If you want to get into how things scale, this is essential. You might have heard someone say "the real equation is dimensionless". Well there's something to it.
There's a bunch of flow related stuff that ends up being all about dimensional analysis. Basically, things aren't as simple as multiplying all the quantities by a constant.
Probably the one everybody's heard of is "what would happen if animal X were bigger/smaller" -> weight goes up ^3, but cross section of legs ^2. Heat escapes ^2 but is generated ^3.
In a lecture on scaling laws, a professor once explained that an early study of LSD gave the drug to elephants with doses based of relative heights of elephants compared to humans. The elephants died from the overdose. Scaling a dose based on height was inappropriate.
Back in the 90s, I (and many people) believed that when the Internet gave everyone instant access to all the world's information, urban legends would die out because it would be so easy to fact check things and surely nobody would spare a few minutes of research to avoid propagating a half-truth. Alas, this theory didn't fully account for human nature.
TLDR: it's uncertain if the elephant died from the LSD or from the massive amounts of thorazine and barbiturate that were injected into his ear in an attempt to counteract the effects of the LSD overdose.
The Buckingham pi theorem typically doesn't tell you which scaling laws are valid, just how many of them there are consistent with the variables you believe are involved with the problem.
The Froude number appears to be a dimensionless parameter. Dimensionless parameters and the Buckingham Pi Theorem are fundamental to physics, and especially fluid flow. It boils (ha!) down to the ideas that 1) A fundamental law of physics must have consistent units, and 2) Dimensionless quantities function as similarity parameters. The Reynolds Number is arguably the most famous of these (alright, Mach number <sighs>), the ratio of inertial to viscous forces in a fluid flow. ("How much like water divided by how much like honey" is a pretty good heuristic.) You can actually derive fundamental physical laws through dimensional analysis. Powerful stuff. One could do far worse than tracking down as much as one can about these principles as early in one’s engineering or scientific career as possible. It’s as big a shortcut in the hard sciences as Latin is for medicine.
If you want to get into how things scale, this is essential. You might have heard someone say "the real equation is dimensionless". Well there's something to it.
There's a bunch of flow related stuff that ends up being all about dimensional analysis. Basically, things aren't as simple as multiplying all the quantities by a constant.
Probably the one everybody's heard of is "what would happen if animal X were bigger/smaller" -> weight goes up ^3, but cross section of legs ^2. Heat escapes ^2 but is generated ^3.