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In a hourglass, does the sand flow through the neck depend on the amount of sand in the upper glass? If we consider a sand flow analogous to fluid flow, then it should depend linearly, but in that case amount of sand to represent the given time would rise squared depending on time?

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Actually, in the case of a fluid, I think the flow rate would vary as the square root of the fluid height, but it also depends on the flow regime. – Alan Rominger Oct 17 '11 at 13:47
@Zassounotsukushi : I thought the flow rate depend linearly on the water height in case of the fluid. – mbaitoff Oct 17 '11 at 18:59
If there is one thing you can't do is compare the sand to fluid. Sand might get stuck in a sharp slopes which fluid will flow easily. There is a whole engineering field about this topic. – Yotam Oct 17 '11 at 19:14
up vote 4 down vote accepted

Fluid approximations do not work well at the scale of sand in hourglasses for most hourglasses. Almost all of the sand is statically braced against the walls and floor of the hourglass. Instead, you have a small region of instability above the hole where it is not possible for the sand to be braced; as that unstable portion falls through the hole, more falls in from above. There is slow flow of sand downwards, but it's still mostly statically braced. Thus, to a first approximation, flow rates are determined by grain size and shape (and material), and the immediate geometry around the hole (predominantly the size).

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The flow I observed is on the surface to the center (like sand down the leeward side of a dune) and then in some way through the center. This friction controlled stream at the center I'd like to see. :=) Is it straight down, or meandering? +1 – Georg Oct 17 '11 at 18:13

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