Engineering references that specify formulas with variables with specified units, instead of constants with defined units, are a travesty.
I refer to Crane Technical Paper 410 in this instance.
Why would I want
ΔP = 32000 μ L v/d^2 (for laminar flow)
You’d expect this to be a normal formula, which you do your own dimensional analysis, but no. Units are specified. But not even on the same page, no no, on a “nomenclature” page you have to know to look for.
ΔP in Pa
μ in cP
L in m
v in m/s
d in mm
When I could have
ΔP=32 μ L v/D²
and YOU use whatever units you want.
Hell I could even put imperial units in here if I were a masochist. Very upsetting.
Engineering textbooks/technical papers need to find Pure Math Jesus.
Formulas with hidden units? Not even once.
Crane TP 410. How could you?
I think it’s because in the more practical applications variables are presented with units which were actually measured, because translating them would introduce inaccuracies. And then formulas are adjusted so that you just “plug everything in and it works”
I thank you for your engagement. If you’ll indulge me further, please read on. The units you’ve measured in are irrelevant. We live in the same universe, and units are perfectly interchangeable (though, some systems are more internally consistent than others…)
This is a solved problem, may I introduce: constants.
PV=znRT is most certainly a formula derived from experiments.
R, is the gas constant, it’s a value with units :O
(For example 8.314 m3⋅Pa⋅K−1⋅mol−1)
(Many, many constants in formulas have units. It’s just engineers being weirdos specifying variable units instead)
My point is to stop making me look up the units on a different page. Variables should not have specified units. It’s never necessary (possibly some edge case I haven’t considered?)
Constants should have specified units.
Translating them into a constant introduces no inaccuracies, it’s just multiplication.
I could be a weirdo and say P⋅V=z⋅n⋅8.314⋅T and make you look up on another page what the units are (grumble), oooor you could just specify your constant units so that the user can either convert their units to something suitable for the constant, or more easily convert the constant into the units they want. Forcing the user to first derive the constant by referring to another page is frustrating.
That’s how the gas law equation (from above) works. The gas constant has units, and you can quickly look up whichever variation to want to save time, or convert it yourself if you’re using a particular set of units all the time that’s not common enough to be on the Wikipedia list.
For the gas law, this formula is super basic, so many know it like the back of their hand. But in engineering there are all sorts of approximations out there with all sorts of complicated equation forms that you need to keep referring back to.
Just give me the constant with units, gaddamn.
My gripe from the the original post exemplifies this. The Crane TP 410 has a factor of 32000 because of the units being baked in. And for what?
I know I’m onto something here because I have anecdotal evidence it confuses people. The calculation template my company uses for pump sizing was doing some bizarre conversion first into imperial, then into metric, all because they must have thought they had to use the formula as written (they had used a different version of the reference I was talking about, written in imperial units).
Sooooooo dumb, because in this case, the constant is dimensionless. The constant is just 32. The formula should be written the same, regardless of imperial or metric units, but it isn’t.
We don’t need two formulas for two different sets of units. Formula should remain exactly the same, only the constant should change.
And when the constant is dimensionless, even more so.
Thanks for coming to my TED Talk :)