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Diffstat (limited to 'Elementary_Fluid_Mechanics/ch2.ipynb')
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diff --git a/Elementary_Fluid_Mechanics/ch2.ipynb b/Elementary_Fluid_Mechanics/ch2.ipynb new file mode 100755 index 00000000..5fbe2709 --- /dev/null +++ b/Elementary_Fluid_Mechanics/ch2.ipynb @@ -0,0 +1,505 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:fae9d4c3d571f5f27d1259174500abbced27ed669ce1d759f1518557eb996672" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2 : Fluid Statics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1 Page No : 32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "# variables\t\t\n", + "T = 68;\t\t#degreeF\n", + "p = 10;\t\t# psi\n", + "d = 15;\t\t# feet\n", + "rho = 1.59;\t\t#specific gravity\n", + "\n", + "# calculations \n", + "gam = rho*62.4;\t\t#lb/cuft\n", + "p1 = gam*d + p*144;\t\t#psf\n", + "\n", + "# results \n", + "print 'p1 = %d psf = %.1f psi '%(p1,p1*0.00694);\n", + "\n", + "#incorrect answer given in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "p1 = 2928 psf = 20.3 psi \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2 Page No : 32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# variables\t\t\n", + "h = 35000;\t\t# feet\n", + "p1 = 14.7;\t\t# psia\n", + "T1 = 519;\t\t# degreeR\n", + "gam1 = 0.0765;\t\t# lb/cuft\n", + "p2 = 504;\t\t# psfa\n", + "\n", + "# calculations \n", + "T2 = T1 - h*0.00356;\t\t# degreeR\n", + "gam2 = p2/(53.3*T2);\t\t# lb/cuft\n", + "\n", + "# results \n", + "print 'p2 = %d psfa = %.2f psia \\nspecific weight = %.3f lb/cuft'%(p2,p2*0.00695,gam2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "p2 = 504 psfa = 3.50 psia \n", + "specific weight = 0.024 lb/cuft\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3 Page No : 35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\t\t\n", + "# variables\n", + "h1 = 12.5;\t\t# inches\n", + "p1 = 14.50;\t\t# psia\n", + "\n", + "# calculations \n", + "p = p1 - h1*(14.70/29.92);\t\t#absolute pressure in psia\n", + "\n", + "# results \n", + "print 'Absolute pressure = %.2f psia'%(p);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Absolute pressure = 8.36 psia\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4 Page No : 37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# variables\t\t\n", + "gam1 = 0.9*62.4;\n", + "gam2 = 13.55*62.4;\n", + "l1 = 10;\t\t# feet\n", + "l2 = 15./12;\t\t# feet\n", + "\n", + "# calculations \n", + "p_x = gam2*l2 - gam1*l1;\t\t# psf\n", + "\n", + "# results \n", + "print 'The gauge reading = %d psf = %.2f psi'%(p_x,0.00694*p_x);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The gauge reading = 495 psf = 3.44 psi\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5 Page No : 42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "from scipy.integrate import quad \n", + "\t\t\n", + "# variables \n", + "l1 = 4.;\t\t# feet\n", + "b1 = 6.;\t\t# feet\n", + "b2 = 6.;\t\t# feet\n", + "l2 = 2.55;\t\t# feet\n", + "t = 1.; \t\t# feet\n", + "\n", + "# calculations \n", + "F1 = 0.5*l1*b1*62.4*(0.5*l1 + t) ;\t\t# lb\n", + "F2 = 0.25*math.pi*b2**2 *62.4*(l2 + t);\t\t# lb\n", + "a1 = l1*b2**3 /(36*0.5*b2*0.5*l1*b1);\t\t# feet\n", + "a2 = 70/((0.5*l2 + t)*28.3);\t\t# feet\n", + "l_p = (F1*(0.5*l1 + a1)+F2*(l2+a2))/(F1+F2) +1;\t\t#feet\n", + "x_p1 = (0.5*l1-a1) - a1*2/b2;\t\t# feet\n", + "\n", + "def f2(y): \n", + "\t return (62.4/2)*(36-y**2)*(y+1)\n", + "\n", + "M = quad(f2,0,6)[0]\n", + "\n", + "x_p2 = M/F2;\t\t# feet\n", + "x_p = (x_p2*F2 - F1*x_p1)/(F1+F2);\t\t# feet\n", + "\n", + "# results \n", + "print 'Total force on composite area is %d lb'%(F1+F2); \n", + "print ' Vertical location of resultant force is %.2f ft below the water surface'%(l_p);\n", + "print ' Horizontal location of resultant force is %.3f ft right of the water surface'%(x_p);\n", + "\n", + "#incorrect answer given in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total force on composite area is 8509 lb\n", + " Vertical location of resultant force is 4.38 ft below the water surface\n", + " Horizontal location of