How did hourglass happen? How did they even get the right amount/size of each sand particle/other physical aspects to be aligned with the time?

Question

How did hourglass happen? How did they even get the right amount/size of each sand particle/other physical aspects to be aligned with the time?

In: Physics

Answer 1

I’ve got a related question: do hourglasses run faster over time as the sand inside abrades itself?

Edit: Since this seems unlikely to be answered here, I researched it and found it a bit outside of ELI5 territory. Anyway there is this thing called the Hagen-Beverloo law on the outflow of granular solids that seems to indicate that yes, provided the total mass of the particles and the size of the funnel aperturue remains constant, the hourglass will speed up if the diameter of the grains were assumed to decrease over time due to wear. Specifically given `d.I` and `d.F` representing initial and final grain diameter and `a` the funnel aperture size, the ratio of total time will change by `T(d.I)/T(d.F) = (a-d.I / a-d.F)^(2/5)` leading to the conclusion, that as seems to be intuitive, the hourglass will speed up if the sand was able to wear itself down and become smaller or alternatively to wear the aperture to become larger.

Anyone with kids: this would be a solid science fair project.