Basic geometry question

[Glyn DaviesParticipant @glyndavies49417]

Hi there,

 

Had a touch of brain fade today and I wonder if anyone can help.

 

I have a cylinder 52mm diameter by 170mm tall. I want to fill it with 4.76mm diameter ball bearings. How do I calculate how many bearings I need to buy?

 

Thanks

 

Otley

 

 

[Glyn DaviesParticipant @glyndavies49417]

[Roderick JenkinsParticipant @roderickjenkins93242]

Otley,

 

Vol of cylinder is pi x r^2 x h – 361,078 cubic mm

vol of sphere is 4/3 x pi x r^3 – 56.48 cubic mm

 

divide one by the other gives 6393 balls, BUT

 

Packing density of spheres is about 60% (from wikipedia) so you will only need 3836 balls.

 

Well, that’s my attempt. Are you making canister shot, are you troubled by pirates?

 

cheers,

 

Rod

[Tony MartyrParticipant @tonymartyr14488]

I think that requires more than basic geometry because it depends on the vertical stacking pattern, in that the balls of second and subsequent layers should rest in the space between every four balls below so while you can lay out the number of balls in the 52mm circle the number of rows above before you run out of headroom is a ‘bit tricky’

I suggest the answer is a bag full but someone with a CAD system should work it out.

Tony

[The Merry MillerParticipant @themerrymiller]

Otley,

 

You will find how to get your answer on this website :

 

http://news.sciencemag.org/sciencenow/2011/11/christmas-ornaments-packed-like-.html

 

It ain’t easy as you probably already know.

 

 

Len. P.

 

 

 

 

[Jim GreetheadParticipant @jimgreethead]

Buy 6000, sell the rest on eBay and get your money back.

 

Jim

 

[NJHParticipant @njh]

Hi Otley

 

What on earth were you doing that made you pose that question?

Regards

Norman

[BazyleParticipant @bazyle]

Why is this being performed at such low temperature that the balls have shrunk from their room temp size of 4.7625mm? And won’t it be rather dangerous putting them into the red hot tube?

[SpringbokParticipant @springbok]

Unless you are trying to reinact the pirates of the carribean purchase your cylinder 52mm diameter by 170mm tall and bearings drop them in one by one counting as you go easy, it is like the question how many jelly beans are in this jar, depends on how you shake it and how they settle.

Like NJH why may I ask what are you doing to ask this question.

Bob.

 

 

[Terry LaneParticipant @terrylane]

Yeah, well now that we are all curious ……. WHY??????

[David ColwillParticipant @davidcolwill19261]

Some kind of mini fractionating column?

[SpringbokParticipant @springbok]

As there is only 7 posts is this is only a spoof.

[David Clark 13Participant @davidclark13]

Hi There

The thread has been running one day, how many posts would you expect?

regards David

 

 

[Martin WParticipant @martinw]

David

 

I think Springbok was referring to the number of posts by the originator ‘Otley’ rather than the number of replies from members.

 

I must admit it is a strange question for a model engineering site .

 

Cheers

 

Martin

Edited By Martin W on 11/01/2012 11:35:53

[Glyn DaviesParticipant @glyndavies49417]

Hi there,

My question is an honest one – why would it be a spoof? Many thanks to those who troubled to reply. I have bought a small dive compressor that I intend to use for filling dive cylinders and also for my ACME patented instantaneous tyre inflator.

The former needs properly filtered air, the latter can make do with just dried air. So the 52 dia x 170 tall filter stack is filled with a combination of silica gel and activated carbon as standard. This has a limited life and is a pain to keep regenerating/renewing. So I thought if I filled the filter canister with stainless ball bearings (£12.50 per K on ebay), the moisture in the compressed air would condense on the balls and give me air dry enough for the tyre inflator. Opening the filter cylinder dump valve and leaving the filter on a radiator for a while should dry it out ready for the next time.

I did the calcs based on 100% packing density assuming firstly 4.76 spheres, then again assuming 4.76 cubes. I was slightly surprised to get figures between 6000 odd and 3000 odd. And I know that 3/16” is actually 4.7625 mm.

I’m concluding now that I’ll stick with the silica and carbon rather than blow £60 on ball bearings to find that it either doesn’t work, or that the pressure drop across the stack damages my filter casing.

Thanks again for the help,

Glyn

[BazyleParticipant @bazyle]

The balls would only condense the moisture if cold enough anyway. You can extend the life of you filter pack with a prefilter of eg sections of cooker hood filter and a condenser made of copper pipe in an ice bath.

It did look rather like a school engineering exam problem to test 3d geometry that had been ‘metrified’ by a lazy teacher. Nice opportunity for a bit of head scratching which I enjoy though some people get worried we are being used for nefarious purposes.

[BazyleParticipant @bazyle]

The balls would only condense the moisture if cold enough anyway. You can extend the life of you filter pack with a prefilter of eg sections of cooker hood filter and a condenser made of copper pipe in an ice bath.

It did look rather like a school engineering exam problem to test 3d geometry that had been ‘metrified’ by a lazy teacher. Nice opportunity for a bit of head scratching which I enjoy though some people get worried we are being used for nefarious purposes.

[NJHParticipant @njh]

Hi Glyn

Well that answers my query – maybe a bit more context to start with would have been valuable.

As far as your ” why would it be a spoof” goes I guess the regular readers of this forum are a bit wary as there have been a few spoofs of late. You will find that folk here are very willing to go a lot of trouble with their replies in the desire to help others. You will understand that they are then none too happy when the query turns out to be specious.

 

Regards

 

Norman

[MICHAEL WILLIAMSParticipant @michaelwilliams41215]

(1)You can remove water at inlet or outlet of a compressor – different methods but many standard ones to choose from .

 

(2) A simple solution would be to use an off the shelf paper cartridge filter and a jet or cyclone condenser as used in garage and spraybooth airlines .

 

Posher versions of basically the same thing are available for pneumatic systems and cabin air systems .

 

MW

 

[Swarf, Mostly!Participant @swarfmostly]

Hi there, Otley,

 

If you’re going to breathe the air from your compressor you shouldn’t second guess the requirements for filtration!

 

Yes, you need to remove any water because it corrodes the interior of your diving cylinders. However, you also need to remove oil – it can cause lung disease.

 

You also need to take care what other vapours/gases are within the reach of the compressor intake – read Jacques Cousteau’s account of their dives at the Fountain of Vaucleuse. (Apologies to any French readers if I haven’t remembered or spelt the names correctly.)

 

If your compressor is specified as suitable for diving/breathing air and assuming that the makers/suppliers are a reputable outfit, I would personally recommend that you stick with their filtration system.

 

Best regards,

Swarf, Mostly,

(British Sub-Aqua Club, 1956-1977, sometime assistant equipment officer, London Branch)

 

 

[Sub MandrelParticipant @submandrel]

Murphy’s law suggests that replacing the proper filter could lead to you forgetting teh ball bearings were there when filling cylinders…

 

To be honest I thought your Model Engineering Club was planning something along the lines of ‘guess the number of beans in the jar’ and you wanted to avoid counting them…

 

Neil

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