{ "metadata": { "name": "", "signature": "sha256:981874370471c716824dfdef461e37258f322dfc13d6037062140fc3ad5e0ae2" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Chapter 5: Flow

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.1, Page Number: 310

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "#(i)\n", "\n", "#variable declaration\n", "d=75.0*10**-3 # diameter of pipe\n", "a=math.pi*d**2/4 # area of cross section of pipe\n", "v=760.0*10**-3 # flow velocity\n", "\n", "#calculation\n", "Q=v*a\n", "Q=Q*10**3\n", "print('(i)\\nVolume Flow Rate Q=%.3f *10^-3 m^3/sec' %Q)\n", "rho=1000.0\n", "W=rho*Q*10**-3\n", "\n", "#result\n", "print('\\n(ii)\\nMass Flow rate W=%.3f kg/sec' %W)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)\n", "Volume Flow Rate Q=3.358 *10^-3 m^3/sec\n", "\n", "(ii)\n", "Mass Flow rate W=3.358 kg/sec" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.2, page Number:310

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#variable declaration\n", "D=40.0 # Diameter of pipe\n", "d=20.0 # Diameter of Orifice\n", "mr=15.0 # Manometer reading\n", "\n", "#calculation\n", "h=(13.6-1)*15.0*10.0\n", "B=d/D\n", "M=1/math.sqrt(1-(B**4))\n", "Cd=0.5999\n", "x=math.sqrt(2*9.8*h*(10**-3))\n", "Q=x*Cd*M*(math.pi*((20*(10**-3))**2))/4\n", "Q=Q*3600.0\n", "\n", "#result\n", "print('Volumetric flow rate Q= %.4f m^3/hr' %Q)\n", "#Answer slightly deviates from answer given in the book because of pi value.\n", "#if pi=3.14, then answer is same as in textbook " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Volumetric flow rate Q= 4.2649 m^3/hr" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.3, Page Number: 310

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "#variable declaration\n", "Re=10.0**5 # Reynolds number\n", "D=40.0*10**-3 # Diameter of pipe \n", "v=10**-6 # Kinematic viscosity in m^2/sec\n", "\n", "#calculation\n", "V1=Re*v/D\n", "A1=(math.pi*(40.0*10**-3)**2)/4\n", "A2=(math.pi*(20.0*10**-3)**2)/4\n", "V2=V1*A1/A2\n", "\n", "#result\n", "print('V2=%.1f m/sec' %V2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "V2=10.0 m/sec" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.4, Page Number: 311

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#variable declaration\n", "Cd=0.61 # discharge coefficient\n", "D=40.0*10**-3 # Diameter of pipe\n", "d=20.0*10**-3 # Diameter of Orifice \n", "\n", "#calculation\n", "M=1/math.sqrt(1-(d/D)**4)\n", "V2=10.0\n", "rho=1000.0\n", "g=9.8\n", "X=V2*math.sqrt(rho/(2*g))/(Cd*M)\n", "p_diff=X**2\n", "p_diff=math.floor(p_diff/100)\n", "p_diff=p_diff/100.0\n", "\n", "\n", "#result\n", "print('P1-P2 = %.2f kg/cm^2'%p_diff)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "P1-P2 = 1.28 kg/cm^2" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.5, Page Number: 312

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#variable declaration\n", "Cd=0.6 # discharge coefficient\n", "D=150.0*10**-3 # Diameter of pipe\n", "d=75.0*10**-3 # Diameter of Orifice \n", "p=250.0 # pressure recorded\n", "g=9.8 # acceleration due to gravity\n", "rho=1000.0 # Water density \n", "s=75.0*10**-3 # venturi tube size\n", "\n", "#(a)\n", "\n", "#calculation\n", "Q=Cd*math.pi*s**2*math.sqrt(2*g*p/rho)/(4*math.sqrt(1-(d/D)**4)) \n", "\n", "#result\n", "print('(a) For orifice plate\\nQ=%f m^3/sec = %.3f litres/sec'%(Q,Q*1000))\n", "\n", "#calculation\n", "Cd1=0.99\n", "Q2=Cd1*math.pi*s**2*math.sqrt(2*g*p/rho)/(4*math.sqrt(1-(d/D)**4))\n", "\n", "#result\n", "print('\\n\\n(b)For venturi tube\\nQ=%f m^3/sec = %.2f litres/sec'%(Q2,Q2*1000))\n", "#Answer slightly deviates from answer given in the book because of pi value.\n", "#if pi=3.14, then answer is same as in textbook " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) For orifice plate\n", "Q=0.006060 m^3/sec = 6.060 litres/sec\n", "\n", "\n", "(b)For venturi tube\n", "Q=0.009999 m^3/sec = 10.00 litres/sec" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.6, Page Number: 312

