# CU-Boulder MCEN 3037 - 9 (18 pages)

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- Pages:
- 18
- School:
- University of Colorado at Boulder
- Course:
- Mcen 3037 - Data Analysis

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Say y f x1 x2 x3 Then y f x1 x2 x3 y 2 y 2 y 2 And u y x u x1 x u x 2 x u x 3 1 2 3 or n 2 u y i ui i 1 1 2 1 2 Manometers are pressure measuring devices that determine a pressure by measuring the height of a column of fluid We would like to achieve an accuracy of 1 of the maximum reading 10kPa This is to be done using a well manometer which has a 0 2 mm resolution Estimate the uncertainty that can be tolerated in the density of the gage fluid which has a nominal value of 2500 kg m3 The relationship between the pressure and column height is P rgh Assume we know g to a higher degree of accuracy than the other variables If we are going to meet the design specifications we need to have a maximum uncertainty in P of uP 0 01 10 000 100 Pa 95 What is the instrument resolution uncertainty u0 0 0001 m 95 Ok to make things easier let s write out the full expression for the uncertainty 1 0 P 2 P 2 P 2 2 uP uh ur ug 100 Pa 95 h r g Let s fill in P kg rg 2500 9 81 24525 0 2 2 h ms P gh 9 81 h r Looking for this What is the expected value of h 2 P m P 10 000 gh 9 81 0 408 4 00 2 h 0 408 m r s rg 2500 9 81 Now we have all of the information that we need to solve P 2 P uP uh ur h r 1 2 2 100 Pa uP 24525 0 0 0001 4ur 1 2 2 2 95 100 Pa 95 We can report our answer as ur 10 kg m3 10 19 0 4 2500 95 Maximum allowable uncertainty in the fluid density Check the specs on the fluid density Carefully Zero order analysis Scatter in the data due to resolution First Order Uncertainty time dependent processes producing scatter in the measured data Nth order Overall measurement uncertainty instrument calibration information Systematic error will be denoted by B Bias does not vary during repeated measurements and is independent of sample size Random error will be denoted by P Precision We will use the statistical analysis developed in earlier classes to deal with these errors Systematic and Random Uncertainties must be evaluated with the same confidence level 95 to be combined In advanced stage

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