{ "metadata": { "name": "", "signature": "sha256:04c1d9ce4358772aaf36727d98b4d1c000b18de791fe80fc4e6e1ac3cabc0050" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 5: The Momentum Equation and its Applications" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.1, Page 119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", " #Initializing the variables \n", "\n", "l = 60 ; #Length of pipeline\n", "rho = 1000; # Density of liquid\n", "a = 0.02; #Acceleration of fluid\n", "\n", " #Calculations\n", "delP = rho*l*a; #Change in pressure\n", "print \"Increase of pressure difference required (kN/m2):\",delP/1000" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Increase of pressure difference required (kN/m2): 1.2\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.2, Page 121" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", " #Initializing the variables \n", "v = 5; #Velocity of jet \n", "rho = 1000; #density of water\n", "d = 0.025; #Diameter of fixed nozzle\n", "\n", " #Calculations\n", " #--Part(a) Variation of force exerted normal to the plate with plate angle--//\n", "header = \"Theta\\t vcos(x)\\t pAv\\t Force\"\n", "unit = \"deg\\t m/s\\t kg/s\\t N\"\n", "\n", "A = math.pi*d**2/4;\n", "x = range(0,91,15);\n", "for c in range(len(x)):\n", " x[c]=1.0*x[c]\n", "m = round(rho*A*v,2);\n", "ma = [m,m,m,m,m,m,m];\n", "vcomp=[]\n", "force=[]\n", "for c in x:\n", " vcomp.append(round(v*math.cos(math.radians(c)),2))\n", " force.append(round((rho*A*v**2)*math.cos(math.radians(c)),2))\n", "\n", "print header\n", "print unit\n", "for c in range(len(x)):\n", " mm=str(x[c])+' \\t '+str(vcomp[c])+' \\t'+str(ma[c])+' \\t'+str(force[c])\n", " print mm\n", "##value = [x,vcomp,ma,force]\n", "##print value,unit, header\n", "\n", " #--Part(b) Variation of force exerted normal to the plate with plate velocity--// \n", "header =\"Theta\\t v\\t u\\t v-u\\t pA(v-u)\\t Force\\t\"\n", "unit =\"deg\\t m/s\\t m/s\\t m/s\\t kg/s\\t N\\t\"\n", "x = [0,0,0,0,0]\n", "v = [5,5,5,5,5]\n", "u = range(2,-3,-1);\n", "D=[]\n", "Prod=[]\n", "Force=[]\n", "for c in range(5):\n", " D.append(v[c]-u[c])\n", " Prod.append(round((rho*A*D[c]),2))\n", " Force.append(round((rho*A*D[c]**2),2))\n", " \n", "print '\\n',\"(b)\",\"\\n\",header\n", "print unit\n", "for c in range(len(x)):\n", " mm=str(x[c])+' \\t '+str(v[c])+' \\t '+str(u[c])+' \\t '+str(D[c])+' \\t '+str(Prod[c])+' \\t '+str(Force[c])\n", " print mm\n", " \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Theta\t vcos(x)\t pAv\t Force\n", "deg\t m/s\t kg/s\t N\n", "0.0 \t 5.0 \t2.45 \t12.27\n", "15.0 \t 4.83 \t2.45 \t11.85\n", "30.0 \t 4.33 \t2.45 \t10.63\n", "45.0 \t 3.54 \t2.45 \t8.68\n", "60.0 \t 2.5 \t2.45 \t6.14\n", "75.0 \t 1.29 \t2.45 \t3.18\n", "90.0 \t 0.0 \t2.45 \t0.0\n", "\n", "(b) \n", "Theta\t v\t u\t v-u\t pA(v-u)\t Force\t\n", "deg\t m/s\t m/s\t m/s\t kg/s\t N\t\n", "0 \t 5 \t 2 \t 3 \t 1.47 \t 4.42\n", "0 \t 5 \t 1 \t 4 \t 1.96 \t 7.85\n", "0 \t 5 \t 0 \t 5 \t 2.45 \t 12.27\n", "0 \t 5 \t -1 \t 6 \t 2.95 \t 17.67\n", "0 \t 5 \t -2 \t 7 \t 3.44 \t 24.05\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.3, Page 123" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", " \n", "\n", " #Initializing the variables \n", "x = 60; #Angle of deflection theta\n", "rho = 1000; # Density of liquid\n", "V1 = 30; #Acceleration of fluid\n", "V2 = 25;\n", "m = .8; #Discharge through A\n", "\n", " #Calculations\n", "def Reaction(Vin , Vout):\n", " R = m*(Vin -Vout) ;\n", " return R\n", "Rx = Reaction(V1,V2*math.cos(math.radians(x)));\n", "Ry = -Reaction(0,V2*math.sin(math.radians(x)));\n", "print \"Reaction in X-direction (N) :\",Rx\n", "print \"Reaction in Y-direction (N) :\",round(Ry,2)\n", "print \"Net Reaction (N) :\",round((Rx**2 +Ry**2)**0.5,2)\n", "print \"Inclination of Resultant Force with x-direction (Degrees):\",round(180/math.pi*math.atan(Ry/Rx),2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Reaction in X-direction (N) : 14.0\n", "Reaction in Y-direction (N) : 17.32\n", "Net Reaction (N) : 22.27\n", "Inclination of Resultant Force with x-direction (Degrees): 51.05\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.4, Page 125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables \n", "v1 = 36 ; #Exit velocity\n", "u = 15; #Velocity of vane\\\n", "x = 30; # Angle between vanes and flow\n", "rho = 1000; # Density of water\n", "d = .1; # Diameter of jet\n", "\n", " #Calculations\n", "alp = (180/math.pi)*math.atan((v1*math.sin(math.radians(x))/(v1*math.cos(math.radians(x))-u)));\n", "v2 = 0.85*v1*math.sin(math.radians(x));\n", "bta = (180/math.pi)*math.acos((u*math.sin(math.radians(alp))/v2));\n", "m = (rho*math.pi*v1*d**2)/4;\n", "Vin = v1*math.cos(math.radians(x));\n", "Vout = v2*math.cos(math.radians(90));\n", "Rx = m*(Vin-Vout);\n", "\n", "\n", "print \"Inlet Angle (Degrees) :\", round(alp,2)\n", "print \"Outlet Angle (Degrees) :\", round(bta,2)\n", "print \"Force exerted by vanes (N) :\", round(Rx) \n", " " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Inlet Angle (Degrees) : 48.05\n", "Outlet Angle (Degrees) : 43.18\n", "Force exerted by vanes (N) : 8815.0\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.5, Page 127" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables \n", "rho = 850 ; # Density of liquid\n", "a = 0.02 #Acceleration of fluid\n", "x = 45 ;\n", "d1 = .5 ;\n", "d2 = .25;\n", "p1 = 40*10**3;\n", "p2 = 23*10**3;\n", "Q = .45;\n", " \n", " #Calculations\n", "A1 = (math.pi*d1**2)/4;\n", "A2 = (math.pi*d2**2)/4;\n", "v1 = Q/A1;\n", "v2 = Q/A2;\n", "\n", "Rx = p1*A1 - p2*A2*math.cos(math.radians(x)) - rho*Q*(v2*math.cos(math.radians(x))-v1);\n", "Ry = p2*A2*math.sin(math.radians(x)) + rho*Q*v2*math.sin(math.radians(x));\n", "\n", "print \"Resultant force on the bend (kN) :\",round((Rx**2 +Ry**2)**0.5/1000,3)\n", "print \"Inclination of Resultant Force with x-direction (Degrees):\",round(math.atan(Ry/Rx)*180/math.pi)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resultant force on the bend (kN) : 6.362\n", "Inclination of Resultant Force with x-direction (Degrees): 31.0\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.6, Page 129" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables \n", "v = 4.9; #Velocity of Jet\n", "rho = 