8 ms·

"It’s worth stressing that in these static cases the pressure at a given level depends purely on the height of the body of water." How did I not know this? It'

"It’s worth stressing that in these static cases the pressure at a given level depends purely on the height of the body of water." How did I not know this? It's so counter intuitive that a thin column of water can cause the same pressure as a wide one. The video they link shows this in action: https://www.youtube.com/watch?v=EJHrr21UvY8 https://www.youtube.com/watch?v=EJHrr21UvY8 One mind bending fact she shares in the video is that a thin layer of water, touching the damn wall, is the same pressure as an entire lake.

pkaye 5y ago
Its basically the Bernoulli's equation. Its because pressure is force over area and the mass of the body of water above it is area times height time density so the area cancels out. You can add velocity into the equation and its a conservation of energy equation. Similarly there is a continuity equation which is a conservation of mass. These two are the backbone of a beginning fluid mechanics course in engineering.
- jvanderbot 5y ago
  Intuition fails! Quick, point out the math! Your comment is exactly what is derived / demonstrated in the article. Parent was simply commenting how that math was not intuitive (and so repeating that it was just math doesn't do much).
  - deleted 5y ago
    [deleted]
palijer 5y ago
This is one of those physics phenomenon where I feel like they are a software bug. Bell's Theorem and a lot of quantum entanglement stuff is like that as well. https://youtu.be/zcqZHYo7ONs https://youtu.be/zcqZHYo7ONs
- jschwartzi 5y ago
  It’s actually quite intuitive, as the force is distributed over a larger area. So although the pressure gradient isn’t affected by the discontinuity in the container size, if you compare forces exerted by the pressure on a plate in either section of the chamber you’ll observe that the force on the wider plate would be reduced to compensate for the increased area in the presence of the same pressure.
  - garmaine 5y ago
    I'm not sure why you're being down-voted. If you double the size of a water column, you of course double the total weight pressing down. But you've also doubled the cross-sectional area, so the weight-per-unit-area (pressure) remains the same. This is pretty intuitive if you understand what pressure is.
    - dan-robertson 5y ago
      Perhaps because the explanation (and indeed concept) isn’t that intuitive so the comment may be read as dismissive? If you see pressure as coming from the weight of the fluid above and now replace fluids with solids for a mental model, it obviously doesn’t work: imagine two parallel rigid plates connected by some rigid structure. The top plate will represent the (fluid) boundary between the top of the barrel and the tube and the bottom plate the bottom of the barrel. If you put a narrow column of metal on the top of the top plate, then the pressure exerted by the bottom plate is, say, p. If you make that column much wider, increasing the weight above, the pressure is say 10p. I think the problem is that this intuitive model of pressure is just wrong but if it doesn’t come from the weight of the water above, it is hard to intuitively see where it does come from.
      - garmaine 5y ago
        Your example is completely different though. Considering neighboring water columns isn't like adding more to the top of the plate, it's like setting up an entirely different plate next door. Which of course doesn't affect the first instance at all.
morpheos137 5y ago
why is it counter intuitive for you? It is not to me at all. Gravity pulls down. There is essentially no lateral component to gravity. Height is measured in the verticle dimension, the same as gravity. Now imagine water column as a stack of pennies. The more pennies are added to the stack the more pressure is on the lower pennies. It does not matter how many stacks are in front of or behind or to side of the stack you are looking at.
- jvanderbot 5y ago
  This is a great explanation, actually.
  - JKCalhoun 5y ago
    Hmmm ... reinforces my counter-intuition. The stack of pennies might explain why the bottom of the jar would explode, but not the sides, area not below the stack of pennies. My intuition (wrong here) is that the extra surface not beneath the stack of pennies (your analogy) would in fact distribute the pressure and therefore represent a lower PSI on all sides of the jar.
    - jvanderbot 5y ago
      I guess I translated "pennies" into "little bags of water". The little bag of water at the bottom only gets pressurized from the little bags of water above it. And so the bottom bag's "pushing" outward from compression would be affected only by those above it.
- Nathanael_M 5y ago
  Super conter-intuitive for me as well. I appreciate your explanation!
- RealityVoid 5y ago
  Actually, yours is not such a great explanation, since a stack of quarters would manifest greater pressure than a stack of pennies. Whereas, a fluid column would manifest the same pressure no matter the diameter.
tobmlt 5y ago
Fluid has so much to bend the mind. Soliton waves, shocks, expansions, critical transition phenomena (besides phase transition) Look at froude number and planning hulls, the purpose of chines, steps, etc. in a high speed hull to manage skin friction vs wave drag. Wave Dispersion, wave superposition, etc. the free surface itself means if you are solving for flow, flow then determines the free surface which then determines the flow.. add infinitum. It’s nonlinear like a baby general relativity in that way. The shallow water equations are hyperbolic so you get shocks etc. deep water, long wavelength waves act in linear fashion so you get superposition effects. On and on. Fun times.
- awestroke 5y ago
