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Format for lab reports-lab1

# Format for lab reports-lab1 - FLUID STATICS Derivation for...

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FLUID STATICS Derivation for Propagation of uncertainty for FULLY SUBMERGED case: ) ( 3 2 d L L y R - - = …………………………………………………………………… (1) A l d A l d A l d d F R ) 2 ( 2 ) ( 2 )] ( [ - = - + - - = γ γ γ …………………………………….. (2) R F WL L 1 2 = …………………………………………………………………………….. (3) Substituting Eq.(2) and Eq.(3) in to in Eq.(1) ) ( ) 2 ( 2 3 1 d L A l d WL y R - - - = γ …………………………………………………………… (4) Using the equation for propagation of uncertainty in L 1 , L 3 and d into y R : 2 2 2 3 2 3 2 1 2 1 2 ) ( ) ( ) ( ) ( ) ( ) ( ) ( dd d y dL L y dL L y dy R R R R + + = ……………………………….. (5) Taking the partial derivative of Eq.(4) and substituting in Eq.(5) gives: 2 2 1 2 3 2 2 1 2 1 ) 2 ( 1 4 ) ( ) 1 ( ) ( ) 2 ( 2 ) ( + - - + - + - = l d A WL dL dL A l d W dy R γ γ ……………… (6) 1

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Fluid Statics Calculation Four types of Errors are calculated from spreadsheet Actual Error Actual absolute error (theoretical – experimental) Actual relative error ([theoretical-experimental]/theoretical) Propagated Error Propagated absolute error ( R dy ) – error due to uncertainties in measurements Propagated relative error ( R dy / (exp) R y ) – relative error due to uncertainties in measurements ANALYSIS: Do the analysis for partially submerged and fully submerged cases separately. OBJECTIVE 1 • Is equation for Y R accurate? • Use your engineering judgment to determine what is mean by accurate ( error <10% ?) • Use ACTUAL ERROR for analysis NOTE: Do Not Average Errors- Give Ranges of Errors for both Partially and Fully Submerged Cases. OBJECTIVE 2 • Does uncertainty account for inaccuracies found in objective 1? • Plot Y R vs d with error bars R dy 2 ± or 2 ± standard deviations • Is theoretical line within error bars? • Compare actual error with propagated error. If actual error is LESS than Propagated Error means uncertainty explains inaccuracies. If actual error is GREATER than Propagated Error means uncertainty does NOT explain inaccuracies. Look at plot also.
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