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.
This is also why trees are so fucking crazy to think about. It is impossible to pump water up a hose more than ~32 feet. Like it’s literally physically impossible to stick a pump at the top of a tall building and suck water straight up a pipe. You need a complicated series of pumps and one-way valves to pump it up in stages. Because you’re not really “sucking” the water up the pipe. You’re just lowering the pressure in the pipe, and atmospheric pressure pushes the water upwards to fill the low pressure. After 32 feet tall, the top of the hose/pipe will be a perfect vacuum, atmospheric pressure won’t be able to push liquid water upwards any farther, and the water will just begin cold-boiling in the top of the pipe as the liquid water turns into gas (steam) to fill the vacuum.
But tall trees can move water all the way to their leaves by using only passive capillary action, and suction created by water evaporating out of their leaves. The capillary action is created by tiny straw-like fibers that run all the way up the tree and are bunched together really tightly. Due to surface tension, water is able to “climb” the capillaries as the surface tension fills as much surface area as possible. Then at the top of the tree, as the water evaporates out of the leaves, it draws up fresh water to fill the void.
But that means the bottom of the tree should need to support the pressure of all of the water above it. But it doesn’t, because the surface tension holds the water stable inside of the trunk.
Thank you. Your hypothetical question has been a nagging, unresolved background radiation in my mind for decades, but I’d never gotten around to investigating.
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.
Technically only the pressures are equal, and the actual force will be linearly dependent on the area of the dam (or the surface area of the cylinder). That’s why you can make a tall water tank with relatively thin walls, but an actual dam will have to be quite thicc to handle the tensile stress.
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?
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.
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
This is also why trees are so fucking crazy to think about. It is impossible to pump water up a hose more than ~32 feet. Like it’s literally physically impossible to stick a pump at the top of a tall building and suck water straight up a pipe. You need a complicated series of pumps and one-way valves to pump it up in stages. Because you’re not really “sucking” the water up the pipe. You’re just lowering the pressure in the pipe, and atmospheric pressure pushes the water upwards to fill the low pressure. After 32 feet tall, the top of the hose/pipe will be a perfect vacuum, atmospheric pressure won’t be able to push liquid water upwards any farther, and the water will just begin cold-boiling in the top of the pipe as the liquid water turns into gas (steam) to fill the vacuum.
But tall trees can move water all the way to their leaves by using only passive capillary action, and suction created by water evaporating out of their leaves. The capillary action is created by tiny straw-like fibers that run all the way up the tree and are bunched together really tightly. Due to surface tension, water is able to “climb” the capillaries as the surface tension fills as much surface area as possible. Then at the top of the tree, as the water evaporates out of the leaves, it draws up fresh water to fill the void.
But that means the bottom of the tree should need to support the pressure of all of the water above it. But it doesn’t, because the surface tension holds the water stable inside of the trunk.
Thank you. Your hypothetical question has been a nagging, unresolved background radiation in my mind for decades, but I’d never gotten around to investigating.
Technically only the pressures are equal, and the actual force will be linearly dependent on the area of the dam (or the surface area of the cylinder). That’s why you can make a tall water tank with relatively thin walls, but an actual dam will have to be quite thicc to handle the tensile stress.
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