{ "metadata": { "name": "Chapter_8" }, "nbformat": 2, "worksheets": [ { "cells": [ { "cell_type": "markdown", "source": [ "

Chapter 8:Fundamentals of measuring instruments

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

Example 8.1, Page Number: 507

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''Flux density calculation'''", "", "#variable declaration", "fi=10.0*10**-6 # fi-flux", "inch=2.54*10**-2 # length", "A=inch**2 # area", "", "#calculation", "B =fi/A", "", "#Result", "print('Flux Density B= %.1f mT'%(B*1000))" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Flux Density B= 15.5 mT" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "source": [ "

Example 8.2, Page Number: 508

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''Power Dissipation and accuracy of result'''", "", "#variable Declaration", "i=10*10**-3 # current in A", "R=1000.0 # resistance in ohm", "P=(i**2)*R # Power", "err_R=10.0 # Error in Resistance measurement", "err_I=(2.0/100)*25*100/10 # Error in current measurement", "", "#calculation", "err_I2=2*err_I", "err_p=err_I2+err_R", "", "#Result", "print('%% error in I^2 = \u00b1 %d%%\\n%% error in Power = \u00b1 %d%%'%(err_I2,err_p))" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "% error in I^2 = \u00b1 10%", "% error in Power = \u00b1 20%" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "source": [ "

Example 8.3, Page Number: 508

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''max and min levels of input supply current'''", "", "#variable Declaration", "i1=37.0 # current in branch 1 ", "i2=42.0 # current in branch 2", "i3=13.0 # current in branch 3", "i4=6.7 # current in branch 4", "", "#Calculation", "Imax=(i1+i2)+(i1+i2)*(3.0/100)+(i3+i4)+(i3+i4)*(1.0/100)", "Imin=(i1+i2)-(i1+i2)*(3.0/100)+(i3+i4)-(i3+i4)*(1.0/100)", "", "#result", "print('Maximum level of total supply current = %.3f mA'%Imax)", "print('\\nMinimum level of total supply current = %.3f mA'%Imin)" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum level of total supply current = 101.267 mA", "", "Minimum level of total supply current = 96.133 mA" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "source": [ "

Example 8.4, Page Number:508

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''Time constant for thermometer'''", "", "import math", "", "#(a)", "", "#variable declaration", "T=200.0 # intermediate temperature ", "T0=300.0 # final temperature ", "Ti=70.0 # initial temperature ", "t=3.0 # time in seconds ", "", "#calculation", "x=(T-T0)/(Ti-T0)", "tow=-t/math.log(x)", "", "#result", "print('(a)\\nTime constant tow=%.1f s'%tow)", "", "", "#(b)", "", "#variable declaration", "t1=5.0 # time in seconds ", "#calculation", "T5=T0+((Ti-T0)*math.e**(-t1/tow))", "", "#result", "print('\\n(b)\\nTemperature after 5 seconds T5 = %.2f\u00b0C'%T5)" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)", "Time constant tow=3.6 s", "", "(b)", "Temperature after 5 seconds T5 = 242.61\u00b0C" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "source": [ "

Example 8.5, Page Number:

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''Error calculation of second order instrument'''", "", "import math", "", "#variable declaration", "w=9.0 # excitation frequency", "wn=6.0 # natural frequency", "dr=0.6 # damping ratio", "", "#calculations", "", "x=w/wn", "Ar=1/math.sqrt(((1-(x)**2)**2)+(2*dr*x)**2)", "err=(1-Ar)*100", "", "#Result", "print('A=%.3f'%Ar)", "print('\\nError = %.2f%%'%err)" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "A=0.456", "", "Error = 54.37%" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "source": [ "

Example 8.6, PAge Number: 510

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''Output of first order instrument for unit step input'''", "", "#variable Declaration", "t=2.0 # output to be calculated after t seconds", "", "#calculation", "y=1-math.e**(-(t-1.5)/0.5)", "", "#result", "print('y(t)at t=2 will be y(t)=%.3f'%y)" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "y(t)at t=2 will be y(t)=0.632" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "source": [ "

