Assessment of Methods for Block Volume Measurement

1. Assessment of Methods forBlock 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 cm3 • Volume by measuring dimensions: 4.03 ± 0.15 cm3 • Volume by collecting displaced fluid: 3.06 ± 0.05 cm3 • Volume from change upon displacing fluid: 3.0 ± 1.4 cm3

9. Critical Evaluation of Method ofMeasuring 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 cm3 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 cm3 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 cm3 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.