shear stress at a distance of 0.002m from the lower plate in N/m**2\n",
+ "t= -57.6\n",
+ "The shear stress at a distance of 0.002m from the upper plate in N/m**2\n",
+ "t= 57.6\n",
+ "The opposite signs in t represents the opposite directions.The plus sign is in the direction of flow and the minus sign is in the direction opposite to the flow \n",
+ "The pressure drop over a distance of 2m in N/m**2 is\n",
+ "deltaP= 38400.0\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "import math\n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 6, Example 1\"\n",
+ " #Oil of specific gravity 0.90 and dynamic viscosity (mu=0.1Pa*s) flows between two fixed plates kept 2*b=10mm apart,So b=5mm.\n",
+ "#The average velocity is Uav=1.60m/s\n",
+ "Uav=1.60;\n",
+ "mu=0.1;\n",
+ "b=0.005; #in metre\n",
+ " #Umax is maximum velocity\n",
+ " Umax=(3.0/2)*Uav\n",
+ "print\"Umax in m/s is\"\n",
+ "Umax=(3/2)*Uav\n",
+ "print\"Umax=\",Umax\n",
+ " #The shear stress at the plate is given by T=2*µ*(Umax/b)\n",
+ "print\"The shear stress T in N/m**2\"\n",
+ "T=2*mu*(Umax/b) \n",
+ " #The shear sress at a distance from plate is given by t=y*(dp/dx)\n",
+ "#(dp/dx)=X=-3*mu*(Uav/b**2)\n",
+ "print\"T=\",T\n",
+ "print\"(dp/dx) in N/m**3 is\"\n",
+ "X=-3*mu*(Uav/b**2)\n",
+ " #Taking modulus of X by multipying it with negative sign.\n",
+ "print\"X=\",X\n",
+ "print\"The Shear stress at a distance of 0.002m from the lower plate in N/m**2\"\n",
+ "y=b-0.002;\n",
+ "t=y*(X) #NOTE:Answer given in the book is incorrect (Calculation mistake)\n",
+ "print\"t=\",t\n",
+ "print\"The shear stress at a distance of 0.002m from the upper plate in N/m**2\"\n",
+ "t=-y*(X) #NOTE:Answer given in the book is incorrect (Calculation mistake)\n",
+ "print\"t=\",t\n",
+ "print\"The opposite signs in t represents the opposite directions.The plus sign is in the direction of flow and the minus sign is in the direction opposite to the flow \"\n",
+ " #deltaP is the pressure drop\n",
+ "print\"The pressure drop over a distance of 2m in N/m**2 is\"\n",
+ " #Since pressure drop is considered at a distance of 2m so L=2m\n",
+ "L=2;\n",
+ "deltaP=(-X)*L\n",
+ "print\"deltaP=\",deltaP\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex6.3:pg-229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 6, Example 3\n",
+ "The rate of change of pressure with respect to length in N/m**3\n",
+ "X= 2000\n",
+ "Flow rate(Q) in m**3/s is)\n",
+ "Q= 0.00333333333333\n",
+ "The viscosity of oil(mu)in kg/(m*s)\n",
+ "mu= 0.0920388472731\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "import math\n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 6, Example 3\"\n",
+ " #Oil of specific gravity (sg)=0.90 is discharged at a rate(mdot)=3kg/s under a pressure difference dp=10KN/m**2 over a length dz=5m of a pipe having a diameter(D) of 50mm.\n",
+ "dp=10*10**3; #in N/m**2\n",
+ "dz=5;\n",
+ "D=0.05; #in metre\n",
+ "mdot=3;\n",
+ "sg=0.90;\n",
+ " #X=dp/dz is the rate of change of pressure\n",
+ "print\"The rate of change of pressure with respect to length in N/m**3\"\n",
+ "X=dp/dz\n",
+ "print\"X=\",X\n",
+ " #Flow rate is Q\n",
+ "print\"Flow rate(Q) in m**3/s is)\"\n",
+ "Q=mdot/(sg*10**3)\n",
+ "print\"Q=\",Q\n",
+ " #The viscosity of oil is mu=(pi*D**4*X)/(128*Q*dz)\n",
+ "print\"The viscosity of oil(mu)in kg/(m*s)\"\n",
+ "mu=(math.pi*D**4*X)/(128*Q)\n",
+ "print\"mu=\",mu\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex6.7:pg-250 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Introduction to heat transfer by S.K.Som, Chapter 6, Example 7\n",
