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HW-4_solutions

# HW-4_solutions - PROBLEM 5.6 KNOWN Analog Tachometer...

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PROBLEM 5.6 KNOWN: Analog Tachometer Resolution: 5 rpm Accuracy: within 1% reading FIND: u d at 10, 500, 5000 rpm SOLUTION The design-stage uncertainty is 22 1 / 2 () do c uu u + where u o = ± 2.5 rpm u c = 1% of reading This yields speed u c u o u d [rpm] [rpm] [rpm] [rpm] 10 0.1 2.5 ± 2.5 500 5 2.5 ± 5.6 5000 50 2.5 ± 50 The uncertainty increases with rotational speed. At low speeds it is dominated by the ability to read the tachometer (resolution). At higher speeds the instrument errors dominate. COMMENT The statement "accuracy" is a manufacturer catch-all term that is rarely clearly defined. The "accuracy" statement is presumed to mean that the overall errors do not exceed 1%. We suspect the term to describe the combined effects of all known elemental errors. This misnomer causes confusion. Insist on a detailed description.

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PROBLEM 5.8 KNOWN: Temperature sensor Error limit: ± 0.5 o C Readout Device Resolution: 0.1 o C Accuracy: 0.6 o C FIND: u d SOLUTION The design-stage uncertainty is for the combined system is 22 1 / 2 [( ) ( ) ] dd R d S uuu + where (u d ) R
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HW-4_solutions - PROBLEM 5.6 KNOWN Analog Tachometer...

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