Designer

Bravo, it's the only way you'll get a decent answer.
There are many variables which may effect the answer (pipe diameter being just one).
GA from the Cat.
Oh I'd also suggest doubling the angle anyway, for as we all know as engineers 'if it can go wrong, it will go wrong'. It just needs one sticky recalcitrant grain to mess the whole thing up, if he starts chatting to his buddies and they stop for a drink on the way down the shoot...
Del

Why it is perfectly obvious, the minimum angle is 1.001569. But this is only true when the sand is in a vacuum and subjected to the gravitational field of at least a Jovian satellite.

On a more serious note, this will vary greatly with the smoothness of the incline chute, the initial velocity of the sand and what if any mechanical vibrations are applied to the chute. I would expect that the average grain size of the sand will also have some additional effect on the critical angle.

I do remember that getting sand to start to slide is one of the classic non-linear chaos analysis problems. A pile of sand, at rest on an incline has additional sand slowly added to to the apex of the pile until a slide starts to happen. Always once the slide happens, more sand than was added ultimately slides down the incline. However, how much sand must be added each time to start the slide will be different each and every time. My fuzzy memory tells me that an unexpected organization gets discovered when one does this experiment. After making hundreds of tests the experimenters found that instead of one single peak of a likely critical amount of mass required to start a slide there were multiple peaks that were likely to start a slide.

If it's wet, the angle of repose approaches 90°, as anyone knows who has built a sand castle on the beach.

Pour some of your "Dry Frack" sand on to a table top. When it has stabilized measure the Angle of the pile. That is it.

Most references seem to suggest 32-34° as the angle of repose for dry sand.