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#(i)\n", "\n", "#variable declaration\n", "V=0.02 # volumetric flow rate\n", "d=10*10**-2 # Diameter of pipe\n", "\n", "#calculation\n", "A=math.pi*d**2/4\n", "v=V/A\n", "rho=1000.0\n", "Re=rho*v*d/10**-3\n", "Re=Re/100000.0\n", "\n", "#result\n", "print('(i)\\nReynolds number(Re) = %.3f * 10^5'%Re)\n", "\n", "#(ii)\n", "\n", "#variable declaration\n", "Cd=0.98 # discharge coefficient \n", "D=20*10**-2 # Diameter of pipe \n", "d=10*10**-2 # Diameter of orifice\n", "\n", "#calculation\n", "M=1/math.sqrt(1-(d/D)**4)\n", "a2=math.pi*d**2/4\n", "Q=0.02\n", "g=9.8\n", "X=Q*math.sqrt(rho)/(M*Cd*a2*math.sqrt(2*g))\n", "p_diff=math.ceil(X**2)\n", "\n", "#result\n", "print('\\n(ii)\\nPressur_difference = %d kg/m^2 = %.4f kg/cm^2'%(p_diff,p_diff/10000))\n", "#Answer slightly deviates from answer given in the book because of pi value.\n", "#if pi=3.14, then answer is same as in textbook " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)\n", "Reynolds number(Re) = 2.546 * 10^5\n", "\n", "(ii)\n", "Pressur_difference = 323 kg/m^2 = 0.0323 kg/cm^2" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.7, Page Number: 313

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "\n", "\n", "#variable declaration\n", "g=9.81 #acceleration due to gravity\n", "h=20.0 #height\n", "\n", "#calculation\n", "v=math.sqrt(2*g*h)\n", "d=300.0*10**-3\n", "A=(math.pi*d**2)/4\n", "A=math.floor(A*1000)\n", "A=A/1000.0\n", "Q=A*v\n", "\n", "#result\n", "print('Q = %.3f m^3/sec'%Q)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Q = 1.387 m^3/sec" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.8, Page Number:313

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#variable declaration\n", "Cd=0.6 # coefficient of discharge \n", "g=9.8 #acceleration due to gravity\n", "h=400*10**-3 #height\n", "\n", "#calculation\n", "V=Cd*math.sqrt(2*g*h)\n", "\n", "#result\n", "print('V = %.2f m/sec' %V)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "V = 1.68 m/sec" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.9, Page Number: 314

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#variable declaration\n", "Cd=0.98 # coefficient of discharge\n", "g=9.8 #acceleration due to gravity\n", "h=900.0*10**-3 #height\n", "\n", "#calculation\n", "V=Cd*math.sqrt(2*g*h)\n", "V=math.floor(V*100)\n", "V=(V/100.0)\n", "\n", "#result\n", "print('V = %.2f m/sec' %V)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "V = 4.11 m/sec" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.10, Page Number:314

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#Variable declaration\n", "del_p=20*10**3 #Pa\n", "dens_water=1000 #kg/m^3\n", "dens_air=1.29 #kg/m^3\n", "\n", "#calculations\n", "\n", "#(i)When flowing fluid is water\n", "v=math.sqrt(2*del_p/dens_water)\n", "\n", "#(ii)When flowing fluid is air\n", "v1=math.sqrt(2*del_p/dens_air)\n", "\n", "#result\n", "print('\\n(i)When flowing fluid is water\\n\\tV=%.3f m/sec'%v)\n", "print('\\n(ii)When flowing fluid is air\\n\\tV=%.0f m/sec'%v1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "(i)When flowing fluid is water\n", "\tV=6.325 m/sec\n", "\n", "(ii)When flowing fluid is air\n", "\tV=176 m/sec" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.11, Page Number: 314

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "# variable declaration\n", "dens=1026.0 # density of see water\n", "p=25.0*10**3 # pressure difference in manometer \n", "\n", "#calculation\n", "V=math.sqrt(2*p/dens)\n", "\n", "#result\n", "print('V=%.2f m/sec =%.3f km/hr'%(V,V*18/5))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "V=6.98 m/sec =25.131 km/hr" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.12, Page Number: 314

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "# variable declaration\n", "dens=1.29 # air density at height \n", "\n", "#calculation\n", "p=12.5*1000\n", "V=math.sqrt(2*p/dens)\n", "\n", "\n", "#result\n", "print('V=%.2f m/sec =%.2f km/hr'%(V,V*18/5))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "V=139.21 m/sec =501.16 km/hr" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.13, Page Number: 315

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#variable declaration\n", "Cd=0.6 # discharge coefficient\n", "Dp=0.05 # inside diameter of metering tube \n", "Df=0.035 # diameter of rotameter \n", "g=9.8 # acceleration due to gravity\n", "rho_f=3.9*10**3 # density of cylindrical float\n", "rho=1000.0 # water density \n", "Vf=3.36*10**-5 # volume of the float\n", "\n", "#calculation\n", "Q=Cd*((Dp**2-Df**2)/Df)*math.sqrt(math.pi*g*Vf*(rho_f-rho)/(2*rho))\n", "Q=Q*10000.0\n", "\n", "#result\n", "print('Volumetric flow Q=%.4f *10^-4 m^3/sec' %Q)\n", "#Answer slightly deviates from answer given in the book because of pi value.\n", "#if pi=3.14, then answer is same as in textbook " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Volumetric flow Q=8.4652 *10^-4 m^3/sec" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.14, Page number: 315

