Re: Weighing Freight Car Models with Liquid Gravity
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“Of course, if you have a range of sizes of spheres, the little ones pack between the big ones. But if they are all the same size, using smaller ones changes nothing.”
I may not be reading this the way you intended, so apologies in advance if that is the case. Not quite correct or true to my understanding and experience:
The first part of the statement is true - smaller particles fill the interstitial space. Assume we are talking about a homogenous material – meaning it’s either all Lead spheres or all Tungsten spheres and for purposes of clarity spheres means a round if not uniformly so (i.e. not a perfect sphere) particle geometry.
So, using a range of particle sizes that includes what we may term shot or powder, because, as you state, the little ones pack between the big ones, will increase the mass (weight) contained inside the identical volumetric space (cavity). To be clear, if one fills the cavity with Lead shot and then adds Lead powder to fill the spaces, the mass (weight) of the loaded cavity will increase.
For the second part of the statement; If one has two identical cavities and fills one volume with Lead shot and the other with Lead powder, the cavity filled with Lead powder will have more mass than the one filled with shot. Why? The smaller the particle, the higher the surface area and among homogenous material, the smaller the interstitial spacing – all to say there is more mass of powder in the cavity than mass of shot in the other cavity.
Back in my day when working with metal powders of varying particle size, the key physical property that applies here was tap density and there was/is an ASTM standard to quantify this material property. Similar to specific gravity, tap density is a measurement of mass per unit volume. The smaller the particle size, the greater the tap density and the closer this value approaches the theoretical density or specific gravity of the material.
So in both cases, using powder to fill the space between shot or using a uniform small particle size powder, will increase the mass – weight- of that part. And if the cavity is filled with a 2 micron average diameter particle size powder rather than a 15 micron average diameter particle size powder, the mass of the part will be greater as well.
Again, if I misunderstand your statement, apologies. Now, my head hurts from digging back more than 20 years in memories, so with permission I’ll go back to modeling freight cars.
From: main@RealSTMFC.groups.io [mailto:main@RealSTMFC.groups.io] On Behalf Of Tony Thompson
Sent: Tuesday, October 30, 2018 8:11 PM
Subject: Re: [RealSTMFC] Weighing Freight Car Models with Liquid Gravity
Dave Parker via Groups.Io wrote:
Or to put it another way, the proportion of space occupied by spheres, even in the closest packing, is independent of the size of the spheres.
Of course, if you have a range of sizes of spheres, the little ones pack between the big ones. But if they are all the same size, using smaller ones changes nothing.
Tony Thompson Editor, Signature Press, Berkeley, CA
2906 Forest Ave., Berkeley, CA 94705 www.signaturepress.com
(510) 540-6538; e-mail, tony@...
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