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diff --git a/Mechanics_Of_Fluids/ch9.ipynb b/Mechanics_Of_Fluids/ch9.ipynb new file mode 100755 index 00000000..1e84196c --- /dev/null +++ b/Mechanics_Of_Fluids/ch9.ipynb @@ -0,0 +1,746 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9 : Similarity and Dimensional Analysis" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.1.1 page no : 219" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "pm= 1.6 \t\t\t#lb/ft**3\n", + "vm= 6.2*10**-6 \t\t#ft**2/sec\n", + "R= 1.8 \t\t\t #lbf\n", + "um= 100. \t\t\t#ft/sec\n", + "p= 64. \t\t\t #lb/ft**3\n", + "v= 1.7*10**-5 \t #ft^2/sec\n", + "lm_by_l= 1/10. \t\t#ft\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "u= (um*lm_by_l*v)/vm\n", + "u_knot= ((um*lm_by_l*v)/vm)/1.98 #knot\n", + "F_by_Fm = (p/pm)*(1/lm_by_l)**2*(u/um)**2\n", + "F= F_by_Fm*R\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' speed of torpedo in sea water = %.1f knot'%u_knot\n", + "print ' resistance= %.f lbf '%(F)\n", + "print (1/lm_by_l)**2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " speed of torpedo in sea water = 13.8 knot\n", + " resistance= 541 lbf \n", + "100.0\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.2.1 page no : 222" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "import math \n", + "\n", + "S= 5. \t\t\t#ft\n", + "F= 70. \t\t\t#lbf\n", + "B= 4. \t\t\t#degrees\n", + "l= 1. \t\t\t#ft\n", + "d= 0.002378 \t\t\t#slug/ft**3\n", + "u= 120. \t\t\t#ft/sec\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "L= F*math.cos(math.radians(B))\n", + "D=F*math.sin(math.radians(B))\n", + "S1= S*l\n", + "p= 0.5*d*u**2\n", + "Cl= L/(p*S1)\n", + "Cd= D/(p*S1)\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' coefficient of lift= %.2f'%(Cl)\n", + "print ' coefficient of drag= %.4f'%(Cd)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " coefficient of lift= 0.82\n", + " coefficient of drag= 0.0570\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.2.2 page no : 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "import math \n", + "\n", + "A= 600. \t\t\t#ft**2\n", + "W= 40. \t\t\t#lbf/ft**2\n", + "n= 75. \t\t\t#percent\n", + "r= 10.\n", + "v= 300. \t\t\t#miles/hour\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "L= W*A\n", + "D= L/r\n", + "P= D*v*5280./(60.*33000)\n", + "hp= P*100./n\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' brake horse-power of the engines= %.f h.p'%(hp)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " brake horse-power of the engines= 2560 h.p\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.2.4 page no : 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "W = 22400 # lbf\n", + "p = 0.002378 # slug/ft^3\n", + "S = 500. # ft**2\n", + "b = 398. \n", + "a = 293\n", + "D1 = 1530. # lbf\n", + "U = 200. \n", + "\n", + "\n", + "# Calculation\n", + "#Part a\n", + "U1 = round((2*W/(p*S)),-2)**(1./2) * (b/a)**(1./4)\n", + "P1 = round((D1 * U1)/550)\n", + "\n", + "#Part b\n", + "Umph = U1*0.681818 # ft/sec to m.p.h\n", + "D = round(round((D1/2)*((U/Umph)**2 + (Umph/U)**2),1))\n", + "P = round(D*U*5280./(60*33000),-1)\n", + "U = .76 * U1\n", + "D = (D1/2.)*((U/Umph)**2 + (Umph/U)**2)\n", + "power = round((D * U)*5280./(60*33000),-2)\n", + "\n", + "# Part c\n", + "min_power = .76 * U\n", + "# Results\n", + "print \"a)Power expended for minumum drag is = %.1f h.p.\"%P1\n", + "print \" Speed for minimum power is U = %.1f m.p.h\"%U\n", + "print \"b)Drag for minimum power is = %.0f lbf\"%D\n", + "print \" The minimum power is = %.0f h.p.\"%power\n", + "print \"c) Speed for minimum power is U = %.1f m.p.h\"%min_power\n", + "print \"Answers in book are wrong. Please calculate manually.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a)Power expended for minumum drag is = 583.0 h.p.