Make sure you read the Preface, which describes the learning objectives of the laboratory, and the Appendix, which describes the requirements of the lab reports.
Refer to the solution to MYO Problem 5.18 for an example of numerical integration of the velocity profile. You can download the MATLAB program myo_518.m or the Excel spreadsheet myo_5.18.xls used in the sample solution.
The data from the lab experiment needs to be manipulated before applying the formulas in the sample MATLAB program or sample Excel spreadsheet. The data taken in the lab is in the form u = f(s), where s is the coordinate measured on the scale of the positioning stage. To use the numerical integration formulas you need to
The measurements were taken all at once, but the limits of the numerical integration are r=0 and r=Ro, where Ro is the outer radius of the pipe. The positive and negative sc data sets are just two separate integrals with r taken as the absolute value of sc.
When you split the data, use interpolation to find the value of u at sc=0. Also include values of u=0 at sc=R0.
MATLAB users can download the
function to automate the splitting and replicating of data.
Please send me some sample data sets via email. Only send the plain text files recorded by the LabVIEW VI. Do not send Excel versions of the data files. I need data sets for both the velocity profile and the pressure change versus flow rate measurements. Thanks.
The first experiment (during the first week of classes) involved measuring the relationship between pressure and depth of water in the a tank of stationary water. You can download a spreadsheet of raw data from one of those experiments.
During the fifth week of classes we did a demonstration involving recording the pressure versus time as the tank was allowed to drain. On Tuesday evening, 10-24-2006, photos of the tank were taken as it drained. You can also download the raw voltage versus time data recorded during that experiment. In the data file, the first column is time in seconds and the second column is tranducer output in Volts.
A set of documents related to the sample lab can be downloaded as a single zip archive. The archive contains the following files:
|apparatus.eps||Image of apparatus in Encapsulated Postscript (EPS) format|
|appartaus.png||Image of apparatus in Portable Network Graphics (PNG) format|
|dataReduction.m||MATLAB function to perform data reduction|
|dataReduction.xls||Excel spreadsheet to perform data reduction|
|labReport.doc||Completed lab report as a MS Word document|
|MATLAB.pdf||Descripton of MATLAB calculations in dataReduction.m|
|sampleCalc.jpg||Scanned image of sample calculations|
Note: The links to individual files may cause your browser to open an application program on your computer. This will be the case, for example, if you are using Internet Explorer on Windows. To avoid this, you can right-click on the link and select "Save as...", or you can download the zip archive containing all the files.
Two sources of data for the viscosity of glycerine/water mixtures are available
The reference tables provide the viscosity of glycerine/water mixtures as a function of glycerine concentration by weight, i.e Cweight = Wg/(Wg+Ww), where Wg is the weight of the glycerine, and Ww is the weight of the water.
The following table gives the concentration of glycerine by volume. If Vg is the volume of glycerine in the mixture, and Vw is the volume of water in the mixture, then the concentration of glycerine by volume is Cvol = Vg/(Vg+Vw).
|Label||Percent Glycerine by Volume|
Images from the lab manual are available for you to incorporate in your lab reports. Each time you use one of these images you must give proper attribution. One way to do this is to include something like "Image from EAS 361 lab manual" in the caption for the figure.
The images are available in three formats: Encapsulated Postscript (EPS),
Portable Document Format (PDF), and Portable Network Graphics (PNG). You
should be able to import (at least) one of these formats in most word-processing
programs. The images for each format are combined into one of the following
The PDF and PNG formats are easier to work with if you incorporate the images into a standard word processor such as Microsoft Word. The EPS format gives higher resolution when printing on a Postscript printer. Although I exclusively use EPS in my own document creation, PNG will probably work fine for you. In a recent (September 2004) test with Microsoft Word, a sample PDF image from the image archive produces the poorest printed output, EPS produced the sharpest printed output, and PNG produced medium quality output.
To use the images, first download the archives to your computer. You then insert them into your word-processing document as an external file. Step-by-step instructions for these tasks are given below.
The basic steps for inserting an image from an external file are:
If you need to resize the image: