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diff --git a/Fluid_Mechanics_and_Hydraulic_Machines/ch2.ipynb b/Fluid_Mechanics_and_Hydraulic_Machines/ch2.ipynb new file mode 100755 index 00000000..7308e485 --- /dev/null +++ b/Fluid_Mechanics_and_Hydraulic_Machines/ch2.ipynb @@ -0,0 +1,691 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:b1d2399b6b4acd9a65f6af74a5e09d523ac3468105509cc56b7fc106dd581d3b" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2 : Equilibrium of Floating Bodies" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1 Page No : 41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "l = 4.\n", + "w = 2.\n", + "sg = 0.75\n", + "z = 9810.\n", + "d = 0.5\n", + "\n", + "# Calculations \n", + "v = l*w*d\n", + "wg = v*z*sg\n", + "s = 24000.\n", + "V = ((z*v)-wg)/s\n", + "V1 = (v*z-wg)/(s-z)\n", + "\n", + "# Results \n", + "print \"volume in m3 when block is completely in water\",V,\"m**3\"\n", + "print \"volume in m3 when block and concrete completely under water\",round(V1,5),\"m**3\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "volume in m3 when block is completely in water 0.40875 m**3\n", + "volume in m3 when block and concrete completely under water 0.69133 m**3\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2 Page No : 42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Variables\n", + "d = 1\n", + "s = 0.75\n", + "w = 9810\n", + "\n", + "# Calculations \n", + "a = math.pi*d*d/4\n", + "h = d*0.5\n", + "p = w*h*s \t\t\t# intensity of pressure on at horizontal interface\n", + "v = p*a \t\t\t#vertical upward force\n", + "w1 = w*s*a*d/3 \t\t\t# weight of oil in upper hemisphere\n", + "vf = v-w1 \t\t\t# net vertical upward force\n", + "\n", + "# Results \n", + "print \"minimum weight of upper hemisphere in N\",round(vf,4),\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "minimum weight of upper hemisphere in N 963.0945 N\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3 Page No : 42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "w = 90.\n", + "\n", + "# Calculations \n", + "# By archemde's principle\n", + "# weight of water print alced = weight of sphere\n", + "z = 9810\n", + "v = w/z\n", + "d = (v*12/3.142)**0.33333\n", + "\n", + "# Results \n", + "print \"external diameter of hollow of sphere in m\",round(d,4),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "external diameter of hollow of sphere in m 0.3272 m\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4 Page No : 43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "s1 = 13.6\n", + "s2 = 7.8\n", + "s3 = 1.\n", + "\n", + "# Calculations \n", + "# by archimede principle\n", + "# weight of body = weight of liquid print laced\n", + "# s2 = s1*x+s3*(1-x) \n", + "x = (s2-s3)/(s1-s3)\n", + "\n", + "# Results \n", + "print \"fraction of steel below surface of mercury\",round(x,2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "fraction of steel below surface of mercury 0.54\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5 Page No : 43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Variables\n", + "w = 9810.\n", + "do = 1.25\n", + "a = math.pi*do*do*0.25\n", + "\n", + "# Calculations \n", + "f1 = w*a*1\n", + "f2 = w*a*3 \t\t\t# buoyancy force of 3m lenght of pipe\n", + "di = 1.2\n", + "s = 9.8\n", + "wg = w*s*3*((1.25**2)-(1.2**2))*0.25*math.pi\n", + "fa = f2-wg\n", + "\n", + "# Results \n", + "print \"buoyancy force in N/m\",round(f1,3),\"N/m\"\n", + "print \"upward force on anchor\",fa,\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "buoyancy force in N/m 12038.681 N/m\n", + "upward force on anchor 8367.36499746 N\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6 Page No : 44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "a = 0.25\n", + "s1 = 11.5\n", + "s2 = 1.\n", + "z = 9810.\n", + "v1 = a*a*a*0.5\n", + "wc = v1*z\n", + "h = 0.016\n", + "\n", + "# Calculations \n", + "# by archimede's principle\n", + "v2 = (a*0.5+h)*a*a \t\t\t# volume of cube submergerd\n", + "v = (v2-v1)/(s1-s2)\n", + "wl = v*s1*z\n", + "\n", + "# Results \n", + "print \"weight of lead attached\",round(wl,3),\"N\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "weight of lead attached 10.744 N\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7 Page No : 45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "s1 = 19.3\n", + "s2 = 9.