Packing Densty 2

[Cyclefrog]

Is there a table or formula available to calculate the relative packing density of spherical particles based on the particle size? (i.e. What is the density of a cubic foot of lead shot in the various shot sizes?)

 

[CoryPad]

Here is one way to solve this:

1) Establish a reference volume (you chose 1 foot³)

V_ref = 1 foot³ = 0.028 m³

2) Calculate the volume of a unit cell of the spheres with radius r

V_unit = (2[√]2r)³

3) Calculate the actual volume of spheres

V_sphere = 0.74 V_unit

4) Calculate mass of spheres

m_sphere = [ρ]_mat V_sphere

where [ρ]_mat = mass density of sphere material

5) Calculate reference density

[ρ]_ref = m_sphere [÷] V_ref


Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[unclesyd]

There is whole field (packing of materials) of mathematics based on your question.

I did have some information on the apparent density of iron, steel, and lead shot of the same size, big point. I'll look for it. It was for working with radiation shielding.
I've seen articles on the apparent packing density of iron and lead shot in gun and reloading magazines.

 

[GregLocock]

Are you talking about randomly packed spheres or carefully packed ones?

Are you talking about a mixture of different sizes, or just one size?

Is the size of the sphere significant in comparison with the size of the container?

Is elasticity important?

The direct answer to your initial query is that the packing density is invariant with the size of the sphere in the simplest case.

Cheers

Greg Locock

 

[Cyclefrog]

Thanks Cory, Syd & Greg.

The spheres are commercial lead shot, the application is ballasting a boat. The shot is poured randomly into the keel and bilge area, then stabilized with polyester resin.
Several years ago I weighed 2.5 quarts of the stuff we had on hand at the time, and calculated a density of 440 pounds per cubic foot.

Having seen some other published numbers for the density of generic lead shot, I'd like to be able to do a reality check on the various numbers to see which are likely to be the most correct.

(For anybody out there who needs to ballast something, check out the copper jacketed bullet scrap from ammo manufacturers. It weighs in at 400 pounds per cu ft.)

 

[Metalguy]

You'll get a denser ballast if you mix different shot sizes. The small ones fill in the gaps.

 

[GregLocock]

I find figures of around 64% for randomly packed hard identical spheres (with no bridging), and 77.8% for the best possible arrangement.

The worst is 5.5% but I have no idea how they define that!

http://mathworld.wolfram.com/SpherePacking.html

for more references than you can shake a stick at.



Cheers

Greg Locock

 

[Sparweb]

Mathworld: wow

(Thanks for the link)

Steven Fahey, CET
"Simplicate, and add more lightness" - Bill Stout