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Assessment of Uncertainty and Sensitivity Analysis in Pipe Material Evaluation

Question:

The company you work for (Pipes and Tubing for All, PTFA) has tasked you with assessing the characteristics of the latest piping material that has come out of the R&D labs under the code name “Poly-Uber-Oxyside (PUO)”. To do that you need to evaluate the friction factor (f) and the Reynolds number (Re) of water flowing through a segment of PUO pipe of known length (L). The standardised test set-up (Figure 1) that has been approved by your QA department consists of a known section (L) of tubing, a flowmeter, a variable speed pump and a pressure monitor.

Using the Taylor Series Method (TSM) for uncertainty propagation, determine the expanded uncertainty of the result both for the calculation of the friction factor (f) and the calculation of the Reynolds number (Re). Discuss and justify your assumptions.

Using the Monte Carlo Method (MCM) for uncertainty propagation, determine the expanded uncertainty of the result both for the calculation of the friction factor (f) and the calculation of the Reynolds number (Re). Discuss and justify your assumptions.

Using appropriate graphs, prove that your calculation of the expanded uncertainty has  converged.

Did the values for the expanded uncertainties calculated in (Q1) differ from those calculated in (Q2)? If so, explain why this may be the case. Prove your hypothesis/justification by presenting an appropriate MCM simulation.

Your company is considering refurbishing your QA laboratories and wishes to prioritise expenditure in purchasing high-fidelity equipment for the measurement of the variables with the largest impact on the determination of the friction factor (f) and the Reynolds number (Re). For this question only (i.e. all of question 4), assume that all variables follow a uniform distribution. Perform a Sensitivity Analysis using the Elementary Effects Method for each of the two equations, assuming a range of variation of 50% around the nominal value.

Apply the Elementary Effects Method using the original sampling strategy proposed by Morris [1] and justify/prove convergence [15 marks]

Apply the Elementary Effects Method using a latin hypercube sampling strategy and justify/prove convergence [20 marks]

Apply the Elementary Effects Method using a low discrepancy sequence for sampling and justify/prove convergence [15 marks]

Discuss any limitations of the EET method you have discovered during its implementation and what steps you have taken to alleviate those limitations.

Recommend the priority in which expenditure should be distributed in order to ensure that the best equipment is purchased for the most impactful variables. Justify you answer based on your results from steps (3a, 3b and 3c) and discuss the most appropriate choice of sampling strategy in the context of the present example.