\n", + " Speed for minimum power is U = 159.3 m.p.h\n", + "b)Drag for minimum power is = 1566 lbf\n", + " The minimum power is = 700 h.p.\n", + "c) Speed for minimum power is U = 121.1 m.p.h\n", + "Answers in book are wrong. Please calculate manually.\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.3.1 page no :231" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "va= 0.2\n", + "r= 1./1.25\n", + "r1= 1./50\n", + "P= 20. \t\t\t#atm\n", + "v= 400. \t\t\t#m.p.h\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "Um= v*va/(P*r*r1)\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' Speed of air= %.f m.p.h'%(Um)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Speed of air= 250 m.p.h\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.4.1 page no : 234" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "#initialisation of variables\n", + "\n", + "\n", + "U= 30. \t\t\t#ft/sec\n", + "g= 32.2 \t\t\t#ft/sec**2\n", + "l= 500.\t\t\t#ft\n", + "r= 1./25\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "F=(U**2./(l*g))\n", + "R= math.sqrt(r)\n", + "Um= U*R\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' Froude number= %.4f '%(F)\n", + "print ' speed= %.f ft/sec'%(Um)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Froude number= 0.0559 \n", + " speed= 6 ft/sec\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.4.2 pageno : 234" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "#initialisation of variables\n", + "\n", + "R1= 9.5 \t\t\t#lbf\n", + "f1= 0.01\n", + "S1= 22. \t\t\t#ft**2\n", + "U1= 5.3\n", + "n= 1.825\n", + "l= 540.\t\t\t#ft\n", + "l1= 15. \t\t\t#ft\n", + "C= 0.0087\t\t\t#lbf/ft**2\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "Rr1= round(R1-f1*S1*U1**n,1)\n", + "U= U1*math.sqrt(l/l1)\n", + "r= (l/l1)**3.\n", + "Rr= round(r*Rr1,-3)\n", + "Rf= C*(l/l1)**2*S1*U**n\n", + "R= Rr+Rf\n", + "P= R*U*1.69/550.\n", + "\n", + "\n", + "#RESULTS\n", + "print ' propulsive power= %.f h.p'%(P)\n", + "print 'Answer in book is wrong.'" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " propulsive power= 35755 h.p\n", + "Answer in book is wrong.\n" + ] + } + ], + "prompt_number": 58 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.5.1 pageno : 237" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "#initialisation of variables\n", + "\n", + "s= 20. \t\t\t#ft\n", + "u= 10. \t\t\t#ft/sec\n", + "t= 1. \t\t\t#sec\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "r= s/u*t\n", + "a= r*u/t\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' constant accelaration= %.f ft/sec**2'%(a)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " constant accelaration= 20 ft/sec**2\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.5.2 pageno : 237" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "a= 20. \t\t\t#ft/sec**2\n", + "s= 20.\t\t\t#ft\n", + "u= 10. \t\t\t#ft/sec\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "P= a*s/u**2.\n", + "t= s*2/(u*P)\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' time taken= %.f sec'%(t)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " time taken= 1 sec\n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.6.1 page no : 242\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "s= 0.8\n", + "l= 1.\t\t\t#ft\n", + "r= 8.\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "Hw= (s/r)**(2./3)*l\n", + "Qw= 1.5*Hw**(2.5)\n", + "R= (1./Hw)**2.5\n", + "Q= Qw*R\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' depth of water= %.3f ft'%(Hw)\n", + "print ' rate of flow of fluid= %.1f ft**3/sec'%(Q)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " depth of water= 0.215 ft\n", + " rate of flow of fluid= 1.5 ft**3/sec\n" + ] + } + ], + "prompt_number": 61 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.6.3 pageno : 244" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "Q1= 140. \t\t\t#gallons\n", + "h= 3. \t\t\t#in\n", + "r= 16.