You've got gravity. Dry sand flows pretty well.
Bamboo is
hollow and so can be used to channel dry sand around.
Different lengths of bamboo could be used to introduce
delays. Doubtless you could make basic logic gates.
Some sort of mechanical effort would be needed to lift sand
again in order to combat gravity pulling sand downward.
Not much different from a relay computer really, I suppose.
Just slower.
And more sandy.
And relay computers don't like salt water, but administrators might.
Hmmm, seaside computing. I think we hit on something.