resultant force is 1.423 ft right of the water surface\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6 Page No : 45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy\n", + "\t\t\n", + "# variables\n", + "l = 8.; \t\t#feet\n", + "b = 10.;\t \t# feet\n", + "\n", + "# calculations \n", + "F_h = 0.5*l*b*62.4*(b+2.5);\t\t# lb\n", + "x = 83.2/(40*(b+2.5));\t\t# feet\n", + "F_v = (b+5)*62.4*40-(l*62.4*(25 - 0.25*math.pi*25));\t\t# lb\n", + "F = math.sqrt(F_h**2 + F_v**2);\t\t# lb\n", + "e = (2680*3.91 + 37440*(0.25*b))/F_v ;\t\t# feet\n", + "theta = 180*numpy.arctan(F_v/F_h) /math.pi;\t\t# degrees\n", + "x_p = 0.25*b-x;\t\t# feet\n", + "\n", + "# results \n", + "print 'Magnitude of resultant force is %d lb'%(F);\n", + "print 'Theta = %d degrees'%(theta);\n", + "print 'Location is %.3f feet above and %.2f feet to the right of B'%(x_p,e);\n", + "\n", + "#there are errors in the answer given in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnitude of resultant force is 46709 lb\n", + "Theta = 48 degrees\n", + "Location is 2.334 feet above and 2.99 feet to the right of B\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7 Page No : 48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# variables\n", + "A = 4000.;\t\t# sq.ft\n", + "d1 = 10.;\t\t# feet\n", + "d2 = 2.;\t\t# inches\n", + "rho = 64.;\t\t# lb/cuft\n", + "\n", + "# calculations \n", + "W = A*(d2/12)*rho;\t\t# lb\n", + "\n", + "# results \n", + "print 'Weight of cargo = %d lb'%(round(W,-2));\n", + "\n", + "\t\t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Weight of cargo = 42700 lb\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8 Page No : 49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "# variables\n", + "gam = 53.0;\t\t# lb/cuft\n", + "D = 17.;\t\t# inches\n", + "d = 12.;\t\t# inches\n", + "\n", + "# calculations \n", + "V = (math.pi/6)*(D/d)**3;\n", + "V1 = 0.584;\t\t#cuft\n", + "V2 = 0.711;\t\t#cuft\n", + "W = V*gam;\n", + "F_B = V1*62.4;\n", + "F_ACA = (V2)*62.4;\n", + "F = W+F_ACA-F_B;\n", + "\n", + "# results \n", + "print 'The force exerted between sphere and orfice plate = %.1f lb'%(F);\n", + "\n", + "#incorrect answer for W in textbook. Hence the answer differs" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The force exerted between sphere and orfice plate = 86.8 lb\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9 Page No : 51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from scipy.integrate import quad \n", + "\n", + "# variables\n", + "v = 15;\t\t# ft/sec**2\n", + "d = 5;\t\t# ft\n", + "\n", + "# calculations \n", + "def f3(z): \n", + "\t return -62.4*(v+32.2)/32.2\n", + "\n", + "p = quad(f3,0,-5)[0]\n", + "\n", + "# results \n", + "print 'p = %d psf'%(p);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "p = 457 psf\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10 Page No : 52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# variables\n", + "m = -0.229;\t\t#slope\n", + "a_z = 1.96;\t\t# ft/sec**2\n", + "a_x = 4*a_z;\t\t# ft/sec**2\n", + "a = math.sqrt(a_x**2 + a_z**2);\t\t# ft/sec**2\n", + "\n", + "def f1(z): \n", + "\t return -(32.2 + a_z)*(62.4/32.2)\n", + "\n", + "p = quad(f1,0,-2.75)[0]\n", + "\n", + "# results \n", + "print 'p = %.1f psf'%(p);\n", + "\n", + "#there is an error in the answer given in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "p = 182.0 psf\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11 Page No : 54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\t\t\n", + "# variables\n", + "l1 = 2.;\t\t# feet\n", + "l2 = 3.;\t\t# feet\n", + "rpm = 100;\n", + "\n", + "# calculations \n", + "p_A = (l1+l2)-(2./3)*(2*math.pi*rpm/60)**2 /(2*32.2);\n", + "p_B = (l1+l2)+(1./3)*(2*math.pi*rpm/60)**2 /(2*32.2);\n", + "\n", + "# results \n", + "print 'Pressure heads at point A and point B ae %.2f ft and %.2ft ft respectively'%(p_A,p_B);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure heads at point A and point B ae 3.86 ft and 5.57t ft respectively\n" + ] + } + ], + "prompt_number": 9 + } + ], + "metadata": {} + } + ] +}
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