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diff --git a/Fundamentals_of_Fluid_Mechanics/Ch_7.ipynb b/Fundamentals_of_Fluid_Mechanics/Ch_7.ipynb new file mode 100644 index 00000000..d5266070 --- /dev/null +++ b/Fundamentals_of_Fluid_Mechanics/Ch_7.ipynb @@ -0,0 +1,286 @@ +{ + "metadata": { + "name": "Ch 7" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7 :Similitude ,Dimensional Analysis and Modelling" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.5 Page no.372" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#example 7.5\n", + "#Determine the model dimension and the velocity at which the test should be performed.\n", + "#given\n", + "D=0.1 #m\n", + "H=0.3 #m\n", + "v=50.0 #km/hr\n", + "Dm=20.0 #mm\n", + "T=20.0 #degree C\n", + "fm=49.9 #Hz frequency for the model\n", + "#f=func(D,H,V,d,vis)\n", + "#f=T**(-1) D=l H=L V=L*(T**(-1)) d=M*(L**(-3)) vis=M*(L**(-1))*(T**(-1))\n", + "#by applying pi theorem,\n", + "#(f*D/V)=funct((D/H),(d*V*D/vis))\n", + "#hence Dm/Hm = D/H, dm*Vm*Dm/vism = d*V*D/vis, and (f*D/V)=(fm*Dm/Vm)\n", + "\n", + "#calculation\n", + "Hm=(Dm*H*1000/(D*1000)) #mm\n", + "V=v*1000/3600 #m/s\n", + "vism=0.001 #kg/(m*s)\n", + "vis=1.79*10**-5 #kg/(m*s)\n", + "d=1.23 #kg/(m**3)\n", + "dm=998 #kg/(m**3)\n", + "Vm=(vism*d*D*V*1000)/(vis*dm*Dm) #m/s\n", + "f=(V/Vm)*(Dm/(D*1000))*fm #Hz\n", + "\n", + "#result\n", + "print \"The model dimension =\",round(Hm,3),\"mm\"\n", + "print \"The velocity at which the test should be performed=\",round(Vm,2),\"m/s\"\n", + "print \"The predicted prototype vortex shredding frequency =\",round(f,1),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The model dimension = 60.0 mm\n", + "The velocity at which the test should be performed= 4.781 m/s\n", + "The predicted prototype vortex shredding frequency = 29.0 Hz\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.6 Page no.377" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%pylab inline" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", + "For more information, type 'help(pylab)'.\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Example 7.6\n", + "#What is the required flowrate in the model.\n", + "#given\n", + "D=2.0 #ft\n", + "Q=30.0 #cfs\n", + "Dm=3.0 #in\n", + "#Rem=Re hence (Vm*Dm/kvism)=(V*D/kvis) where kvis is kinematic viscosity\n", + "#kvis=kvism same fluid is used for model and prototype\n", + "#(Vm/V)=(D/Dm)\n", + "#Q=VA hence Qm/Q = (Vm*Am)/(V*A)=(Dm/D)\n", + "\n", + "# calculation\n", + "Qm=(Dm/12)*Q/D #cfs\n", + "\n", + "#result\n", + "print \"The required flowrate in the model=\",Qm,\"cfs\"\n", + "\n", + "#Plot\n", + "import matplotlib.pyplot as plt\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111)\n", + "ax.plot([0.125], [8], 'o')\n", + "ax.annotate('(0.125,8)', xy=(0.125,8.5))\n", + "\n", + "T=[0.04,0.125,0.2,0.6,1]\n", + "K=[25,8,5,2,1]\n", + "xlabel(\"Dm/D\") \n", + "ylabel(\"Vm/V\") \n", + "plt.xlim((0,1))\n", + "plt.ylim((0,25))\n", + "a=plot(T,K)\n", + "show(a)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required flowrate in the model= 3.75 cfs\n" + ] + }, + { + "output_type": "display_data", + "png": 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v5hpERujRo4fhDovl5eWYPXs2bty4geTkZJO+JysrC5MnTwYAjBs3Dp9//jkA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\nTkSuQmCC\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.7 Page no.380" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#example 7.7\n", + "#Find (a)The required air pressure in the tunnel.\n", + "#(b)The corrosponding drag on the prtotype for a 1 lb drag on the model.\n", + "V=240.0 #mph\n", + "ratio=0.1\n", + "Vair=240.0 #mph\n", + "Fm=1.0 #lb Fm =drag force on model\n", + "p=14.7 #psia standard atmospheric pressure\n", + "#Re=Rem\n", + "#(d*V*l/vis)=(dm*Vm*lm/vism)\n", + "#here Vm=V and lm/l=ratio\n", + "#assumption made is that an increase in pressure does not significantly change viscosity\n", + "\n", + "#calculation\n", + "drat=V/(ratio*Vair) #where drat=dm/d\n", + "\n", + "#for an ideal gas p=d*R*T\n", + "#T=Tm\n", + "#hence, pm/p=dm/d pm/p=prat\n", + "pm=p*drat\n", + "#F/(0.5*d*(V**2)*(l**2))=Fm/(0.5*dm*(Vm**2)*(lm**2))\n", + "F=(1/drat)*((V/Vair)**2)*((1/ratio)**2)*Fm\n", + "\n", + "#result\n", + "print \"The required air pressure in the tunnel=\",round(pm,3),\"psia\"\n", + "print \"The corrosponding drag on the prtotype \\nfor a 1 lb drag on the model=\",round(F,3),\"lb\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required air pressure in the tunnel= 147.0 psia\n", + "The corrosponding drag on the prtotype \n", + "for a 1 lb drag on the model= 10.0 lb\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 7.8 Page no.384" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Example 7.8\n", + "#Determine (a)the flowrate and required model width. (b) the operating time.\n", + "#given\n", + "w=20.0 #m\n", + "Q=125.0 #(m**3)/s\n", + "ratio=0.066\n", + "t=24.0 #hours\n", + "wm=ratio*w #m\n", + "#Vm/(gm*lm)**0.5 = V/(g*l)**0.5\n", + "#gm=g\n", + "#Q=VA and lm/l=1/15\n", + "#hence Qm/Q = ((lm/l)**0.5)*((lm/l)**2) = ratio**2.5\n", + "Qm=(ratio**2.5)*Q\n", + "#V=l/t\n", + "#tm/t=(V/Vm)*(lm/l)=ratio**0.5\n", + "tm=(ratio**0.5)*t #hours\n", + "\n", + "#result\n", + "print \"The required model width=\",round(wm,3),\"m\" \n", + "print \"The required model flowrate=\",round(Qm,3),\"m**3/s\"\n", + "print \"The operating time for the model=\",round(tm,1),\"hrs\"\n", + "\n", + "#plot\n", + "import matplotlib.pyplot as plt\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111)\n", + "\n", + "T=[0.02,0.07,0.2,0.4,0.5]\n", + "K=[4,6.20,10,15,17]\n", + "xlabel(\"lm/l\") \n", + "ylabel(\"tm (hr)\") \n", + "plt.xlim((0,0.5))\n", + "plt.ylim((0,20))\n", + "\n", + "ax.plot([0.07], [6.20], 'o')\n", + "ax.annotate('(1/15,6.20hr)', xy=(0.1,6))\n", + "a=plot(T,K)\n", + "show(a)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required model width= 1.32 m\n", + "The required model flowrate= 0.14 m**3/s\n", + "The operating time for the model= 6.2 hrs\n" + ] + }, + { + "output_type": "display_data", + "png": 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