1. Assessment of Methods for Block Volume Measurement Carl R. F. Lund February 28, 1999

2. Business Opportunity with ABC Blocks ABC Blocks may contract with Big C Enterprises for the manufacture of ABC’s blocks ABC Blocks requires production line monitoring of blocks –Must meet volume specification Big C Enterprises currently does not have standardized methods for production line monitoring of block volume

3. Outline Project Objectives Summary of Findings Methods Tested Procedure Results Critical Examination of Methods Conclusions Recommendations

4. Project Objectives Identify different methods that could be used to check the volume of blocks as they come off the production line Compare the accuracy and other merits of the methods Select the best method for development and implementation in the process.

5. Summary Three methods for volume measurement were examined –One based upon direct measurement –Two based upon fluid displacement As tested, none were completely satisfactory A method based upon fluid displacement is recommended for further development –Rapid, lowest cost –Can be implemented with sufficient accuracy

6. Methods Considered Measure length, width and height; multiply to get volume Displace fluid from a container, collect the displaced fluid and measure its volume Displace fluid within a container, measure volume of fluid only, add block and measure volume of block and fluid, find block volume from difference

7. Procedure A test block was machined from pure aluminum –volume was found by weighing, using well- established density of pure aluminum Each method was used in the lab to measure the volume of this same block. –assessed accuracy, ease of implementation, and reliability

8. Results Test block volume: 3.83 cm 3 Volume by measuring dimensions: 4.03 ± 0.15 cm 3 Volume by collecting displaced fluid: 3.06 ± 0.05 cm 3 Volume from change upon displacing fluid: 3.0 ± 1.4 cm 3

9. Critical Evaluation of Method of Measuring Dimensions The method is time-consuming and labor intensive There are multiple sources of error: –Each of 3 dimensional measurements –Block may not be true –Computational errors Any one of these errors can be significant enough invalidate the result Accuracy as tested is not satisfactory –Measured 4.03 ± 0.15 vs. 3.83 cm 3 true volume –Could be improved but might increase time required to make the measurement

10. Critical Evaluation of Collecting Displaced Fluid Results were accurate but imprecise –Measured 3.06 ± 0.05 vs. 3.83 cm 3 true volume –Suspect systematic error in gradations of graduated cylinder –Could repeat, don’t recommend doing so Method is moderately time consuming –Must top off container before each measurement –Requires care not to spill or lose displaced fluid

11. Critical Evaluation of Measuring the Change in Volume As tested the accuracy was not sufficient –Measured 3.0 ± 1.4 vs. 3.83 cm 3 true volume –Can be improved by better design of equipment Method is rapid –Potential operator errors are no worse than with other methods With improvement in accuracy this is the method of choice.

12. Conclusions Measuring dimensions is not accurate enough, time consuming, and subject to several sources of error Collecting displaced fluid is awkward and time- consuming compared to measuring change in fluid volume due to adding block Further development of apparatus for measuring the change in fluid volume is necessary –It is the method of choice –It is accurate (with redesign), rapid, and inexpensive

13. Recommendations Design apparatus specifically for present purposes and ensure accuracy is adequate. –Mark volume gradations on the vessel that are finer than the desired accuracy –Make the container cross-section only slightly larger than the size of the blocks being measured If desired accuracy can’t be attained consider collecting displaced fluid –eliminate systematic errors in equipment.