That's what I have exemplified ad noseum.
However identifying what bamboo means.
Per say: approximate/discretize a PDF ... explicit result.
Pretty easy to explicit sin(30)= rad/°
Engineers manage well non SI projects.
Units war lasted years in Mathsoft Collaboratory.
Typical trig functions are approximated in rad.
What is the SI of Bessel ?

The argument of the Bessel and other special functions is dimensionless, so it is the SI constant one. And the result of the Bessel and the other special functions are dimensionless too. That's the answer to you question.

But ... where do you find a physical, chemical, or any real world problem where the solution is y = Bessel(x) ? Excepting cases where x and y are angles, you will never go to get that. There are many, many examples where the solution is in the form y = A*Bessel(k*x) or lineal combinations of such solutions, where A have the units for the variable y, and k have the inverse of the units of x.

For a simple example, a mechanical oscillation could be y = A*sin(ω*t), with y and A in mm and t in sec and ω in Hz. More or less the same for the current in an electrical circuit if I = Io*sin(ω*t+φ)

That is the correct way in which millions of scientists, technicians, engineers and workers have been doing things for thousands of years: working with magnitudes and their units. This collection standards came from the ancient Egypt: https://upload.wikimedia...egyptiennes-img_2748.jpg

If you know how, all mathematical functions can be manipulated with their corresponding units, when dealing with real world problems. So please stop confusing users with arguments that border on flat earthing.

Best regards.
Alvaro.

What will be your next 'ad hominem" request, SI version for Pythagorean Theorem?
You know, it is originally a mathematical function but it can have units.
There are a lot of fitted projects were done with SI unit, want some examples?

A unit Bessel function is as just Razonar said, A x Bessel(x). Which A is a unit or unitless number.

My guess is that they made their quick calculations in sand, if they were worth it they took them to papyrus, but that those instruments were for the workers who used them in construction sites and workshops, such as looms, blacksmiths and ceramics.

Keeping those units can be very important. For example, although Eratosthenes in the III century BC said that the earth circumference is about 160,000 stadium, it is not clear whether he was referring to Greek or Egyptian stadium, which were slightly different.

Ancient data about the extension of forests or crops, sea levels, percentage of species in ecosystems can be very useful today, to address sustainable irrigation systems, as well as design the best canal layout. But if we don't know the pattern of the drives they used, the data loses much of its usefulness.

Best regards
Alvaro

I find Jean's unitless calculations very very elegant and fascinating (at least for the little that I can understand) and I am not annoyed by his bittersweet/ironic remarks here and there. We don't need to be dogmatic, or to be arbiters of taste... Everything that works, and is understandable, is good, very good! And the diversity of calculation styles that Smath Studio enables and that the creative community is pushing beyond its expected limits, are great features of this software and this forum, and its brilliant users!

My CAD drawings are in mm unit, but I draft on a feet-inches grid, with "snap" on. Because everyone here thinks in feet, not metre. But steel fabrication is in mm. So I use mm as the implied unit for drafting but my dimensions are in feet-inches for the client to understand the dimensions of his building, in mm for detailed fabrication, and in m for structural dimensions which I feed into my excel sheets (and since more recently, in Smath Studio). Because in structural calculations, having all these 12 and 144 factors all over the place is really a pain

Problem is, his calculations are hard to read. Harder to understand, illogical to revise since they are bound to certain units.
Everything is everywhere, they are color racket and there is no heuristical walkthrough in his samples.
There are even some converting numbers, strain you to understand where they come from
Which those convert numbers would be redundant if he bothered to use embedded units.
Those numbers doesn't look not very elegant on page, and not knowing where they come from at first glance is not fascinating.
And sometimes that numbers tend to make serious mistakes, like that kW/hr pump power calculation of his.
Not even a typo, he divided 1hr (3600s) to g.e (9.8), found 367 and used it in that abomination.
I have never seen that kW/hr usage anywhere, but interestingly his pump power results have it.
It should even be kW, not even kW*hr. What will be benefit of pump electrical consumption calculation?


Real problem is, some of his engineering calculations, especially unitless ones, have some serious mistakes.
Most of his viscosity related calculations are wrong due to his lack and denial of unit usage.
If he bothered and learned how to use units, he would see engineering is not just operations on given numbers.
Units and their relations are also very important to obtain correct answer at the end of some calculations.


We wouldn't, unless he didn't propagate new users about his ridiculousness.
He wrongly claim SI units are not for engineering calculations.
I don't know what the hell this statement means, everyone in the world uses SI now.
He can use whatever he want, I personally won't care. He is a lost case.
But encouraging new users (also possibly young students) non-scientific, incorrect and illogical ways is unacceptable.


Imperial units are defined by metric (SI) units nowadays. That's what he meant.
For example, take an inch. An inch is now defined by its metric equivalent. 1 inch equals 25.4mm, nothing else.
No platinum-iridium bar used to define an inch, feet, etc now. Imperial units are based on metric units now.
Same can be said for weight definitions of imperial units or any other distinct units.
By the way, every SI unit has now abandoned man-made artifacts to define them.

https://www.youtube.com/watch?v=SmSJXC6_qQ8
https://www.youtube.com/watch?v=hid7EJkwDNk


All units you wrote are actually SI units. So we are saying the same thing. Using SI units will prone to less errors.
And conversions like that can be done when it is negligible, but it doesn't mean it is correct for every scenario.
It may be usable on earth, when you are going to use that conversion earth off-surface, it will definitely be wrong.


This is because of negligibleness when practical calculation usage is enough.
When simplification of certain functions to a certain degree won't effect the result that much, it can be done.
If you are not writing a scientific paper about stress block, there is no need to include every aspect or dimension to it.
A simplified function won't be totally wrong, it will be "correct enough".


Well, we do. He makes serious mistakes and doesn't accept his failure in almost all cases.
Yet he mock requests, questions, samples, replies, try to hijack peoples topics, spam forum with same answers.
There are 10 page result if you search Colebrook, this is just ridiculous.
He once replied a question with four identical ensuing answer. Not a polite behavior.

Sorry for wall of text, Regards.

Yes, that is exactly what I meant. Definition for imperial measurements no longer exists outside of SI units. Where imperial measurements are provided they are 'SI units converted to imperial using their SI definition'.


Like all sweeping generalizations, this is almost certainly wrong.


I can say with a large amount of certainty that NASA, Roscosmos, SpaceX, RocketLab etc could not get away with that rounding. Perhaps it is just that they are not brilliant engineers?

Here is how dumb-ass maintaining support for imperial is... these two connectors look the same but are incompatible (5mm pitch versus 5.08mm pitch). The outside pins on the imperial compatible (0.2" ) part are 1.2mm further apart.

Connectors with less poles can kind-of work...


This type of thing looks like an industrial (process control even...) accident waiting to happen

Edited by user 22 April 2022 01:52:09(UTC)  | Reason: Not specified

Possibly your "Elephants" are just scrambled-unitless-wrong calculations.
NIST data is not the culprit here presumably, your way of designing is defective.

I don't have defective design.
In fact, your calculations are faulty.
You are not in position to correct someone.
Go correct your pump power calculations first!
Also don't use dynamic viscosity in your formulas.
You should use kinematic viscosity.

https://en.smath.com/forum/yaf_postst7480_Colebrook-Pipe-Data.aspx