  Can you recommend any books on this?
  - mr_overalls 5y ago
    Fluid mechanics is a standard course in many undergraduate engineering curriculum. A quick Google search reveals lots of open-source and downloadable pdfs of printed texts. https://open.umn.edu/opentextbooks/textbooks/85 https://open.umn.edu/opentextbooks/textbooks/85 http://civilcafe.weebly.com/uploads/2/8/9/8/28985467/fluid_mechanics.pdf http://civilcafe.weebly.com/uploads/2/8/9/8/28985467/fluid_m...
  - tobmlt 5y ago
    Mr_overalls has the overview idea covered. I might add that if you start with the Reynolds transport theorem, you can’t go wrong, but that might be the wrong-math-way-around for you. Are there particular aspects you are interested in? E.g. Computational methods Turbulence Topology / geometry Shocks and expansions Superposition, radiation/diffraction, added mass Analogues with other systems Some of this stuff involves simplifying assumptions. Sometimes those reveal neat corners of behavior. (E.g. the superposition business) Some of it might be better introduced qualitatively at first, like say turbulence. It all depends where you are. By the way, I don’t know some great amount of this stuff at some expert level. I may be able to guide you in some direction of interest is all. I wish I knew of an overview which scanned across all this funny behavior but some is pretty widely separated. Naval architecture text books focus on the linear aspects, and the free surface of course. Cfd (computational fluid dynamics) just about has to deal with “everything else” except the topology and “geometry of” (physics, mechanics, fluids, etc) which kind of lives the hermit life, like the quaternions or geometric algebra or something.
ummonk 5y ago
That's interesting because it seems perfectly intuitive to me. Both in terms of understanding the physics (weight of water above the column divided by the area of that column, and then any water around the column just has to have the same pressure to contain that column) and just plain practical experience from e.g. dipping underwater in the ocean and not getting crushed like a bug.
- Iv 5y ago
  It is very counterintuitive when you reason in terms of weight though. If you imagine a pile of rocks for instance, it makes sense that the strain on the base of a pyramid is lower than on the base of a column of the same height and base area. You have to visualize the atmospheric air pressure to reconcile the result with intuition.
  - ummonk 5y ago
    I mean it's perfectly intuitive to me that a pyramid of rocks isn't going to collapse, so you don't need a container to hold it in. The closer analogue would be pouring sand in to a tube vs. pouring it in to a bottle that widens below the neck - it's intuitive to me that the bottle would be under enormous strain to hold the sand in. (And, incidentally, the part of the bottle where it widens would be applying extra "weight" to the sand below it)
marcosdumay 5y ago
On those oddly shaped reservoirs, the walls compensate for the lack of a water column above the places where it widens. The actual force on the water is the same as would be in a cylinder.
abraae 5y ago
I'm building a system for measuring levels in water tanks using submersible pressure sensors (triggered by living in a dry area and being totally dependant on our tanks). Quality sensors cost a lot - too much for domestic purposes. Much cheaper ones can be bought from China, so I've been looking for some way to test them, without actually altering the level in a gigantic water tank. It occurred to me I should be able to just use a thin vertical pipe. But as you say, this seems counter intuitive, especially if the pipe is barely wider than the sensor itself. Just doesn't... Feel right.
- lazide 5y ago
  It’s called head - and it’s a key calculation in if a dam is worthwhile. The pipe feeding the turbine can be quite small for a lot of power if the head is large. You could also use a small pressure vessel/sealed tank, and pump in water with a hand pump. You could simulate nearly any sized tank that way too.
- RantyDave 5y ago
  If you stick the sensor at one end of a hose pipe (with water in it) then you can just change the height of the other end to change the pressure.
  - abraae 5y ago
    Nice idea, thank you.
- RantyDave 5y ago
  Hey, also, why not just find the height of the water level by attaching something ultrasonic to the inspection hatch (or whatever). https://www.adafruit.com/product/4664 https://www.adafruit.com/product/4664
  - vosper 5y ago
    Not only is this a really cool idea, that sensor is awesome! I love that you can get something like that for $30.
zwkrt 5y ago
A fun thought experiment is to realize that if the earths atmosphere were totally removed except for a cylinder that encircled your house and went into space, you would feel physically the same. Just like in the water, in some sense the only thing air pressure cares about is how much air is directly on top of your head.
vishnugupta 5y ago
For me the aha/eureka moment about the force of water pressure was when I read that water jet is used sometimes to precision cut diamonds.
- dan-robertson 5y ago
  Usually some very fine abrasive particles are added to water-jet cutters because the water alone doesn’t cut so quickly if at all. Similarly, the depth of a cut can be limited as it only really works if the water goes all the way through (otherwise the pool slows down and redirects the force from the jet)
zarzavat 5y ago
Perhaps you are conflating pressure and force? Pressure is force per area, the area doesn't matter by definition. Similarly to how we measure rainfall in millimetres: volume / area = length. Whereas if you were to place a bucket of water on your head, the area of the bucket would surely make a big difference to the force you feel, all else being equal.