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "# variable declaration\n", "Cd=1 # discharge coefficient\n", "Dp=0.018 # inside diameter of metering tube \n", "Df=0.015 # diameter of rotameter \n", "g=9.81 # acceleration due to gravity\n", "rho_f=2.7 # density of cylindrical float\n", "rho=0.8 # water density \n", "Vf=520.0*10**-9 # volume of the float\n", "\n", "#case 1\n", "\n", "#caculation\n", "Qmin=Cd*((Dp**2-Df**2)/Df)*math.sqrt(math.pi*g*Vf*(rho_f-rho)/(2*rho))\n", "Qmin=Qmin*100000.0\n", "\n", "#result\n", "print('Case 1: When float is at the bottom\\n Volumetric flow Qmin=%.3f *10^-5 m^3/sec'%Qmin)\n", "\n", "#case 2\n", "\n", "#calculation\n", "Dp2=0.0617\n", "Qmax=Cd*((Dp2**2-Df**2)/Df)*math.sqrt(math.pi*g*Vf*(rho_f-rho)/(2*rho))\n", "Qmax=Qmax*100000\n", "\n", "#result\n", "print('\\n\\nCase 2: When float is at the bottom\\n Volumetric flow Qmax=%.2f *10^-5 m^3/sec'%Qmax)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Case 1: When float is at the bottom\n", " Volumetric flow Qmin=2.879 *10^-5 m^3/sec\n", "\n", "\n", "Case 2: When float is at the bottom\n", " Volumetric flow Qmax=104.17 *10^-5 m^3/sec" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.15, Page Number:316

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# variable declaration\n", "W=165.0 # weight of material on section of length\n", "R=328.0 # Conveyor speed m/min\n", "L=16.0 # Length of weighting platform in m\n", "\n", "#calculation\n", "Q=W*R/L\n", "\n", "#result\n", "print('Flow Rate Q=%.2f kg/min =%.1f kg/hour'%(Q,Q/60))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Flow Rate Q=3382.50 kg/min =56.4 kg/hour" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.16, Page Number:316

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#variable declaration\n", "f=100.0 # beat frequency\n", "d=300.0*10**-3 # Sound path\n", "a=45.0 #angle between transmeter and receiver in degrees\n", "\n", "#calculation\n", "a_rad=45.0*math.pi/180.0\n", "v=f*d/(2*math.cos(a_rad))\n", "\n", "#Result\n", "print('Fluid Velocity V=%.1f m/sec'%v)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fluid Velocity V=21.2 m/sec" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.17, Page Number: 316

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# variable declaration\n", "r=150.0 # speed of rotation\n", "v=120.0 # volume trapped between gears and casting\n", "\n", "#clculation\n", "Q=4.0*v*r\n", "\n", "#result\n", "print('Volume flow rate Q=%d cm^3/min = %d litres/min'%(Q,Q/1000))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Volume flow rate Q=72000 cm^3/min = 72 litres/min" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.18, Page Number: 317

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "# variable declaration\n", "Q=2500.0 # Quantitty flow rate\n", "d=2.75 # inner diameter\n", "\n", "#calculation\n", "a=(math.pi*d**2)/4\n", "v=Q/(60*a)\n", "B=60.0\n", "e=B*d*10**-2*v*10**-2\n", "\n", "#result\n", "print('Induced emf e =%.4f V=%.1f mV'%(e,e*1000))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Induced emf e =0.1157 V=115.7 mV" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.19, Pae Number:317

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# variable declaration\n", "e=0.2*10**-3 # voltage of electromagnetic flow meter\n", "B=0.08 # Flux density\n", "l=10.0*10**-2 # Diameter of pipe\n", "\n", "#calculation\n", "v=e/(B*l)\n", "\n", "#result\n", "print('V = %.3f m/sec = %.2f cm/sec'%(v,v*100))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "V = 0.025 m/sec = 2.50 cm/sec" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.20, Page Number: 317

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# variable declaration\n", "ei=0.15*10**-3 # peak value\n", "em=2*ei # p-p amplifier output \n", "B=0.1 # flux density\n", "l=60.0*10**-3 # diameter of the pipe\n", "\n", "#calculation\n", "v=em/(B*l)\n", "\n", "#result\n", "print('Velocity of flow V = %.2f m/sec = %.1f cm/sec'%(v,v*100))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Velocity of flow V = 0.05 m/sec = 5.0 cm/sec" ] } ], "prompt_number": 20 } ], "metadata": {} } ] }