this post was submitted on 20 Jan 2025
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Consider a dam that is 10m tall
Then consider the height of water behind that dam is 5m tall.
Does the dam need to be built stronger if the water behind it is 1 km long?
How about only 500m?
How about 1m?
The answer is, it doesn't matter. Water exerts pressure equally regardless of how much water is behind it.
Therefore a graduated cylinder that is 10m tall needs to resist the same amount of force as a dam 10m tall regardless of how much water is behind the dam. Even a thin sliver of water 1mm thick and 5m tall has the same force as a 5m lake behind the dam.
Incompressible fluids are pretty insane
That is accounting for static bodies of water, wouldn't there be force generated in a dynamic situation? Ie the flow of a fast river? Or if the lake is large enough tidal forces? I'm sure it's negligible levels but still something that must be accounted for?
No, that's absolutely true. Dynamic loads will need to be accounted for in real world examples.
Another point is that if the dam is 10m tall, it has to be built to withstand 10m of water. just because it sits at 5m most of the time doesn't mean a heavy rain couldn't raise the level, and if the dam collapses that's going to be catastrophic vs just spilling over the top.
I've seen a few dynamic loads in my day and in my professional opinion I must agree