Example 8.7, Page Number: 510

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''Statistic of Temperature readings'''", "", "import math", "", "#variable declaration", "", "#Temperature Readings", "x1=98.5 # Reading 1", "x2=99.0 # Reading 2", "x3=99.5 # Reading 3 ", "x4=100.0 # Reading 4", "x5=100.5 # Reading 5", "x6=101.0 # Reading 6", "x7=101.5 # Reading 7", "# Frequency", "f1=4.0 # Reading 1", "f2=13.0 # Reading 2", "f3=19.0 # Reading 3", "f4=35.0 # Reading 4", "f5=17.0 # Reading 5", "f6=10.0 # Reading 6", "f7=2.0 # Reading 7", "", "#(i) Arithmatic Mean", "", "#calculation", "x_bar=((x1*f1)+(x2*f2)+(x3*f3)+(x4*f4)+(x5*f5)+(x6*f6)+(x7*f7))/(f1+f2+f3+f4+f5+f6+f7)", "", "#result", "print('(i)\\n\\tArithmatic Mean = %.2f\u00b0C'%x_bar)", "", "#(ii) Average Deviation", "", "#calculation", "D=(abs(x1-x_bar)*f1)+(abs(x2-x_bar)*f2)+(abs(x3-x_bar)*f3)+(abs(x4-x_bar)*f4)", "D=D+(abs(x5-x_bar)*f5)+(abs(x6-x_bar)*f6)+(abs(x7-x_bar)*f7)", "D=D/(f1+f2+f3+f4+f5+f6+f7)", "", "#result", "print('\\n(ii)\\n\\tAverage Deviation =%.4f\u00b0C'%D)", "", "#Standard deviation", "", "#Calculation", "sigma=((x1-x_bar)**2*f1)+((x2-x_bar)**2*f2)+((x3-x_bar)**2*f3)+((x4-x_bar)**2*f4)", "sigma=sigma+((x5-x_bar)**2*f5)+((x6-x_bar)**2*f6)+((x7-x_bar)**2*f7)", "sigma=math.sqrt(sigma)", "sigma=sigma/math.sqrt(f1+f2+f3+f4+f5+f6+f7)", "", "#result", "print('\\n(iii)\\n\\tStandard deviation = %.3f\u00b0C'%sigma)", "", "#variance", "", "#result", "print('\\n(iv)\\n\\tVariance = %.4f\u00b0C'%(sigma**2))", "", "#Probable Error", "", "#result", "print('\\n(v)\\n\\tProbable Error= %.4f\u00b0C'%(0.6745*sigma))" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)", "\tArithmatic Mean = 99.93\u00b0C", "", "(ii)", "\tAverage Deviation =0.5196\u00b0C", "", "(iii)", "\tStandard deviation = 0.671\u00b0C", "", "(iv)", "\tVariance = 0.4501\u00b0C", "", "(v)", "\tProbable Error= 0.4525\u00b0C" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "source": [ "

Example 8.8, Page Number: 511

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''Calculation of damping coefficient and natural frequency for 2nd order instrument'''", "", "import math", "", "#variable Declaration", "wn=math.sqrt(3.0) # natural frequency of osscilation", "", "#Calculation", "x=3.2/(2*wn)", "", "#Result", "print('Damping coefficient = %.3f\\nNatural frequency of Oscillation = %.3f'%(x,wn))" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Damping coefficient = 0.924", "Natural frequency of Oscillation = 1.732" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "source": [ "

Example 8.9, Page Number: 512

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''calculation of Amplitude inaccuracy and phase shift from transfer function'''", "", "import math", "#variable declaration", "w=100.0 # natural frequency of osscilation", "", "#calculation", "fi=-math.atan(0.1*w)-math.atan(0.5*w)", "A=1/(math.sqrt(1+(0.1*w)**2)*(math.sqrt(1+(0.5*w)**2)))", "A=1*1000.0/math.ceil(1000*A)", "err=(1-1.0/A)*100", "", "#Result", "print('A=K/%d\\n%% error = %.1f%%\\nfi = %.2f\u00b0'%(A,err,fi*180/math.pi))" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "A=K/500", "% error = 99.8%", "fi = -173.14\u00b0" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "source": [ "

Example 8.10, Page Number: 512

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''temperature and altitude calculation from first order thermometer placed in balloon'''", "", "#calculations", "R=0.15*10/50 # Temperature gradient", "K=1.0 # constant", "tow=15.0 # time constant ", "", "#Calculations", "deg=K*R*tow", "", "#(i)", "a=15-deg", "", "#(ii)", "alt_red=deg*50.0/0.15", "h=5000-alt_red", "", "#result", "print('(i)The actual temperature when instrument reads 15\u00b0C is %.2f\u00b0C'%a)", "print('\\n The true temperature at 5000 metres = %.2f '%a)", "print('\\n(ii)\\nThe true altitude at which 15\u00b0C occurs is %d metres'%h)" ], "language": "python", "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)The actual temperature when instrument reads 15\u00b0C is 14.55\u00b0C", "", " The true temperature at 5000 metres = 14.55 ", "", "(ii)", "The true altitude at which 15\u00b0C occurs is 4850 metres" ] } ], "prompt_number": 10 } ] } ] }