I’m studying for the Environmental FE. I noticed there are 2 different equations to chose from when calculating head loss through a packed bed filtration medium: the Rose Equation and the Carmen-Kozeny equation. Using the same starting information, I was able to use both to get close enough to the correct answer in the multiple choice options. In the future, could there be situations where it’s better to use one over the other?

I noticed that using the Rose equation involves choosing a drag coefficient based on the Reynolds number, which seems less precise than calculating a friction factor to use in the C-K method. Does it ever make a big difference?