+ "The maximum length of plate in m is \n",
+ "L= 2.5\n",
+ "The average skin friction coefficient is\n",
+ "cfL= 1.328\n",
+ "Drag force on one side of plate in N is\n",
+ "Fd= 21.5136\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "import math\n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 6, Example 7\"\n",
+ " #A flat plate B=1.2m wide and of length L is kept parallel to a uniform stream of air of velocity Uinf=3m/s in a wind tunnel.\n",
+ "Uinf=3;\n",
+ "B=1.2;\n",
+ " #If it is desired to have a laminar boundary layer only on the plate \n",
+ "#Assume that the laminar flow exists up to a reynold number(ReL)=5*10**5.Take density of air as rhoair=1.2kg/m**3 and viscosity of air as nuair=1.5*10**-5 m**2/s.\n",
+ "nuair=1.5*10**-5;\n",
+ "rhoair=1.2;\n",
+ "ReL=5*10**5;\n",
+ " #For maximum length of the plate reynolds number is ReL=Uinf*L/nuair\n",
+ "#so L=ReL*nuair/Uinf\n",
+ "print\"The maximum length of plate in m is \"\n",
+ "L=ReL*nuair/Uinf\n",
+ "print\"L=\",L\n",
+ " #The average skin friction coefficient is cfL=1.328/(ReL)**(1/2)\n",
+ "print\"The average skin friction coefficient is\"\n",
+ "cfL=1.328/(ReL)**(1/2)\n",
+ "print\"cfL=\",cfL\n",
+ " #Fd is drag force\n",
+ "print\"Drag force on one side of plate in N is\"\n",
+ "Fd=cfL*(rhoair*Uinf**2/2)*B*L\n",
+ "print\"Fd=\",Fd\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex6.10:pg-268 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 6, Example 10\n",
+ "Wind velocity(Uinf)in m/s is\n",
+ "Uinf= 10\n",
+ "Reynolds number is\n",
+ "ReL= 4000000.0\n",
+ "Friction coefficient is\n",
+ "CbarfL= 0.0735645\n",
+ "Drag force on one side of the plate per unit metre width in Newton is \n",
+ "FD= 26.48322\n",
+ "The turbulent boundary layer thickness at the trailing edge in metre is \n",
+ "delta= 2.274\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "import math\n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 6, Example 10\"\n",
+ " #Wind at a speed of U=36km/hr blows over a flat plate of length,L=6m .If the density and kinematic viscosity of air are rho=1.2kg/m**3 and mu=1.5*10**-5m**2/s respectively.\n",
+ "U=36;\n",
+ "L=6;\n",
+ "rho=1.2;\n",
+ "mu=1.5*10**-5;\n",
+ " #Wind velocity in m/s is Uinf\n",
+ "print\"Wind velocity(Uinf)in m/s is\"\n",
+ "Uinf=U*1000/3600\n",
+ "print\"Uinf=\",Uinf\n",
+ " #Reynolds number is given by ReL=L*Uinf/mu\n",
+ "print\"Reynolds number is\"\n",
+ "ReL=L*Uinf/mu\n",
+ "print\"ReL=\",ReL\n",
+ " #We consider that transition of boundary layer takes place from laminar to turbulent takes place at ReL=5*10**5.\n",
+ "#Therfore the corresponding friction coefficient is given by CbarfL=(0.074-ReL**(1/5))-(1742/ReL)\n",
+ "print\"Friction coefficient is\"\n",
+ "CbarfL=(0.074/ReL**(1/5))-(1742/ReL)\n",
+ "print\"CbarfL=\",CbarfL\n",
+ " #Drag force on one side of the plate per unit metre width is given by FD=CbarfL*rho*Uinf**2*L/2\n",
+ "print\"Drag force on one side of the plate per unit metre width in Newton is \"\n",
+ "FD=CbarfL*rho*Uinf**2*L/2\n",
+ "print\"FD=\",FD\n",
+ " #The turbulent boundary layer thickness at the trailing edge is given by delta=L*(0.379/ReL**(1/5))\n",
+ "print\"The turbulent boundary layer thickness at the trailing edge in metre is \"\n",
+ "delta=L*(0.379/ReL**(1/5))\n",
+ "print\"delta=\",delta\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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