I am trying to determine how sensitive the Ergun equation is to error when using experimentally calculated values. The velocity of the fluid through a loosely packed bed was adjusted and the bed height and pressure drop were measured. The voidage was then calculated and using these values the Pressure drop per unit bed length was calculated. I need to determine how sensitive the Ergun equation is too error. How do I calculate the error for each variable and the total uncertainty with the final pressure drop value?
The error for each variable is half of the smallest scaling division. However, for the whole result, you have to obtain it step by step based on the four basic math operations.
if z = a + b or z = a - b:
dz = sqrt((da^2)+(db^2))
if z = ab:
dz = sqrt((b^2(da)^2) + (a^2(db)^2))
However, if z = a^n:
(dz)/z = n* (da)/a
if z = Ln(a):
d(z) = d(a)/a
Dear Cameorn Jones
this site can help you.
https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Quantifying_Nature/Significant_Digits/Propagation_of_Error
Follow the standard procedure and examples provided in textbooks such as:
Design and Analysis of Experiments, 10th Edition
Douglas C. Montgomery
ISBN: 978-1-119-49244-3
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