I’ve just listened to a podcast about time. The speaker said that the flow of the sand doesn’t change but if it was liquid things would be different because of its changing pressure.
Sorry if I phrased it weirdly, English isn’t my first language. Feel free to correct me.
In: Physics
I’m not so sure it does. Same shape and size opening,would ten times as much sand take ten hours? I imagine the weight on top of the sand affects the flow rate, but they volume we’re working with makes it negligible.
The key, from [your article](https://www.google.com/amp/s/www.technologyreview.com/s/418993/the-mystery-of-sand-flow-through-an-hourglass/amp/), is “*the grains form chains and bridges that transmit their weight to the side of the container where they are supported by friction*”.
As you probably know, but it’s worth thinking through: In a fluid that is almost not moving, there is no friction between the fluid and the walls. The only force between the fluid and the container walls is pressure, which is perpendicular to the surface. So the weight of the fluid is supported by the bottom of the container. So the fluid at the bottom is squeezed by the weight of all the fluid above it. As you go higher in the container, the fluid has less fluid above it, and is thus compressed by less weight, so the pressure goes down. At the top, the pressure is at a minimum. If fluid flows out the bottom, the pressure at the bottom decreases over time, because the depth decreases over time.
Now, to answer your question: If it’s true that the pressure at the bottom of a container of solid particles does not increase linearly (or at all, past some point) with depth, then it must be true that some of the weight of the particles is reacted by friction on the walls. (Otherwise, you’d be back to the fluid situation). One extreme example is if all the particles stick together as though they had been glued in place. If that were the case, the pressure at the bottom would be zero, i.e. you would not need the bottom of the container at all, you could have a hole there and nothing would come out, if the particles are sticky enough. (Hold a tube of toothpaste with the opening pointed downwards, and nothing comes out unless you squeeze it). Reality is somewhere in between: There is some stickiness between the particles and the walls, so you get friction. The particles that are not on the walls can transfer some weight to neighboring particles and then on the walls… not via stickiness, but via diagonal compression. As you probably know, in an [arch](https://i.pinimg.com/originals/89/2a/76/892a766da71f806ca7fa7b64f67633a5.jpg), all the material is in compression, with very little local shear or tensile stresses, so very little friction is required until you get to the ends. (In a perfect [catenary](https://en.wikipedia.org/wiki/Catenary) arch – like the one in St Louis – it’s all compression, there’s zero tension or shear, except for the side-forces caused by the wind). So imagine that the particles mostly support themselves by transferring their weight to the wall along arch-shaped clusters – which rest on the walls by friction – and [only the particles near the bottom rest on the bottom rather than on an arch](https://imgur.com/a/xBybe8N). Does that help?
Edit: Fixed “arc” to “arch”.
Hourglasses definitely slow as they empty. You can simply visibly notice it. Not sure why you or the podcast host think they don’t.
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