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author | tslee | 2014-11-27 17:17:59 +0530 |
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committer | tslee | 2014-11-27 17:17:59 +0530 |
commit | 6e3407ba85ae84e1cee1ae0c972fd32c5504d827 (patch) | |
tree | b89808101c39b1db1e3793eada2c8b702f856606 /Fluid_Mechanics_With_Engineering_Applications/ch10.ipynb | |
parent | 36a03d6d76bac315dba73b2ba9555c7e3fe0234f (diff) | |
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diff --git a/Fluid_Mechanics_With_Engineering_Applications/ch10.ipynb b/Fluid_Mechanics_With_Engineering_Applications/ch10.ipynb new file mode 100644 index 00000000..87e81c80 --- /dev/null +++ b/Fluid_Mechanics_With_Engineering_Applications/ch10.ipynb @@ -0,0 +1,455 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:d2599cf416e0a07710e4c3d128cbc7fa43fd432b07cfc1f586c709ffa82e3638" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 10 : Forces on Immersed Bodies" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.1 Page No : 301" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "nu = 0.001 \t#ft**2 /s\n", + "L = 1.5 \t#ft\n", + "U = 2. \t#ft/s\n", + "s = 0.925\n", + "ro = 1.94\n", + "b = 6.\n", + "\t\n", + "#calculations\n", + "R = L*U/nu\n", + "Cf = 1.328/math.sqrt(R)\n", + "Ff = Cf*s*ro*U*b/12 *L\n", + "delta = 4.91 *L/math.sqrt(R)\n", + "T0 = 0.332*nu*s*ro*U/L *math.sqrt(R)\n", + "print R\n", + "#Results\n", + "print \"Friction drag = %.3f lb\"%(Ff)\n", + "print \" Thickness of boundary layer = %.4f ft\"%(delta)\n", + "print \" Shear stress = %.4f lb/ft**2\"%(T0)\n", + "\n", + "#Similar calculations are done for SI units case" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "3000.0\n", + "Friction drag = 0.065 lb\n", + " Thickness of boundary layer = 0.1345 ft\n", + " Shear stress = 0.0435 lb/ft**2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.2 Page No : 305" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "nu = 0.00015 \t#ft**2/s\n", + "L = 35. \t#ft\n", + "U = 88. \t#fps\n", + "g = 32.2 \t#ft/s**2\n", + "b = 10. \t #ft\n", + "w = 8. \t#ft\n", + "rho = 0.0725\n", + "\t\n", + "#calculations\n", + "R = L*U/nu\n", + "Cf = 0.455 /(math.log10(R))**2.58\n", + "B = 2*b + w\n", + "Ff = Cf*rho/g *U**2 /2 *L*B\n", + "Rx = R/10**5\n", + "delta = L*0.377 /(b* Rx**(0.2))\n", + "T0 = 0.0587 *rho/g *U**2 /2 *(nu/(L*U))**(0.2)\n", + "\t\n", + "#Results\n", + "print \"Frictional drag = %.1f lb\"%(Ff)\n", + "print \" Thickness of boundary layer = %.3f ft\"%(delta)\n", + "print \" Shear stress = %.4f lb/ft**2\"%(T0)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frictional drag = 22.9 lb\n", + " Thickness of boundary layer = 0.455 ft\n", + " Shear stress = 0.0176 lb/ft**2\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.3 Page No : 308" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "nu = 0.0000166 \t#ft**2 /s\n", + "U = 5.06 \t#fps\n", + "L = 50. \t#ft\n", + "g = 32.2\n", + "dia = 10. \t#ft\n", + "\t\n", + "#calculations\n", + "R = L*U/nu\n", + "Cf = 0.0028\n", + "Ff = Cf*64/g *U**2 /2 *math.pi*dia*L\n", + "Rx = R/L\n", + "ec = 26*nu/U *Rx**(0.25)\n", + "Rx2 = Rx*L/2\n", + "T02 = 0.0587*U**2 /2 /(Rx2)**(0.2)\n", + "delta2 = 60*nu/math.sqrt(T02)\n", + "\t\n", + "#Results\n", + "print \"Friction drag = %.f lb\"%(Ff)\n", + "print \" Critical roughness = %.4f ft\"%(ec)\n", + "print \" height of roughness = %.4f ft\"%(delta2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Friction drag = 112 lb\n", + " Critical roughness = 0.0020 ft\n", + " height of roughness = 0.0056 ft\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.4 Page No : 314" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "Cd = 0.45\n", + "rho = 0.0725/32.2\n", + "V = 88. \t#fps\n", + "A = 8*10.