Hello, Jean.

Thank you for this sample! Just a small hint: if you do not want (for any reason) to use units in your calculations you can still use real units in results - just specify output units and use Ignore units item in region's context menu.



Best regards!

Thanks Mike,

Very interesting your Colebrook iterative solver. In that kind of stuff,
"accuracy" does not mean much. Pumps/motors are 15 % oversised by practice.
Next, to complete the tour: valve sizing [hope Smath will like it as well].
It's the plot that takes time. Smath solve block is much faster than the
user iterative. "solve" is built-in < 0.1 sec.

Thanks Kamarad Mike. I think "Spoutnik" means "Companion" ?

I got familiarised with Russian 50 years ago ... all gone !
My GrandKids are acustomed to visit friends from Russia.

Just reposted the "Colebrook Project"

Jean

In the range tested [...Re 10^6]
Haaland leading coefficient 1.7935
Swamee leading coefficient 0.249
They are all interesting for pocket calculators. Colebrook solves iteratively Torricelli law.
In 3 terms it solves for the 3 variates ε, D, R. There are physical boundary conditions,
otherwise Colebrook is the golden bullet. The 19 approximations are reverse engineering by approximtion of Colebrook.

Jean

Inst_Colebrook_Haaland.sm (199kb) downloaded 50 time(s).

You seem to ignore what you are told.

Assigning "Colebrook:=line(...)", and measuring the time that this assignment took, ISN'T productive. SMath DOESN'T do actual calculations at this point. It only stores the formula, to be used later. Only when you USE the previously-created "Colebrook" variable somewhere (e.g., by plotting, or by taking nth member), SMath does actually grinds numbers, and takes its time! Only then may you actually measure its performance.

And BTW, what is that "Torricelli's law" that Colebrook solves??? (Hint: Torricelli idealized the flow, ignoring the friction.)

Edited by user 03 April 2016 05:36:27(UTC)  | Reason: Not specified

Well, then.
Colebrook formula does not solve any law. It is empirical formula that approximates experimental data that Colebrook and others were gathering in 1930s, working with pipes having real roughness. His formula gives Darcy factor to empirical Darcy-Weisbach formula.

In 1920s-1930s, Nikuradze, while working at Prandtl's laboratory and experimenting with pipes with artificial roughness, made his semi-empirical formulas for turbulent flow: one for smooth walls, other for rough walls. His smooth-walls formula was implicit, and differed from theoretical logarithmic law formula by its coefficients (to better match experimental data; thus semi-empirical).
Later, Colebrook and others had conducted a number of experiments to find out if the Nikuradze formulas hold true for real-life rough pipes, i.e. if artifical roughness is adequate model for real roughness.
It turned out that the relation holds only approximately, real data being more smooth in transitional region. So, Colebrook took Nikuradze's approach to create his own formula, that would combine both of Nikuradze's formulas in one, and to select coefficients that would better approximate real pipes experimental data.
His formula isn't particularily precise, and substantially overestimates real Darcy factor for transitional region. But traditionally, it is used as reference in this area.

Torricelli, on the other side, didn't deal with duct flow, but rather studied discharge through nozzles. He ignored friction (that is essential for Colebrook) completely.

So, bottom line is, they have nothing in common, except both relate to hydraulics.

Wrt timing. Unfortunately, I cannot tell if solve() efficiency has improved. My computer with last SMath (5935) takes 2.4 min. to process your Moody chart implementation, that's less than your 6.1 min. But taking into account that you have rather slow laptop, this doesn't say much, because we have incomparable hardwares. Anyway, in his release notes, Andrey didn't tell anything about solve() speed-up...

Edited by user 03 April 2016 10:02:53(UTC)  | Reason: Not specified

Oh! I suppose it's Idelchik's reference book (I.E.Idelchik is its author). There hydraulic resistances (both from pipes and local - such as fittings) were given very precise formulations. Its second edition went in 1975, and third in 1992. Unfortunately, I don't have it in other languages, but Russian. I agree, that's really fundamental work!