Uncertainty Analyses
A detailed analysis regarding the uncertainties within the equipment, measurements and results is carried out, which cumulatively is 8.90% with 95% confidence level, According to Kline and McClintock [19] the total uncertainty propagation for \(r=f(v_{j=1\ldots n})\) is summarized in eqn. 1 which is commonly used in calculating the related uncertainties in any experiment.
\(u\left(r\right)=\sqrt{\sum_{j=1}^{n}{[\frac{\partial r}{{\partial v}_{j}}u(v_{j})]}^{2}}\ldots\ldots\ldots(1)\)
Here, u stands for the standard uncertainty, which is equivalent to the standard deviation, and vj stands for the variables that contribute to the uncertainty in the result r that revolves around any data reduction equation. Thus finally, the relative uncertainties for h can be cumulatively expressed as in