If you have a box full of granular material like sand grains and you know the diameter (possibly average) of the particles and the packing fraction (or volume fraction) with which they fill the space (which would be 0.63 for a random packing), does that tell us the density of the granular material (ie. the usual density in terms of kilograms per cubic metre)?
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$\begingroup$ Yes if you know the volume and the weight of the content of the box. $\endgroup$– trulaCommented Jul 24 at 17:12
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$\begingroup$ OK so halving the volume of the sand in the box increases the density of the granular material in there by a factor of $2$? That just seemed a bit counter-intuitive to me for some reason. $\endgroup$– TomCommented Jul 24 at 17:17
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$\begingroup$ So what is the actual equation here to calculate it? $\endgroup$– TomCommented Jul 24 at 17:24
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1 Answer
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If you have the volume and mass, then let our first equation be $$Density={\frac {mass} {volume} }$$ Here,
$$Mass=Mass_{box}+ Mass_{grain}$$
Also
$$Volume_{grain}=packing fraction×Volume_{box}$$
We have calculated the density from 1st equation, Now calculate volume of the grains from the third equation, to obtain density use
$$Density_{grain}= (Packing Fraction × Density_{box}) - {\frac {Mass_{box}}{Volume_{grain}}}$$
Hope it helped. Please upvote if it did.
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$\begingroup$ Oh I see, so basically because of the container you can halve the volume of the granular material without changing the packing fraction and the density of the granular material will be changed? $\endgroup$– TomCommented Jul 24 at 18:15
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$\begingroup$ No, @Tom , if the volume of the granular matter changes wouldn't the packing fraction change considering the entire box? But in both the cases the density would be same. $\endgroup$ Commented Jul 25 at 1:55