1000; # Density of water\n", "d = 0.05;\n", "u = 1.2 # Velocity of tank\n", " #Calculations\n", "Vout = v;\n", "Vin = 0;\n", "m = rho*math.pi*d**2*v/4;\n", "R = m*(Vout-Vin);\n", "print \"Reaction of jet on tank (N) :\",round(R,2)\n", "print \"Work done per second (W) :\",round(R*u,2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Reaction of jet on tank (N) : 47.14\n", "Work done per second (W) : 56.57\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.7, Page 130" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "from scipy import integrate\n", " \n", " \n", "\n", " #Initializing the variables \n", "Vj = 5*10**6; # Velocity of Jet\n", "Mr = 150000; # Mass of Rocket\n", "Mf0 = 300000; # Mass of initial fuel\n", "Vr = 3000; # Velocity of jet relative to rocket\n", "g = 9.81; # Acceleration due to gravity\n", "\n", " #Calculations\n", "m = Vj/Vr; #Rate of fuel consumption\n", "T = Mf0/m; # Burning time\n", "\n", "def f(t,m,Vr,Mr,Mf0,g):\n", " return m*Vr /(Mr + Mf0 - m*t) - g;\n", " \n", "args = (5000/3,3000,150000,300000,9.81)\n", "Vt = integrate.quad(f, 0.0, 180, args)\n", "\n", "def h(t,Vr,g):\n", " return -g*t - Vr*math.log(1 - t/269.95);\n", " \n", "args = (3000,9.81)\n", "Z1 = integrate.quad(h, 0.0, 180, args)\n", "Z2 = Vt[0]**2/(2*g);\n", "\n", "print \"(a)Burning time (s) :\",T\n", "print \"(b)Speed of rocket when all fuel is burned (m/s):\",round(Vt[0],2)\n", "print \"(c)Maximum height reached (km) :\",round((Z2+Z1[0])/1000,1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)Burning time (s) : 180.0\n", "(b)Speed of rocket when all fuel is burned (m/s): 1530.04\n", "(c)Maximum height reached (km) : 203.8\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.8, Page 134" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", " #Initializing the variables \n", "V = 200; #Velocity in still air\n", "Vr = 700; #velocity of gas relative to engine\n", "mf = 1.1; # Fuel Consumption\n", "r = 1/40 ; \n", "P1 =0;\n", "P2 = 0;\n", "\n", " #Calculations\n", "m1 = mf/r;\n", "T = m1*((1+r)*Vr -V);\n", "print \"(a)Thrust (kN) :\",T/1000\n", "\n", "W = T*V;\n", "print \"(b)Work done per second (kW) :\",W/1000\n", "\n", "Loss = 0.5*m1*(1+r)*(Vr-V)**2;\n", "print \"(c)Efficiency (%) :\",round(W/(W+Loss)*100,1) " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)Thrust (kN) : 22.77\n", "(b)Work done per second (kW) : 4554.0\n", "(c)Efficiency (%) : 44.7\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.10, Page 140" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", " #Initializing the variables \n", "rho = 1000; # Density of water\n", "Q = 10; #Acceleration of fluid\n", "r2 = 1.6;\n", "r1 = 1.2;\n", "V1 = 2.3;\n", "V2 = 0.2;\n", "rot = 240; \n", "\n", " #Calculations\n", "Tf = rho*Q*(V2*r2 - V1*r1);\n", "T = -Tf;\n", "n = rot / 60;\n", "P = 2*round(math.pi,3)*n*T;\n", "\n", "print \"Torque exerted by fluid (N.m):\",T\n", "print \"Theoretical power output (kW) :\",round(P/1000,2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque exerted by fluid (N.m): 24400.0\n", "Theoretical power output (kW) : 613.32\n" ] } ], "prompt_number": 9 } ], "metadata": {} } ] }