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+{
+ "metadata": {
+ "name": "Chapter_8"
+ },
+ "nbformat": 2,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "source": [
+ "<h1>Chapter 8:Fundamentals of measuring instruments <h1>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "<h3>Example 8.1, Page Number: 507<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.2, Page Number: 508<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.3, Page Number: 508<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.4, Page Number:508<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.5, Page Number:<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.6, PAge Number: 510<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.7, Page Number: 510<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.8, Page Number: 511<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.9, Page Number: 512<h3>"
+ ]
+ },
+ {
+ "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": [
+ "<h3>Example 8.10, Page Number: 512<h3>"
+ ]
+ },
+ {
+ "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
+ }
+ ]
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 11:50:07 +0000