\n", + "\t\n", + "#calculations\n", + "Fd = Cd*rho*V**2 /2 *A\n", + "Drag2 = 23\n", + "D = Fd-Drag2\n", + "\t\n", + "#Results\n", + "print \"Pressure drag = %.f lb\"%(D)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure drag = 291 lb\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.5 Page No : 315" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from sympy import Symbol,solve\n", + "import math\n", + "\n", + "#Initialization of variables\n", + "Cd = 0.2\n", + "D = 8.5/12 \t#in\n", + "v = 1.57*10**-4\n", + "rho = 0.00238\n", + "\t\n", + "#calculations\n", + "A = (math.pi*D**2)/4\n", + "#From trail and error method,\n", + "V = 412 \t#fps\n", + "R = (D*V)/v\n", + "\n", + "\t\n", + "#Results\n", + "print \"Free fall velocity = %.2e fps\"%(R)\n", + "print \"Since the values of R and Cd check with the figure, V = 412 fps\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Free fall velocity = 1.86e+06 fps\n", + "Since the values of R and Cd check with the figure, V = 412 fps\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.6 Page No : 319" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\n", + "#Initialization of variables\n", + "nu = 1.15*10**-5 \t#m**2/s\n", + "D = 2.*10**-3 \t #m\n", + "V = 15. \t#m/s\n", + "T = -20. \t #C\n", + "\t\n", + "#calculations\n", + "R = D*V/nu\n", + "f = 0.2 *V/D *(1+T/R)\n", + "\t\n", + "#Results\n", + "print \"Frequency of oscillation = %d Hz\"%(round(f,-2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of oscillation = 1500 Hz\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.7 Page No : 324" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "n = 90. \t#rpm\n", + "R = 2. \n", + "rho = 0.0765/32.2\n", + "B = 25.\n", + "U = 120. \t#fps\n", + "\t\n", + "#calculations\n", + "vt = 2*math.pi*R*n/60\n", + "T = 2*math.pi*R*vt\n", + "Fl = rho*B*U*T\n", + "theta = math.degrees(math.asin(-T/(4*math.pi*R*U)))\n", + "\n", + "#Results\n", + "print \"Peripheral velocity = %.2f fpx\"%vt\n", + "print \"Value of circulation = %.f ft62/s\"%(T)\n", + "print \" Transverse or lift force = %d lb\"%(round(Fl,-1))\n", + "print \" Position of stagnation points = %.1f degrees\"%(180-theta)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Peripheral velocity = 18.85 fpx\n", + "Value of circulation = 237 ft62/s\n", + " Transverse or lift force = 1690 lb\n", + " Position of stagnation points = 184.5 degrees\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.8 Page No : 331" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "B = 36. \t#ft\n", + "c = 6. \t#ft\n", + "Cl = 0.8\n", + "tau = 0.175 \n", + "rho = 0.001756\n", + "V = 300. \t#fps\n", + "\t\n", + "#calculations\n", + "alphai = Cl/(math.pi*B/c) *(1+tau) *180/math.pi\n", + "alpha = 5.4 \n", + "lift = -5.6 \t#degrees\n", + "alphao = alpha-alphai\n", + "alphaod = alphao-lift\n", + "alphaor = alphaod*math.pi/180\n", + "eta = Cl/(2*math.pi*alphaor)\n", + "Fl = Cl*rho*V**2 /2 *B*c\n", + "Fd = 0.047/Cl *13680\n", + "HP = Fd*V/550\n", + "\t\n", + "#Results\n", + "print \"Friction coefficient = %.3f \"%(eta)\n", + "print \" weight of the wing = %d lb\"%(round(Fl,-1))\n", + "print \" Horsepower required = %d hp\"%(HP)\n", + "\n", + "# rounding off error" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Friction coefficient = 0.896 \n", + " weight of the wing = 13650 lb\n", + " Horsepower required = 438 hp\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.9 Page No : 334" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "k = 1.4\n", + "R = 287.\n", + "T = 249. \t#K\n", + "v = 600. \t#velocity - m/s\n", + "d = 0.2 \t#diameter - m\n", + "\t\n", + "#calculations\n", + "c = math.sqrt(k*R*T)\n", + "M = v/c\n", + "Cd = 0.62\n", + "rho = 47.22*10**3 /(R*T)\n", + "Fd = Cd*rho*v**2 /2 *math.pi*d**2 /4\n", + "\t\n", + "#Results\n", + "print \"Drag = %d N\"%(Fd)\n", + "\n", + "# note : answer is accurate" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Drag = 2316 N\n" + ] + } + ], + "prompt_number": 15 + } + ], + "metadata": {} + } + ] +}
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