I guess this is a question about the way an hourglass works. If I were to have an hourglass that emptied in one minute on Earth and took it to Jupiter, for instance, would the increased gravity cause the hourglass to take much less than a minute or is the time restricted by the space allowed for the sand to pass through?
What other factors might be at play?
Some quick research suggests that the answer is yes.
The math is a bit beyond me, but they cite a paper that suggests that the two variables that matter here are the size of the hole through which sand will flow and the local gravity. How high the sand is piled doesn’t matter because granular solids interact with the hourglass wall through friction in a different way than liquids do, so the pressure is constant.
(I probably mangled that explanation but the relevant bit is that gravity is of concern here)
This abstract of a science paper indocates that flow rate of an hourglass is indeed affected by gravity.
https://www.sciencedirect.com/science/article/abs/pii/0032591096801513
This paper presents the effect of gravity on the mass flow rate of granular materials in an hour glass. It is shown that the Beverloo correlation is strongly valid up to at least 13 g0 where g0 is the natural gravitational acceleration.
I don’t have access to the paper itself, but the TL;DR seems on point.
One factor which may or may not have been considered: would the sand be subject to compaction (and therefore reduced flow) because of gravity? I’m thinking of an effect like vacuum weld or other situation where the apparent viscosity of the sand is impeded.
Not to mention the sand breaking through the hourglass, or it collapsing under its own weight.
Well, I’m willing to stipulate a spherical cow indestructible hourglass. And a gravity field low enough that the sand grains won’t accelerate to relativistic falling velocities.
Then the answer appears to be yes.
Presumably though there would be some kind of limit.
Is the bottom of the hourglass a vacuum or filled with air? That could matter.
Maybe the speed of sound in sand is the limit, at least until gravity starts tocget high enough that things get wonky. But that’s a WAG.
Angle of repose is a pertinent factor here; granular materials like sand typically have a point at which they will no longer heap up and begin to flow instead - this is experienced as the angle of the slope of the heap once it has settled.
Angle of repose is affected by gravity - the higher the gravity, the lower the angle - that is, the more flow and the less heaping - and vice versa - in lower gravity, more heaping, less flow, higher angle.
Thanks all - you can tell I’ve been playing board games over the holidays!
You could test it fairly easily with a centrifuge. It wouldn’t even be very hard to set up: Put your hourglass on the end of a string, and twirl it around in a circle.
And…Chronos has come up with his next doctoral thesis!
Would the idea be to spin around with the hourglass pointing directly away from you, with the sand side initially closer to you, and to go fast enough that the sand experiences >1g outwards?
Would the sideways gravity from the Earth’s pull mess things up?
You could position the hourglass in the centrifuge at an angle, so that the combined acceleration from the centrifugal force plus Earth’s gravity is along the axis of the hourglass.
In a centrifuge, certainly, but that seems challenging to do with string tied around the hourglass as proposed by @Chronos
Attach the string to the center of the top and attach a heavy weight on the bottom and the hourglass should naturally orient itself at the right angle. The weight does not need to be super heavy, but if it outweighs the rest of the hourglass, that’ll be enough.
Don’t forget to adjust for time dilation (experienced by the rapidly moving hourglass)
Or use a “tripod” of string, to balance the hourglass evenly. If it’s upright when it’s just hanging there, no matter how you accomplish that, it’s fine: If it hangs that way in 1 g, it’ll hang that way in any number of gs. The “real” gravity due to the Earth and the “fake” gravity due to rotation (scare quotes because they’re fundamentally both exactly the same phenomenon) will add together into a single gravity vector.
Yeah, if you make sure the axis of the hourglass is in line with the string, then the fake gravity will be experienced in that axis too. If you measure the angle of the string and you know the length, you can probably work out the g
Just the angle is enough. The gravity will be \frac{g_0}{cos(\theta)}, where \theta is measured from the vertical.
A thought experiment should suffice: put the hourglass in zero gravity and the sand should not flow, as no force would act upon it. Therefore, more gravity, more flow. Up until other factors get the upper hand with enormous gravitational forces (what has been mentioned already: relativistic effects, compactation of the sand, shattering of the glass, etc.)
To simulate zero gravity, let the hourglass fall from a tall building (ignoring air friction, close enough at the beginning, say the first five to ten stories).
This suggests a different (but related) question – how is the time keeping of a klepsydra (water clock) affected by gravity. Because it that case there IS a change in the pressure due to gravity.