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diff --git a/Fluid_Mechanics-Fundamentals_&_Applications/Chapter11_2.ipynb b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter11_2.ipynb new file mode 100755 index 00000000..31185c9b --- /dev/null +++ b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter11_2.ipynb @@ -0,0 +1,328 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:09f3cec4160faaa4e2a9f5ff2c23e2a27e23b91a36394dba268c313658b30c58" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11:External Flow:Drag and Lift" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11-1, Page No:589" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "Fd=300 #Drag Force in N\n", + "A=2.07 #Frontal Aera in m^2\n", + "rho=1.204 #denisty of air in kg/m^3\n", + "V=95 #Velocity of the fluid around the body in km/h\n", + "C=3.6 #Conversion factor \n", + "\n", + "#Calculations\n", + "Cd=(2*Fd*C**2)/(rho*A*V**2) #Coefficient of Drag of the Car\n", + "\n", + "#Result\n", + "print \"The Coefficient of Drag of the Car is\",round(Cd,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Coefficient of Drag of the Car is 0.35\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11-2,Page No:599" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "W=1.85 #Width of the car in m\n", + "H=1.7 #Height of the car in m\n", + "Cd=0.3 #Drag Coefficient\n", + "rho=1.20 #Denisty of air in kg/m^3\n", + "V=95 #Velocity of the car in km/h\n", + "C=3.6 #Conversion Factor\n", + "L=18000 #Distance travelled by the car in one year in km\n", + "n_car=0.3 #Efficiency of the car in fraction\n", + "HV=44000 #Heating Value of the fuel in kJ/kg\n", + "rho_fuel=0.74 #Density of the fuel in kg/L\n", + "Unit_Cost=0.95 #Unit cost of fuel per litre in $\n", + "Hnew=1.55 #New design height in m\n", + "\n", + "#Calculation\n", + "#Drag Force before Redesigning\n", + "Fd=Cd*W*H*rho*V**2*0.5*(1/C) #Drag Force in N\n", + "W_drag=Fd*L #Work Done to overcome the drag force in kJ/year\n", + "E_in=W_drag/n_car #Energy required in kJ/year\n", + "#Amount of fuel\n", + "Amount_of_fuel=E_in/(HV*rho_fuel) #Amount of fuel required in L/year\n", + "Cost=Amount_of_fuel*Unit_Cost #Total cost per year in $/year\n", + "\n", + "#Reduction ratio\n", + "Reduction_Ratio=(H-Hnew)/H #Reduction ratio\n", + "#Fuel Reduction\n", + "Fuel_Reduction=Reduction_Ratio*Amount_of_fuel #Fuel reduced in L/year\n", + "Cost_Reduction=Reduction_Ratio*Cost #Cost Reduction in $/Year\n", + "\n", + "#Result\n", + "print \"The Reduction Ratio of the redesigned car is\",round(Reduction_Ratio,3)\n", + "print \"Therefore the cars height reduces the fuel consumption by\",round(Reduction_Ratio*100),\"%\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Reduction Ratio of the redesigned car is 0.088\n", + "Therefore the cars height reduces the fuel consumption by 9.0 %\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11-3,Page No:604" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "L=5 #Length on the flat plate in m\n", + "V=2 #Full stream velocity in m/s\n", + "v=2.485*10**-4 #Kinematic Viscosity in m^2/s\n", + "rho=876 #Density of the fluid in kg/m^3\n", + "\n", + "#Calculations\n", + "Rel=(V*L)/v #Reynolds Number\n", + "Cf=1.328*Rel**-0.5 #Average Friction Coefficient\n", + "\n", + "#As pressure drag is zero Cd=Cf\n", + "Fd=Cf*L*rho*V**2*0.5 #Drag Force in N\n", + "\n", + "#Result\n", + "print \"The total Drag Force per Unit Width is\",round(Fd),\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total Drag Force per Unit Width is 58.0 N\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11-4,Page No:609" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "D=0.022 #Diameter of the pipe in m\n", + "rho=999.1 #Density of the fluid in kg/m^3\n", + "u=1.138*10**-3 #Dynamic Viscosity in kg/m.s\n", + "V=4 #Velocity in m/s\n", + "Cd=1 #Coefficent of Drag\n", + "L=30 #Width of the river in m\n", + "\n", + "#Calculations\n", + "Re=(rho*V*D)/u #Reynolds Number\n", + "Fd=Cd*D*L*rho*V**2*0.5 #Drag Force in N\n", + "\n", + "#Result\n", + "print \"The drag force on the pipe is\",round(Fd),\"N\"\n", + "#The answer in the textbook has been approximated to a large value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The drag force on the pipe is 5275.0 N\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11-5,Page No:616" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "m=70000 #Mass of the airplane in kg\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "V_k=558 #Velocity of the airplane in km/h\n", + "rho=1.2 #Denisty of air in kg/m^3\n", + "Cl_max1=1.52 #Coefficient of lift case 1\n", + "Cl_max2=3.48 #Coefficient of lift case 2\n", + "A=150 #Area in m^2\n", + "rho_h=0.312 #Density at crusing altitude in kg/m^3\n", + "Cd=0.03 #Coefficient of drag at crusing altitude\n", + "\n", + "#Calculations\n", + "W=m*g #Weight of the aircraft in N\n", + "V=V_k/3.6 #Velocity in m/s\n", + "\n", + "#Part (A)\n", + "V_min1=((2*W)/(rho*Cl_max1*A))**0.5 #Minimum stall speed in m/s without flap\n", + "V_min2=((2*W)/(rho*Cl_max2*A))**0.5 #Minimum stall speed in m/s with flap\n", + "V_min1_safe=1.2*V_min1 #Safe minimum velocity to avoid stall in m/s without flap\n", + "V_min2_safe=1.2*V_min2 #Safe minimum velocity to avoid stall in m/s with flap\n", + "\n", + "#Part(B)\n", + "Fl=W #Lift force required in N\n", + "Cl=(2*Fl)/(rho_h*A*V**2) #Coefficient of lift\n", + "\n", + "#Part(C)\n", + "Fd=Cd*A*rho_h*V**2*0.5*10**-3 #Drag Force in kN\n", + "Thrust=Fd #thrust Force in kN\n", + "Power=Thrust*V #Power required in kW\n", + "\n", + "#Result\n", + "print \"The safe speed limits without and with flaps are\",round(V_min1_safe,1),\"m/s and\",round(V_min2_safe,1),\"m/s\"\n", + "print \"The lift coefficient is\",round(Cl,2),\"and the corresponding angle of attack is 10\u02da\"\n", + "print \"The power required to provide enough thrust is\",round(Power),\"kW\"\n", + "#The final power answer has been rounded in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The safe speed limits without and with flaps are 85.0 m/s and 56.2 m/s\n", + "The lift coefficient is 1.22 and the corresponding angle of attack is 10\u02da\n", + "The power required to provide enough thrust is 2614.0 kW\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11-6, Page No:618" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "m=0.057 #mass of the tennis ball in kg\n", + "D=0.0637 #Diameter of the tennis ball in m\n", + "V_k=72 #Velocity with which th ball is hit in km/h\n", + "w_rpm=4800 #backspin given to the ball in rpm\n", + "Cl=0.21 #Coefficient of lift\n", + "rho=1.184 #Density of the fluid in kg/m^3\n", + "g=9.81 #Aceleration due to gravity in m/s^2\n", + "\n", + "#Calculations\n", + "V=V_k/3.6 #Velocity of the ball in m/s\n", + "w=(w_rpm*2*pi)/60 #Angular velocity in rad/s\n", + "\n", + "#non dimensional rate of rotation\n", + "#Changing the notation from the one used in the textbook to simplify\n", + "ror=(w*D)/(2*V) #Non dimnsional rate of rotation\n", + "A=4**-1*pi*D**2 #Frontal Area in m^2\n", + "Fl=Cl*A*rho*V**2*0.5 #Lift force in N\n", + "W=m*g #Weight of the ball in N\n", + "F=W-Fl #Combined force in N\n", + "\n", + "#Result\n", + "print \"The ball will drop due to a combined effect of lift and gravity with a force of\",round(W,3),\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ball will drop due to a combined effect of lift and gravity with a force of 0.559 N\n" + ] + } + ], + "prompt_number": 16 + } + ], + "metadata": {} + } + ] +}
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