\n", + "x = 14./24\n", + "\n", + "# Calculations \n", + "wg = x*10\n", + "wc = (1-x)*10\n", + "vg = wg/s1\n", + "vc = wc/s2\n", + "vt = vg+vc\n", + "\n", + "# Results \n", + "print \"volume of 10gm,14 carat gold in cm3\",round(vt,3),\"cc\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "volume of 10gm,14 carat gold in cm3 0.765 cc\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8 Page No : 46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "h1 = 0.05\n", + "h2 = 0.015\n", + "s = 41./40\n", + "l = h1/(s-1)\n", + "w1 = 25\n", + "\n", + "# Calculations \n", + "# applying bakance in vertical direction\n", + "w = w1*(l+h1)/(h2)\n", + "\n", + "# Results \n", + "print \"weight of ship in in N\",round(w,3),\"kN\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "weight of ship in in N 3416.667 kN\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9 Page No : 47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "w = 700.\n", + "w1 = 20000.\n", + "d = 0.5\n", + "h = 1.\n", + "wd = 250.\n", + "z = 9810.\n", + "\n", + "# Calculations \n", + "f = z*3.142*d*d*2*0.25/3\n", + "n = (w*4+w1)/(f-250)\n", + "n1 = round(n)\n", + "\n", + "# Results \n", + "print \"number of drums\",n1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "number of drums 22.0\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10 Page No : 47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "a = 0.12\n", + "l = 1.8\n", + "s = 0.7\n", + "z = 9810.\n", + "wp = s*a*a*l*z\n", + "v = a*a*(l-0.2)\n", + "w = v*z\n", + "t = w-wp\n", + "sp = 110000.\n", + "\n", + "# Calculations \n", + "# applying equilibrium balance\n", + "w = t/(1-(9810/sp)) \n", + "\n", + "# Results \n", + "print \"weight of lead in N\",round(w,3),\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "weight of lead in N 52.733 N\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11 Page No : 48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "d = 4.\n", + "h = 4.\n", + "s = 0.6\n", + "s1 = 1.\n", + "\n", + "# Calculations \n", + "h1 = s*h/s1\n", + "v = 3.142*d*d*0.25*h1\n", + "x = h1/2\n", + "cog = h/2\n", + "h2 = cog-x\n", + "a = 3.142*d*d*d*d/64\n", + "bm = a/v\n", + "mh = bm-h2\n", + "\n", + "# Results \n", + "print \"metacentric height in m,negative sign indicte that cylinder is in unstable equilibrium\",round(mh,4),\"m\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "metacentric height in m,negative sign indicte that cylinder is in unstable equilibrium -0.3833 m\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.12 Page No : 49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "d = 4.\n", + "s1 = 0.6\n", + "s2 = 0.9\n", + "l = 1.\n", + "\n", + "# Calculations \n", + "h = s1*l/s2\n", + "cob = h/2\n", + "cog = l/2\n", + "dcog = cog-cob\n", + "i = 3.142*d*d*d*d/64\n", + "v = 3.142*0.25*d*d*h\n", + "bm = i/v\n", + "bm = dcog\n", + "l = (6*1.5)**0.5\n", + "\n", + "# Results \n", + "print \"maximium lenght of cylinder in m\",l,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "maximium lenght of cylinder in m 3.0 m\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.13 Page No : 51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "s = 2.\n", + "w = 340.\n", + "v = 0.5*s*s*s\n", + "z = 9810.\n", + "\n", + "# Calculations \n", + "w1 = z*4\n", + "gb = s/4-s/8\n", + "i = s*s*s*s/(12)\n", + "v = 4\n", + "bm = i/v\n", + "gm = bm+gb\n", + "p = w/(w1*gm)\n", + "theta = math.degrees(math.atan(p))\n", + "\n", + "# Results \n", + "print \"angle through which cube will tilt in minutes\",round((theta*60),3)\n", + "\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angle through which cube will tilt in minutes 51.059\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.14 Page No : 51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "l = 60.\n", + "b = 9.\n", + "w = 16.*1000000\n", + "w1 = 160.*1000\n", + "y = 6.\n", + "q = 3.\n", + "sp = 10104.\n", + "\n", + "# Calculations \n", + "i = 0.75*l*b*b*b/12\n", + "v = w/sp\n", + "bm = i/v\n", + "gm = (w1*y)/(w*(math.tan(math.radians(q))))\n", + "mcd = 2-bm\n", + "cogd = gm+mcd\n", + "\n", + "# Results \n", + "print \"metacentric height %.3f m \"%gm\n", + "print \"position of centre of gravity below the water line %.3f m\"%cogd\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "metacentric height 1.145 m \n", + "position of centre of gravity below the water line 1.419 m\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15 Page No : 53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "w = 450000.\n", + "y = 5.5\n", + "w1 = 80.*1000000\n", + "q = 3.\n", + "\n", + "# Calculations \n", + "gm = (w*y)/(w1*math.tan(math.radians(q)))\n", + "p = 12.5*1000\n", + "n = 120.\n", + "T = (p*60000)/(2*math.pi*n)\n", + "z = T/(w1*gm)\n", + "theta = math.degrees(math.atan(z))\n", + "\n", + "# Results \n", + "print \"angle of heel in degree %.4f\"%theta\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angle of heel in degree 1.2066\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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