Presets
Playback
Glass and grains
Narrow the neck below 3 grain diameters to see the flow jam.
Layers
Model checks
The science
Why the hourglass runs at a constant rate
In a liquid the outflow speed grows with the head of liquid above the hole (Torricelli, v = √(2 g h)). In a granular column the grains arch against the walls and the pressure saturates at the bottom (Janssen effect), so the flow through the neck does not depend on the sand height and the hourglass keeps time. The empirical Beverloo law gives the mass flow W = C ρb √g (D - k d)5/2 for a round hole in 3D and (D - k d)3/2 per unit width for a slot, with C about 0.6 and k about 1.4 for round grains; k d is the empty annulus at the orifice edge.
The discrete model
Each grain is a spinning disc. Overlapping grains repel with a spring-dashpot normal force Fn = k δ - c vn (the damping sets the restitution), and the tangential friction force is capped by μ Fn (Coulomb). Units are the grain diameter and g, so 1 time unit is √(d/g): 10 ms for 1 mm grains. Below about 3 grain diameters stable arches form and the flow stops.
Honest simplifications: 2D discs instead of 3D spheres (so the exponent is 3/2, not 5/2 as in a real round neck), a few hundred grains with no cohesion, humidity, air drag or electrostatics, and a playback slowed by 30 to 100 times; real hourglass sand is polydisperse.
What to try
- Fine sand preset: the counter graph is a straight line, so the rate does not depend on sand height.
- Wide neck preset: faster flow, following (D - 1.4 d) to the power 1.5.
- Narrow neck (3 d): arches form and the flow stops.
- Raise friction: the pile below gets steeper.