pkaye 5y ago

Its basically the Bernoulli's equation. Its because pressure is force over area and the mass of the body of water above it is area times height time density so the area cancels out. You can add velocity into the equation and its a conservation of energy equation. Similarly there is a continuity equation which is a conservation of mass. These two are the backbone of a beginning fluid mechanics course in engineering.

jvanderbot 5y ago
Intuition fails! Quick, point out the math! Your comment is exactly what is derived / demonstrated in the article. Parent was simply commenting how that math was not intuitive (and so repeating that it was just math doesn't do much).
- deleted 5y ago
  [deleted]

palijer 5y ago

This is one of those physics phenomenon where I feel like they are a software bug. Bell's Theorem and a lot of quantum entanglement stuff is like that as well. https://youtu.be/zcqZHYo7ONs https://youtu.be/zcqZHYo7ONs

jschwartzi 5y ago
It’s actually quite intuitive, as the force is distributed over a larger area. So although the pressure gradient isn’t affected by the discontinuity in the container size, if you compare forces exerted by the pressure on a plate in either section of the chamber you’ll observe that the force on the wider plate would be reduced to compensate for the increased area in the presence of the same pressure.
- garmaine 5y ago
  I'm not sure why you're being down-voted. If you double the size of a water column, you of course double the total weight pressing down. But you've also doubled the cross-sectional area, so the weight-per-unit-area (pressure) remains the same. This is pretty intuitive if you understand what pressure is.
  - dan-robertson 5y ago
    Perhaps because the explanation (and indeed concept) isn’t that intuitive so the comment may be read as dismissive? If you see pressure as coming from the weight of the fluid above and now replace fluids with solids for a mental model, it obviously doesn’t work: imagine two parallel rigid plates connected by some rigid structure. The top plate will represent the (fluid) boundary between the top of the barrel and the tube and the bottom plate the bottom of the barrel. If you put a narrow column of metal on the top of the top plate, then the pressure exerted by the bottom plate is, say, p. If you make that column much wider, increasing the weight above, the pressure is say 10p. I think the problem is that this intuitive model of pressure is just wrong but if it doesn’t come from the weight of the water above, it is hard to intuitively see where it does come from.
    - garmaine 5y ago
      Your example is completely different though. Considering neighboring water columns isn't like adding more to the top of the plate, it's like setting up an entirely different plate next door. Which of course doesn't affect the first instance at all.

morpheos137 5y ago

why is it counter intuitive for you? It is not to me at all. Gravity pulls down. There is essentially no lateral component to gravity. Height is measured in the verticle dimension, the same as gravity. Now imagine water column as a stack of pennies. The more pennies are added to the stack the more pressure is on the lower pennies. It does not matter how many stacks are in front of or behind or to side of the stack you are looking at.

jvanderbot 5y ago
This is a great explanation, actually.
- JKCalhoun 5y ago
  Hmmm ... reinforces my counter-intuition. The stack of pennies might explain why the bottom of the jar would explode, but not the sides, area not below the stack of pennies. My intuition (wrong here) is that the extra surface not beneath the stack of pennies (your analogy) would in fact distribute the pressure and therefore represent a lower PSI on all sides of the jar.
  - jvanderbot 5y ago
    I guess I translated "pennies" into "little bags of water". The little bag of water at the bottom only gets pressurized from the little bags of water above it. And so the bottom bag's "pushing" outward from compression would be affected only by those above it.
Nathanael_M 5y ago
Super conter-intuitive for me as well. I appreciate your explanation!
RealityVoid 5y ago
Actually, yours is not such a great explanation, since a stack of quarters would manifest greater pressure than a stack of pennies. Whereas, a fluid column would manifest the same pressure no matter the diameter.

tobmlt 5y ago

Fluid has so much to bend the mind. Soliton waves, shocks, expansions, critical transition phenomena (besides phase transition) Look at froude number and planning hulls, the purpose of chines, steps, etc. in a high speed hull to manage skin friction vs wave drag. Wave Dispersion, wave superposition, etc. the free surface itself means if you are solving for flow, flow then determines the free surface which then determines the flow.. add infinitum. It’s nonlinear like a baby general relativity in that way. The shallow water equations are hyperbolic so you get shocks etc. deep water, long wavelength waves act in linear fashion so you get superposition effects. On and on. Fun times.

