{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 7 : The momentum balance" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.2 page no : 248\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calulate the final velocity of duck after being hit by a bullet\n", "\n", "# Variables \n", "m_duck=3. #lbm\n", "v_duck=-15. #ft/s due west\n", "m_bullet=0.05 #lbm\n", "v_bullet=1000. #ft/s due east\n", "\n", "# Calculation \n", "#total initial momentum = final momentum\n", "v_sys=((m_duck*v_duck)+(m_bullet*v_bullet))/(m_duck+m_bullet)#ft/s\n", "\n", "# Result\n", "print \"The final velocity of the duck is %f ft/s\"%v_sys" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The final velocity of the duck is 1.639344 ft/s\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.3 page no : 250\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#calculate the force required to hold of water from a hoze\n", "\n", "# Variables \n", "rho=998.2 #Kg/m^3\n", "q=0.01 #m^3/s\n", "v_initial=30. #m/s\n", "v_final=0. #m/s\n", "\n", "# Calculation \n", "F=q*rho*(v_final-v_initial) #N\n", "\n", "# Result\n", "print \"The force required to hold of water from a hoze %f N\"%F\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The force required to hold of water from a hoze -299.460000 N\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.4 page no : 251\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#calculate the force required to hold of water from a hoze\n", "\n", "# Variables \n", "rho=998.2 #Kg/m^3\n", "q=0.01 #m^3/s\n", "v_initial=30. #m/s\n", "v_final=-15. #m/s\n", "\n", "# Calculation \n", "F=q*rho*(v_final-v_initial) #N\n", "\n", "# Result\n", "print \"The force required to hold of water from a hoze %f N\"%F" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The force required to hold of water from a hoze -449.190000 N\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.5 page no : 252\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the force exerted on the flange when the valve of the nozzle is closed\n", "\n", "# Variables \n", "#Let the gauge pressure be denoted by Pg\n", "Pg=100. #lbf/in^2\n", "A=10. #in^2\n", "\n", "# Calculation \n", "#F_bolts = -F_liq-F_atm\n", "#F_bolts = -(Pg + P_atm)A - (-P_atm.A)\n", "#F_bolts = -Pg.A\n", "F_bolts=-Pg*A\n", "\n", "# Result\n", "print \"The force exerted on the flange when the valve of the nozzle is closed is %d lbf\"%F_bolts" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The force exerted on the flange when the valve of the nozzle is closed is -1000 lbf\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.6 page no : 254\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the force exerted on the flange\n", "\n", "# Variables \n", "dP=100. #lbf/in^2\n", "A_out=1. #in^2\n", "rho=62.3 #lbm/ft^3\n", "ratio_A=0.1 #dimentionless\n", "\n", "# Calculation \n", "#1 ft = 12 in\n", "#1 lbf.s^2 = 32.2 lbm.ft\n", "v_out=(2*dP/rho/(1-ratio_A**2)*32.2*144)**0.5 #ft/s\n", "v_in=12.3 #ft/s\n", "\n", "m=rho*A_out*v_out/144. #lbm/s\n", "F=m*(v_out-v_in)/32.2 #lbf\n", "\n", "# Result\n", "print \"The force exerted on the flange is %f lbf\"%F" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The force exerted on the flange is 181.755634 lbf\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.7 page no : 255\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the support forces in x and y direction in a 90 degree bend tube\n", "\n", "# Variables \n", "p1=200. #KPa\n", "A=0.1 #m^2\n", "m=500. #Kg/s\n", "rho=998.2 #Kg/m^3\n", "q=m/rho #m^3/s\n", "v=q/A #m/s\n", "Vx_initial=v #m/s\n", "Vx_final=0. #m/s\n", "Vy_initial=0. #m/s\n", "Vy_final=-v #m/s\n", "\n", "# Calculation and Result\n", "neg_Fx=m*(Vx_final-Vx_initial)-p1*1000*A #N\n", "Fx = neg_Fx\n", "print \"The support force in the x direction is %f N\"%Fx\n", "neg_Fy=m*(Vy_final-Vy_initial)-p1*1000*A#N\n", "Fy = neg_Fy\n", "print \"The support force in the y direction is %f N\"%Fy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The support force in the x direction is -22504.508115 N\n", "The support force in the y direction is -22504.508115 N\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.8 page no : 258\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the thrust on a rocket\n", "\n", "# Variables \n", "m=1000. #Kg/s\n", "v_out=-3000. #m/s its in the negative y direction\n", "v_in=0. #m/s\n", "A=7. #m^2\n", "P=35000. #Pa\n", "\n", "# Calculation \n", "F_thrust=(-m*(v_out-v_in)+P*A)/1000000.0 #MN\n", "\n", "# Result\n", "print \"The thrust on the rocket is %f MN\"%F_thrust" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The thrust on the rocket is 3.245000 MN\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.9 