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author | Thomas Stephen Lee | 2015-09-04 22:04:10 +0530 |
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committer | Thomas Stephen Lee | 2015-09-04 22:04:10 +0530 |
commit | 41f1f72e9502f5c3de6ca16b303803dfcf1df594 (patch) | |
tree | f4bf726a3e3ce5d7d9ee3781cbacfe3116115a2c /Fluid_Mechanics/Chapter_5.ipynb | |
parent | 9c9779ba21b9bedde88e1e8216f9e3b4f8650b0e (diff) | |
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diff --git a/Fluid_Mechanics/Chapter_5.ipynb b/Fluid_Mechanics/Chapter_5.ipynb deleted file mode 100755 index b12249f7..00000000 --- a/Fluid_Mechanics/Chapter_5.ipynb +++ /dev/null @@ -1,517 +0,0 @@ -{ - "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": {} - } - ] -}
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