awestroke 5y ago
Can you recommend any books on this?
- mr_overalls 5y ago
  Fluid mechanics is a standard course in many undergraduate engineering curriculum. A quick Google search reveals lots of open-source and downloadable pdfs of printed texts. https://open.umn.edu/opentextbooks/textbooks/85 https://open.umn.edu/opentextbooks/textbooks/85 http://civilcafe.weebly.com/uploads/2/8/9/8/28985467/fluid_mechanics.pdf http://civilcafe.weebly.com/uploads/2/8/9/8/28985467/fluid_m...
- tobmlt 5y ago
  Mr_overalls has the overview idea covered. I might add that if you start with the Reynolds transport theorem, you can’t go wrong, but that might be the wrong-math-way-around for you. Are there particular aspects you are interested in? E.g. Computational methods Turbulence Topology / geometry Shocks and expansions Superposition, radiation/diffraction, added mass Analogues with other systems Some of this stuff involves simplifying assumptions. Sometimes those reveal neat corners of behavior. (E.g. the superposition business) Some of it might be better introduced qualitatively at first, like say turbulence. It all depends where you are. By the way, I don’t know some great amount of this stuff at some expert level. I may be able to guide you in some direction of interest is all. I wish I knew of an overview which scanned across all this funny behavior but some is pretty widely separated. Naval architecture text books focus on the linear aspects, and the free surface of course. Cfd (computational fluid dynamics) just about has to deal with “everything else” except the topology and “geometry of” (physics, mechanics, fluids, etc) which kind of lives the hermit life, like the quaternions or geometric algebra or something.

ummonk 5y ago

That's interesting because it seems perfectly intuitive to me. Both in terms of understanding the physics (weight of water above the column divided by the area of that column, and then any water around the column just has to have the same pressure to contain that column) and just plain practical experience from e.g. dipping underwater in the ocean and not getting crushed like a bug.

Iv 5y ago
It is very counterintuitive when you reason in terms of weight though. If you imagine a pile of rocks for instance, it makes sense that the strain on the base of a pyramid is lower than on the base of a column of the same height and base area. You have to visualize the atmospheric air pressure to reconcile the result with intuition.
- ummonk 5y ago
  I mean it's perfectly intuitive to me that a pyramid of rocks isn't going to collapse, so you don't need a container to hold it in. The closer analogue would be pouring sand in to a tube vs. pouring it in to a bottle that widens below the neck - it's intuitive to me that the bottle would be under enormous strain to hold the sand in. (And, incidentally, the part of the bottle where it widens would be applying extra "weight" to the sand below it)

marcosdumay 5y ago

On those oddly shaped reservoirs, the walls compensate for the lack of a water column above the places where it widens. The actual force on the water is the same as would be in a cylinder.

abraae 5y ago

I'm building a system for measuring levels in water tanks using submersible pressure sensors (triggered by living in a dry area and being totally dependant on our tanks). Quality sensors cost a lot - too much for domestic purposes. Much cheaper ones can be bought from China, so I've been looking for some way to test them, without actually altering the level in a gigantic water tank. It occurred to me I should be able to just use a thin vertical pipe. But as you say, this seems counter intuitive, especially if the pipe is barely wider than the sensor itself. Just doesn't... Feel right.

lazide 5y ago
It’s called head - and it’s a key calculation in if a dam is worthwhile. The pipe feeding the turbine can be quite small for a lot of power if the head is large. You could also use a small pressure vessel/sealed tank, and pump in water with a hand pump. You could simulate nearly any sized tank that way too.
RantyDave 5y ago
If you stick the sensor at one end of a hose pipe (with water in it) then you can just change the height of the other end to change the pressure.
- abraae 5y ago
  Nice idea, thank you.
RantyDave 5y ago
Hey, also, why not just find the height of the water level by attaching something ultrasonic to the inspection hatch (or whatever). https://www.adafruit.com/product/4664 https://www.adafruit.com/product/4664
- vosper 5y ago
  Not only is this a really cool idea, that sensor is awesome! I love that you can get something like that for $30.

zwkrt 5y ago

A fun thought experiment is to realize that if the earths atmosphere were totally removed except for a cylinder that encircled your house and went into space, you would feel physically the same. Just like in the water, in some sense the only thing air pressure cares about is how much air is directly on top of your head.

vishnugupta 5y ago

For me the aha/eureka moment about the force of water pressure was when I read that water jet is used sometimes to precision cut diamonds.

dan-robertson 5y ago
Usually some very fine abrasive particles are added to water-jet cutters because the water alone doesn’t cut so quickly if at all. Similarly, the depth of a cut can be limited as it only really works if the water goes all the way through (otherwise the pool slows down and redirects the force from the jet)

zarzavat 5y ago

Perhaps you are conflating pressure and force? Pressure is force per area, the area doesn't matter by definition. Similarly to how we measure rainfall in millimetres: volume / area = length. Whereas if you were to place a bucket of water on your head, the area of the bucket would surely make a big difference to the force you feel, all else being equal.