When sand drops from the upper chamber of an hourglass, it makes a pile in the lower chamber. The sides of the cone-shaped pile form at a specific angle. What is this angle?
Is this angle the same regardless of what the material is?
Or does it vary depending on the size, shape, or surface of the particles being dropped? Would smooth-surfaced spheres make the same angle as rough-surfaced cubes?
It’s called the angle of repose, and yes, it does vary with the shape and physical properties of the particles in a pile.
Materials have a characteristic “friction angle,” which is defined as the angle of internal shearing resistance expressed in degrees. It is dependent on how fine the material is, the angularity of the particles, and the amount of water present.
More info:
http://www.brookes.ac.uk/geology/sedstruc/repose/landslid.htm
http://www.tubbs.com/geotech/geotech.htm
The term “angle of repose” is somewhat ambiguous, as noted in the first link.
I gotta ask: did you know that off the top of your head, or did you have to google? Hats off to you if that was just laying around the **Squink ** noggin.
I keep that one in a big pile of occasionally useful facts. 
Facts are roughly shaped and can be piled high.
Driving through the northern states, you’ll notice that the sheds used by highway departments to store sand for road use in winter are pitched to match their contents’ angle.
But not as high as horse manure.