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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 /Principles_Of_Fluid_Mechanics/ch2.ipynb | |
parent | 36a03d6d76bac315dba73b2ba9555c7e3fe0234f (diff) | |
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diff --git a/Principles_Of_Fluid_Mechanics/ch2.ipynb b/Principles_Of_Fluid_Mechanics/ch2.ipynb new file mode 100644 index 00000000..a8c9b316 --- /dev/null +++ b/Principles_Of_Fluid_Mechanics/ch2.ipynb @@ -0,0 +1,823 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:29c2c55c7f92ba07b1426c985419398b6baf83f563e8d0219eeaa4d84ad525c8" + }, + "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 : 44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "h1 = 1.5 \t\t\t#m\n", + "h2 = 2. \t\t\t#m\n", + "g1 = 800. \t\t\t#kg/m**3\n", + "g2 = 1000. \t\t\t#kg/m**3\n", + "g = 9.81\n", + "\t\t\t\n", + "#calculations\n", + "P = h1*g*g1 + h2*g*g2\n", + "\t\t\t\n", + "#results\n", + "print \"Pressure at the bottom of the vessel = %.2f kN/m**2\"%(P/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure at the bottom of the vessel = 31.39 kN/m**2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2 Page No : 44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "depth = 8000. \t\t\t#m\n", + "sw = 10.06 \t\t\t#kN/m**3\n", + "BM = 2.05*10**9 \t\t\t#N/m**2\n", + "\t\t\t\n", + "#calculations\n", + "g = sw*10**3 /(1- sw*10**3 *depth/BM)\n", + "Ph = 2.3*BM*math.log10(BM/(BM-depth*9.81*1025))\n", + "\t\t\t\n", + "#results\n", + "print \"Specific weight = %.2f kN/m**2\"%(g/1000)\n", + "print \" Pressure at depth h = %.2f MN/m**2\"%(Ph/10**6)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Specific weight = 10.47 kN/m**2\n", + " Pressure at depth h = 81.97 MN/m**2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3 Page No : 55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "Patm = 101.3/9.81 \t\t\t#m of water\n", + "x1 = 0.45 \t\t\t#m\n", + "x2 = 0.3 \t\t\t#m\n", + "s1 = 920. \t\t\t#Kg/m**3\n", + "s2 = 13.6 \t\t\t#Kg/m**3\n", + "g = 9.81 \t\t\t#m/s**2\n", + "\t\t\t\n", + "#calculations\n", + "Pa = (s1*x1*g + s2*x2*g)/1000\n", + "Pa2 = Pa*10**3/(1000*g)\n", + "Pa3 = Pa/(s2)\n", + "\t\t\t\n", + "#results\n", + "print \"Pressure at A = %.1f kPa\"%Pa\n", + "print \" Pressure at A = %.3f m of water\"%(Pa2)\n", + "print \" Pressure at A = %.3f m of mercury\"%(Pa3)\n", + "print \" Pressure at A = %.1f m of water absolute\"%(Pa/1000 +101.3)\n", + "print \" Pressure at A = %.3f m of mercury\"%(Pa2+10.3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure at A = 4.1 kPa\n", + " Pressure at A = 0.418 m of water\n", + " Pressure at A = 0.302 m of mercury\n", + " Pressure at A = 101.3 m of water absolute\n", + " Pressure at A = 10.718 m of mercury\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4 Page No : 55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "sg = 1.25 # gravity\n", + "d = 0.5 \t\t\t#m\n", + "d2 = 13.5*10**-2\t#m\n", + "sw = 9.81 \t\t\t#specific weight of water - kN/m**2\n", + "\t\t\t\n", + "#calculations\n", + "sl = sg*sw #specific weight of liquid\n", + "sm = 13.6*sw #specfic weight of mercury\n", + "Pa = sl*d - sm*d2\n", + "\t\t\t\n", + "#results\n", + "print \"Pressure at A = %.2f kN/m**2 vacuum \"%(-Pa)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure at A = 11.88 kN/m**2 vacuum \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5 Page No : 56" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "#Following values are ontained from the figure 2.17\n", + "s1 = 0.85\n", + "s2 = 13.6\n", + "z1 = 30\n", + "z2 = 15\n", + "z3 = 20\n", + "z4 = 35\n", + "z5 = 60\n", + "\t\t\t\n", + "#calculations\n", + "dHa = s1*(z1+z5+z3-z4) +s2*z4 -z3+s2*z2-s1*(z1+z2) #Ha-Hb\n", + "Pd = 1000*9.81*dHa/100 #Pa-Pb\n", + "\t\t\t\n", + "#results\n", + "print \"Pressure difference = %.2f kN/m**2\"%(Pd/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure difference = 67.25 kN/m**2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6 Page No : 57" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "P = 450 \t\t\t#pressure - kN/m**2\n", + "alt = 2000 \t\t\t#altitude - m\n", + "r = 610 \t\t\t#atmospheric pressure - mm of mercury\n", + "\t\t\t\n", + "#calculations\n", + "Pat = 760-r\n", + "Pat2 = Pat*13.6*9.81*10**-3\n", + "Pg = Pat2+P\n", + "\t\t\t\n", + "#results\n", + "print \"Gauge reading = %.2f kN/m**2\"%(Pg)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Gauge reading = 470.01 kN/m**2\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7 Page No : 62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#kN/m**2\n", + "hc = 16.25 \t\t\t#m\n", + "w = 1.5 \t\t\t#width - m\n", + "b = 2.5 \t\t\t#depth - m\n", + "f = 0.3 #coefficient of friction\n", + "Pi = 50. \t\t\t#weight of gate - kN\n", + "\t\t\t\n", + "#calculations\n", + "P = g*hc*w*b\n", + "Preq = Pi+f*P\n", + "\t\t\t\n", + "#results\n", + "print \"Force required to lift the gate = %.2f kN\"%(Preq)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Force required to lift the gate = 229.34 kN\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8 Page No : 62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "a = 6. \t\t\t#m\n", + "b = 8. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "Ixy = 9./32 *b**4 /4\n", + "xp = Ixy/(2./3 *b *1./2 *a*b)\n", + "ICG = 1./36 *a*b**3\n", + "yp = 2./3*b + ICG/(2./3 *b* 1./2 *a*b )\n", + "\t\t\t\n", + "#results\n", + "print \"The coordinates of centre of pressure are %.2f,%d\"%(xp,yp)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The coordinates of centre of pressure are 2.25,6\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9 Page No : 63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "z = 1.2 \t\t\t#m\n", + "y = 1. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "hp = 0.6 + 1./12 *y*z**3 /(0.6*y*z)\n", + "\t\t\t\n", + "#results\n", + "print \"Position of hinge = %.1f m\"%(hp)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Position of hinge = 0.8 m\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10 Page No : 64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from sympy import *\n", + "\t\t\t\n", + "#Initialization of variables\n", + "r = 0.75 \t\t\t#radius of plane - m\n", + "gam = 8. \t\t\t#specific weight of fluid - kN/m**3\n", + "\t\t\t\n", + "#calculations\n", + "P = gam*2./3 *r**3\n", + "hp = Symbol('hp')\n", + "hp = 4*r/(3*math.pi) + (math.pi/gam - gam/(9*math.pi)) * r**4/(4*r/(3*math.pi) * 1./2*math.pi*r**3)\n", + "\n", + "\t\t\t\n", + "#results\n", + "print \" Total pressure = %.2f kN\"%(P)\n", + "print \"Total pressure location = %.3f m\"%(hp)\n", + "\n", + "# note : answer is slightly different because of rounding off error. please check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Total pressure = 2.25 kN\n", + "Total pressure location = 0.483 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11 Page No : 65" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "B = 3. \t\t\t#m\n", + "b = 2. \t\t\t#m\n", + "h1 = 0.75 \t\t\t#m\n", + "h2 = 1. \t\t\t#m\n", + "sg = 0.9 #specific gravity\n", + "\t\t\t\n", + "#calculations\n", + "IP = sg*9.81*h2\n", + "F1 = 0.5*IP*h2\n", + "F2 = IP*h1\n", + "F3 = 0.5*(9.81*h1)*h1\n", + "F = B*(F1+F2+F3)\n", + "ybar = (F1*(h1+ 1./3) + F2* h1/2 + F3* h1/3)/(F1+F2+F3)\n", + "\t\t\t\n", + "#results\n", + "print \"Total force = %.2f kN\"%(F)\n", + "print \"Location = %.3f m from the base\"%(ybar)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total force = 41.39 kN\n", + " Location = 0.577 m from the base\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.12 Page No : 67" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad\n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 1000*9.81 \t\t\t#kg/m**3\n", + "hc = 20. \t\t\t#m\n", + "Ax = 40.*1 \t\t\t#m**2\n", + "y1 = 0. \t\t\t#m\n", + "y2 = 40. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "Fx = g*hc*Ax\n", + "def fy(y):\n", + " return (12*y)**(1./3)\n", + "\n", + "Fy = quad(fy,y1,y2)\n", + "Fy = g*Fy[0]\n", + "F = math.sqrt(Fx**2 +Fy**2)\n", + "\t\t\t\n", + "#results\n", + "print \"Net force = %d kN\"%(F/1000)\n", + "#The answer is a bit different due to rounding off error in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Net force = 8179 kN\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.13 Page No : 68" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#kN/m**2\n", + "hc = 1. \t\t\t#m\n", + "l = 3. \t\t\t#m\n", + "b = 0.5 \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "Ax = l*b \t\t\t#m**2\n", + "Fx = g*hc*Ax\n", + "Fz = g*(0.5* math.pi/4 *b**2)*l\n", + "F = math.sqrt(Fx**2 + Fz**2)\n", + "theta = math.degrees(math.atan(Fz/Fx))\n", + "\t\t\t\n", + "#results\n", + "print \"Magintude of resultant force = %.3f kN\"%(F)\n", + "print \" Direction of the resultant force = %.1f deg\"%(theta)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magintude of resultant force = 14.996 kN\n", + " Direction of the resultant force = 11.1 deg\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.14 Page No : 71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "r1 = 920. \t\t\t#density of ice - kg/m**3\n", + "r2 = 1030. \t\t\t#density of sea water - kg/m**3\n", + "\t\t\t\n", + "#calculations\n", + "VtbyV2 = r2/r1\n", + "V1byV2 = VtbyV2-1\n", + "V1byVt = 1./(1+1/V1byV2)\n", + "\t\t\t\n", + "#results\n", + "print \"fraction = %.3f \"%(V1byVt)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "fraction = 0.107 \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15 Page No : 72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "d = 3. \t\t\t #diameter of balloon - m\n", + "rh1 = 1.19 \t\t\t#density of air - kg/m**3\n", + "rh2 = 0.17 \t\t\t#density of helium - kg/m**3 \n", + "g = 9.81 \t\t\t#m/s**2\n", + "\t\t\t\n", + "#calculations\n", + "pay = (rh1-rh2)*g*math.pi/6 *d**3\n", + "\t\t\t\n", + "#results\n", + "print \" Pay load = %.2f N\"%(pay)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Pay load = 141.46 N\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.16 Page No : 76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import roots\t\t\t\n", + "#calculations\n", + "y = [6,-6,1]\n", + "z = roots(y)\n", + "\t\t\t\n", + "#results\n", + "print \"For stability, s must be greater than %.2f and less than %.2f and must be less than 1\"%(z[0],z[1])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "For stability, s must be greater than 0.79 and less than 0.21 and must be less than 1\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.17 Page No : 81" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "ax = 1.5 \t\t\t#m/s**2\n", + "g = 9.81 \t\t\t#m/s**2\n", + "\t\t\t\n", + "#calculations\n", + "alpha = math.degrees(math.atan(ax/g))\n", + "\t\t\t\n", + "#results\n", + "print \"The interface is inclined at %.f degrees with the horizontal\"%(alpha)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The interface is inclined at 9 degrees with the horizontal\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.18 Page No : 81" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "d = 10. \t\t\t#diameter - cm\n", + "h = 25. \t\t\t#height - cm\n", + "hw = 15. \t\t\t#cm\n", + "g = 9.81 \t\t\t#m/s**2\n", + "\t\t\t\n", + "#calculations\n", + "z = d**2 *d*2/d**2\n", + "w = math.sqrt(z*2*g/(d/2)**2 *100)\n", + "N = w/(2*math.pi) *60\n", + "\t\t\t\n", + "#results\n", + "print \"Speed of rotation = %d rpm\"%(N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of rotation = 378 rpm\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.19 Page No : 82" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad\n", + "\t\t\t\n", + "#Initialization of variables\n", + "dia = 1. \t\t\t#diameter - m\n", + "h = 3. \t\t\t #height - m\n", + "rho = 1000. \t\t#kg/m**3\n", + "N = 80. \t\t\t#rpm\n", + "g = 9.81 \t\t\t#m/s**2\n", + "\n", + "#calculation\n", + "w = 2*math.pi*N/60\n", + "def fun(r):\n", + " return 0.5*rho*w**2 *r**3 *2*math.pi\n", + "\n", + "vec = quad(fun,0,dia/2)\n", + "Pt = vec[0] + math.pi/4 *dia**2 *(h-dia)*rho*g\n", + "\t\t\t\n", + "#results\n", + "print \"Total pressure on base = %.2f kN\"%(Pt/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total pressure on base = 18.85 kN\n" + ] + } + ], + "prompt_number": 15 + } + ], + "metadata": {} + } + ] +}
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