outline

# outline - Outline and Equation Sheet for M E 345 Author...

This preview shows pages 1–2. Sign up to view the full content.

Outline and Equation Sheet for M E 345 Author: John M. Cimbala, Penn State University Latest revision, 15 April 2008 Introduction Primary dimensions – mass, length, time, temperature, current, amount of light, and amount of matter. Significant digits – the rules for multiplication and division, and for addition and subtraction. Rounding off round up if the least significant digit is odd , and truncate if the least significant digit is even . Dimensional Analysis Law of dimensional homogeneity Every additive term in an equation must have the same dimensions . The method of repeating variables – there are 6 steps: 1. List the parameters and count them, n . 2. List the primary dimensions of each parameter. 3. Set the reduction, j , as the number of primary dimensions in the problem. Then knj =− . [Reduce j by one if necessary.] 4. Choose j repeating variables. 5. Construct the k Π s, and manipulate as necessary. 6. Write out the final dimensionless functional relationship ( ) 12 3 function , ,... k Π Π Π and check your algebra. Dimensional analysis is often extremely useful in setting up and designing experiments. Errors and Calibration Systematic errors (bias errors) – consistent, repeatable errors. Random errors (precision errors) – scatter in data, a lack of repeatability, unrepeatable, inconsistent errors. Accuracy accuracy error is the measured value minus the true value . Precision precision error is the reading minus the average of readings . Other errors – zero, linearity, sensitivity, resolution, hysteresis, instrument reapeatability, drift. Calibration – static (time not relevant) vs. dynamic (time is relevant) calibration. Mean bias error – defined as true 1 true 1 MBE n i i x x nx = = , and usually expressed as a percentage. Basic Statistics Definitions – sample mean 1 1 n i i x x n = = , sample standard deviation () 2 2 11 nn ii dx S == −− ∑∑ x , sample variance ( S 2 ), sample median (half lower, half higher), sample mode (most probable value – one that occurs most frequently), population (all values) vs. sample (a selected portion of the total population). Excel – learn how to use Excel’s built-in statistics functions. Root mean square error – defined as 2 true 1 true 1 RMSE n i i xx = ⎛⎞ = ⎝⎠ , and usually expressed as a percentage. Histograms and Probability Density Functions Histogram plots – frequency, bins or classes, bin width or class width, Sturgis and Rice rules. Normalized histograms – how to normalize the vertical scale and the horizontal scale. PDF – how to create a probability density function from a histogram. Expected value – same as population mean. Standard deviation – same as population standard deviation.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

outline - Outline and Equation Sheet for M E 345 Author...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online