Engineering Fundamentals and Problem Solving, 6e

Transcription

1 Engineering Fundamentals and Problem Solving, 6e Chapter 5 Representation of Technical Information Chapter Objectives 1. Recognize the importance of collecting, recording, plotting, and interpreting technical data for engineering analysis and design 2. Put into practice methods for graphical presentation of scientific data and graphical analysis of plotted data 3. Develop the ability to graph data using uniform and nonuniform scales 4. Apply methods of selected points and least squares for determining the equation that gives the best-fit line to the given data 5. Determine the most appropriate family of curves (linear, power, or exponential) that gives the best fit to the given data 2 1

2 General Graphing Procedures 1. Select the type of graph paper rectangular [aka rectilinear] semilog log-log) and appropriate grid spacing for the given data. 2. Choose the location of the horizontal and vertical axes. 3. Determine the scale units (range) for each axis 4. Graduate and calibrate the axes using the 1, 2, 5 rule. 5. Identify each axis completely. 3 General Graphing Procedures-cont d 6. Plot points and use permissible symbols. 7. Double check any point that deviates from the line. 8. Draw the curve or curves. 9. Identify each curve, add title, and include other necessary notes. 10. Darken lines for good reproduction. 4 2

3 Log log and Semilog graph paper Log-log: Power curves: y=bx m Semilog: Exponential curves: y=be mx 5 Axis designations 6 3

4 Axis breaks Axes should begin at zero 7 Graduations and Calibrations Scale marks (ticks) are Graduations. Numerical values assigned to significant graduations are Calibrations 8 4

5 1, 2, 5 Rule The smallest division of the axis should be a positive or negative integer power of 10 times 1, 2, or 5. 9 Axis Labeling The axis label should contain the name of the variable, its symbol, and its units. 10 5

6 Calibrating log scales Preferred method of calibrating log scales uses powers of 10 on major graduations 11 Plotting data points Observed: Data points connected by straight irregular line segments. Line does not penetrate circles Empirical: Interpretation of what occurs between data points. Smooth line fitted to the data points. Data may or may not fall on curve. Theoretical: Graph of an equation. Smooth and without symbols. Every point is a data point. 12 6

7 Graph key Defines symbols and line types. On a portion of the grid. Enclosed in a border. 13 Method of selected points for linear equations 1. Plot the data on rectangular paper, draw in best straight line to fit plotted points 2. Select 2 points on the line (not necessarily data points) and record their values 3. Substitute points into the linear equation y=mx+b 4. Solve for m and b 5. Chose a third point on the line to verify the equation 14 7

8 Example Problem 1 The velocity of an experimental automobile is measured at specified time intervals. Determine the equation of a straight line constructed through the points recorded in the following table. Time, t, s Velocity, V, m/s Example Problem 1 cont d Procedure: Plot data on rectangular graph paper. Select two points on the line, A(t 1, V 1 ) and B(t 2, V 2 ), and record the values of these points. 16 8

9 Example Problem 1 cont d Procedure: Plot data on rectangular graph paper. Select two points on the line, A(t 1, V 1 ) and B(t 2, V 2 ), and record the values of these points. A(10, 60) B(35, 165) 17 Example Problem 1 cont d Substitute the points A and B into V = mt + b. 60 = m(10) + b 165 = m(35) + b Solve the equations for m and b giving: V = 4.2t

10 Method of selected points for power curves 1. Plot the data on log-log paper, draw in best straight line to fit plotted points 2. Select 2 points on the line (not necessarily data points) and record their values 3. Substitute points into the power equation log y = m log x + log b, 4. Solve for m and b 5. Chose a third point on the line to verify the equation 20 Method of selected points for exponential curves 1. Plot the data on semilog paper, draw in best straight line to fit plotted points 2. Select 2 points on the line (not necessarily data points) and record their values 3. Substitute points into the exponential equation log y = mx log e + log b, 4. Solve for m and b 5. Chose a third point on the line to verify the equation 21 10

11 Example Problem 2 A solid object is dropped from a tall building, and the values, time versus distance are as recorded in the table below. 22 Example Problem 2 - cont d Procedure: Plot the data on log-log paper. Select two points on the line. A(1.5,11) B(6,175) 23 11

12 Example Problem 2 - cont d Substitute these values into the general equation log s = m log t + log b. log 175 = m log 6 + log b log 11 =m log log b Solve for m and b resulting in: s = 4.9t