An hourglass is a terrible clock. The flow rate of sand through a narrow neck changes with humidity, with the shape of the grains, and with how full the lower bulb is, because the pile changes the pressure at the aperture. Sailors used them anyway, because what they needed was not accuracy but a guarantee: that the sand would run out, and that you could turn it over and watch it do so again.
Inside the neck the grains are in free fall, and the flow rate is set by the aperture and by the pressure difference across it — which is why the flow is not constant as the upper chamber empties, and why the last grains run slowly and unevenly.
In the lower bulb the grains arrive and pile up. Sand has an angle of repose of about thirty-four degrees, and the pile will not hold a steeper slope than that: grains on the surface keep rolling downhill until the slope relaxes. So the heap is a cone with a flat top, and it grows by eating its own sides.
The pile here is a height field: a row of columns across the floor of the bulb, each holding some quantity of sand. When a grain lands it adds to its column, and then the whole row relaxes — any pair of neighbouring columns that differ by more than the angle of repose allows passes sand downhill until it does not. That is the whole of the physics of a heap, and it is why the heap has a cone shape and not a bump.
Turn the glass over and the pile is mirrored to the top, the floor is cleared, and the whole business starts again — with the heap in the upper bulb settling into the shape it had in the lower one, which is a pleasing little inaccuracy that every hourglass has always had.