\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "H= h*r/12.\n", + "Q2= round(Q1*H**5.,-3)\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' corresponding head over the full-scale wier= %.f ft'%(H)\n", + "print ' discharge over the latter= %.f gal/min'%(Q2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " corresponding head over the full-scale wier= 4 ft\n", + " discharge over the latter= 143000 gal/min\n" + ] + } + ], + "prompt_number": 63 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.7.1 page no: 248" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "r= 0.448\n", + "R= 0.868\n", + "r1= 0.152\n", + "R1= 0.807\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "P= R**3./r**2.\n", + "U= R/r\n", + "P1= R1**3./r1**2.\n", + "U1= R1/r1\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' power ratio in case 1= %.2f '%(P)\n", + "print ' velocity ratio in case 1= %.2f '%(U)\n", + "print ' power ratio in case 2= %.2f '%(P1)\n", + "print ' velocity ratio in case 2= %.1f '%(U1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " power ratio in case 1= 3.26 \n", + " velocity ratio in case 1= 1.94 \n", + " power ratio in case 2= 22.75 \n", + " velocity ratio in case 2= 5.3 \n" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.7.2 page no : 249" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#initialisation of variables\n", + "w= 1. \t\t\t#gf/cm**3\n", + "Ss= 7.8\n", + "Sl= 0.9\n", + "D= 1. \t\t\t#cm\n", + "D1= 0.1 \t\t\t#cm\n", + "g= 981. \t\t\t#cm/sec**2\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "F= w*(Ss-Sl)*4.*math.pi*D**3./(3.*8000)\n", + "v= F*g/(3*math.pi*D1*2.)\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' coefficient of viscosity= %.2f poise'%(v)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " coefficient of viscosity= 1.88 poise\n" + ] + } + ], + "prompt_number": 65 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.7.4 page no : 251" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "T= 15. \t\t\t#C\n", + "T1= -44. \t\t\t#C\n", + "P= 24. \t\t\t#atm\n", + "s= 0.374\n", + "m= 6. \t\t\t#tonf\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "r= ((T+273.)/(T1+273))**0.75\n", + "R= P/s\n", + "R1= r**2./R\n", + "F= R1*m*2240.\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' lift force= %.1f lbf'%(F)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " lift force= 295.4 lbf\n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.7.5 page no : 253\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "u= 80. \t\t\t#ft/sec\n", + "n= 62.\n", + "r= 1./4\n", + "v= 11. \t\t\t#ft**3\n", + "w= 62.3\t\t\t#lbf/ft**3\n", + "p= 2. \t\t\t#lbf/in**2\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "uw= u*n/(r*v*w)\n", + "R= v*w*(uw/u)**2.\n", + "P= r**2.*p/R\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' water velocity= %.f ft/sec'%(uw)\n", + "print ' pressure drop= %.5f lbf/in**2 per ft'%(P)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " water velocity= 29 ft/sec\n", + " pressure drop= 0.00139 lbf/in**2 per ft\n" + ] + } + ], + "prompt_number": 67 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 9.8.3 pageno : 259" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#initialisation of variables\n", + "\n", + "N= 1800. \t\t\t#rev/min\n", + "Vm= 60. \t\t\t#mile/hour\n", + "V= 300. \t\t\t#mile/hour\n", + "r= 10.\n", + "\t\t\t\n", + "#CALCULATIONS\n", + "Nm= N*Vm*r/V\n", + "\t\t\t\n", + "#RESULTS\n", + "print ' rotary speed= %.f rev/min'%(Nm)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " rotary speed= 3600 rev/min\n" + ] + } + ], + "prompt_number": 68 + } + ], + "metadata": {} + } + ] +}
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