[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 342
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If n=3, the formula is the same, if n=5, it is different, and if n=20, it is quite different :)
Surely there are engineering packages in which such problems are solved practically.
P.S. Try to come up with an optimal configuration for 8 circles.
P.P.S. Strange thing. I've posted it in the beginning, when Richie's post wasn't there. After editing it, it appeared before mine. And it's not the first time it's happened.
Зачод, TheXpert. Next:
Плоская выпуклая фигура ограничена отрезками AB и AC и дугой BC некоторой окружности.
Постройте какую-нибудь прямую, которая делит пополам:
а) периметр этой фигуры;
б) ее площадь.
P.S. Вероятно, предполагается, что АВ != АС.
It is easier to calculate the angle and divide it in half!!!!And immediately, please, a proof that the areas will be equal.
Здравствуйте!
Тут как то по работе пришлось попутно решать такую геометрическую задачу: есть труба или гильза диаметром D в которой нужно проложить кабели диаметром d в количестве n штук, причем должен соблюдаться зазор (дельта) между трубой (гильзой) и ближайшим кабелем. Никак не могу составить формулу или ряд по которым в исходных данных прописываю d, n, дельта - а на выходе D
Так чтобы диаметр трубы (гильзы) был минимален.
I think there's also a condition on how long your pipe or sleeve is???The problem strongly depends on n, because there are different packages of circles.
If n=3, the formula is the same, if n=5, it is different, and if n=20, it is quite different :)
Surely there are engineering packages where such problems are solved practically.
Exactly, different formulas. By the way, not all cables are round, there are cables with e.g. oval shape. If we're talking about power cables with big cross-section (diameter over 30 mm), they are usually placed each in its own pipe.
Besides, a distance of several times the diameter of the cables themselves has to be kept between power cables as it is necessary for their cooling.
One more thing. The diameter of the pipe must not only depend on the diameter of the cable bundle, but also on the length of the pipe. The longer the pipe, the larger the diameter,
otherwise the bundle just won't fit. The stiffness of the cables must also be taken into account. Armoured cables and single-wire cables are more rigid.
-
Unfortunately there are no engineering packages for such calculations yet.
Здравствуйте!
Тут как то по работе пришлось попутно решать такую геометрическую задачу: есть труба или гильза диаметром D в которой нужно проложить кабели диаметром d в количестве n штук, причем должен соблюдаться зазор (дельта) между трубой (гильзой) и ближайшим кабелем. Никак не могу составить формулу или ряд по которым в исходных данных прописываю d, n, дельта - а на выходе D
Так чтобы диаметр трубы (гильзы) был минимален.
That won't do the trick?First get the inner liner area yourself, but including the gap
then divide by D^2
get the number n
The same applies vice versa, so you get the area and diameter of the thermowell, including the clearance.
D diameter of one conductor
the bigger n is, the more accurate the answer is
The problem is not calculating the diameter of the beam. The problem is how to make up a general formula - for any n.
P.S. I strongly doubt that even the "pure" problem is solved in general form: to find such a packing of circles of equal diameter, at which the large circle covering it has minimal area (or minimal diameter).
It won't work. Richie, you yourself wrote that the cables have to be cooled, the length of the pipe has to be taken into account, etc. It will be a typical problem with dozens of data, not directly related to the geometry of the "pure" problem. And the real solution will be taken by eye, with a margin. And all this pure mathematics will be of no use to anyone.
Yeah. I used to write a program like that. There was also a calculation of friction resistance, so cables could be pulled through the pipes. But that was in a past life, this life is my other speciality. So, qwerty1235813 don't make your life harder - take one cable per pipe.
By the way, the diameter of the bundle, if anyone doesn't know, depends on the pitch of the bundle. A twisted bundle has a larger diameter.