page no : 258\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the specific impulse for a rocket\n", "\n", "# Variables \n", "Vy_exh=-3000. #m/s in negative y direction\n", "\n", "# Calculation \n", "Isp=-Vy_exh/1000.0 #KN.s/Kg\n", "\n", "# Result\n", "print \"The specific impulse on the rocket is %d KN.s/Kg\"%Isp" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The specific impulse on the rocket is 3 KN.s/Kg\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.10 page no : 259\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the Mass air flow rate required by a jet engine\n", "\n", "# Variables \n", "F_thrust=20000. #lbf\n", "Vx_out=1350.0 #ft/s\n", "Vx_in=0. #ft/s\n", "\n", "# Calculation \n", "#1 lbf.s^2 = 32.2 lbm.ft\n", "m=F_thrust/(Vx_out-Vx_in)*32.2 #lbm/s\n", "\n", "# Result\n", "print \"The mass air flow rate required by a jet engine is %d lbm/s\"%m" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The mass air flow rate required by a jet engine is 477 lbm/s\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.12 page no : 267\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the final velocity of a rocket after launch\n", "import math\n", "\n", "# Variables \n", "Isp=430. #lbf.s/lbm specific impulse\n", "#1 lbf.s^2 = 32.2 lbm.ft\n", "Vrel_out=-Isp*32.2 #ft/s\n", "ratio_m=0.1 #dimentionless (ratio of final mass to initial mass)\n", "\n", "# Calculation \n", "v_final=Vrel_out*math.log(ratio_m) #ft/s\n", "\n", "# Result\n", "print \"The velocity of the rocket after launch is %d ft/s\"%v_final" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The velocity of the rocket after launch is 31881 ft/s\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.15 page no : 278\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the velocity and height of flow in an open channel\n", "\n", "# Variables \n", "v1=4. #ft/s\n", "g=32.2 #ft/s^2\n", "z1=0.0005 #ft\n", "Fr=v1**2/(g*z1) #dimentionless (Fraude number)\n", "ratio_z=-0.5+(0.25+2*Fr)**0.5 #dimentionless\n", "\n", "# Calculation \n", "#ratio_z = z2/z1\n", "z2=ratio_z*z1 #ft\n", "#print \"The height of flow in open channel is %f ft\"%z2\n", "v2=v1/(ratio_z) #ft/s\n", "\n", "# Result\n", "print \"The velocity of flow in open channel is %f ft/s\"%v2" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The velocity of flow in open channel is 0.090734 ft/s\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.16 page no : 280\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#calculate the verticle downward velocity of air hitting an aircraft wing\n", "\n", "# Variables \n", "l=15. #m length of wing\n", "b=3. #m thickness of wing\n", "A=l*b #m^2 area of the colliding surface of the wing\n", "rho_air=1.21 #Kg/m^3\n", "Vx=50. #m/s\n", "m=rho_air*A*Vx #Kg/s\n", "Fy=9810. #N Weight of the aircraft\n", "\n", "# Calculation \n", "Vy=Fy/m #m/s\n", "\n", "# Result\n", "print \"The verticle downward velocity of air hitting the aircraft wing is %f m/s\"%Vy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The verticle downward velocity of air hitting the aircraft wing is 3.603306 m/s\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.17 page no : 281\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the ratio of the total weight of the aircraft to the weight of engine\n", "\n", "# Variables \n", "#Let ratio of weight to thrust be denoted by r1\n", "#Let ratio of thrust to the engine weight be denoted by r2\n", "r1=10. #dimentionless\n", "r2=2. #dimentionless\n", "\n", "# Calculation \n", "#weight/engine wt = (weight/thrust)*(thrust/engine wt)\n", "#let ratio of total wt to engine wt be denoted by r3\n", "r3=r1*r2 #dimentionless\n", "\n", "# Result\n", "print \"The ratio of the total weight of the aircraft to the weight of engine is %d\"%r3" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The ratio of the total weight of the aircraft to the weight of engine is 20\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 7.18 page no : 284\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate the torque exerted on the rotor in a centrifugal pump\n", "import math\n", "\n", "# Variables \n", "q=100. #gal/min\n", "rho=8.33 #lbm/gal\n", "m=rho*q #lbm/min\n", "f=1800. #rev/min frequency of impeller\n", "omega=2*(math.pi)*f #rad/min\n", "r_in=1/12.0 #ft\n", "r_out=6/12.0 #ft\n", "\n", "# Calculation \n", "#1 min = 60 sec\n", "#1 lbf.s^2 = 32.2 lbm.ft\n", "tou=m*omega*(r_out**2-r_in**2)/32.2/3600. #lbf.ft\n", "\n", "# Result\n", "print \"The torque exerted on the rotor is %f lbf.ft\"%tou" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The torque exerted on the rotor is 19.753523 lbf.ft\n" ] } ], "prompt_number": 1 } ], "metadata": {} } ] }