Water Pressure Depends Only on Depth, Not Container Shape
Вставка
- Опубліковано 2 жов 2024
- The pressure of water at rest in a container depends only on the depth, not the shape of the container. For each additional 10 cm of depth, the pressure increases by 1 kPa (kiloPascal). This means that the pressure is a constant at a given depth, irrespective of the size and shape of the container.
This basic principle of hydrostatics might at first seem to be counter-intuitive. It certainly does not apply to solid objects, like blocks of wood. The difference is that a liquid has no shear strength -- water cannot be bent or twisted. Instead, it transmits forces uniformly in all directions.
Water poured into any container, of any shape, quickly flows to the bottom and arranges itself with uniformly decreasing pressure from bottom to top. If you draw a "topo map" of pressure (viewed from the side of the container), the lines of constant pressure are always uniformly spaced horizontal lines, for any container shape.
The reason is that water exerts a force perpendicular to the container wall, exactly the same as it would against an equivalent shape and volume of water. Thus, any container wall, of any shape or direction, behaves just like an equivalent amount of water. The water "doesn't care" whether it's meeting a wall or more water. It's all the same to the water. So as far as water pressure is concerned, a weird and twisting container is just the same as a rectangular container with parallel vertical sides.
The force of water on the bottom of a container can exceed the weight of all the water in the container. To understand how this is possible, watch the last third of the video presentation, which uses an upside-down T-shaped container as an example, or see the separate video at • Water Pressure on Bott...
More science videos: Electric Circuits and the Hydraulic Analogy
• Electric Circuits and ...
I was not able to wrap my head around this idea for a pretty long time, but now it’s crystal clear.....thanks a lot...it really helped!
Thanks for leaving a comment. This is why I make the videos.
thank you very much for the thorough explanation that even middle schoolers would understand
I made this comment for your second video: Your drawings might confuse people about what a weight scale will read when the containers are placed on it. This is despite your clear explanations on what the weight scale will read!!
At time 11:20 you show an arrow coming from the OUTSIDE bottom of the container. Typically this force will come from the weight scale the container is sitting on and it will act on the container. It will be equal to what the weight scale is reading which is the weight of the whole water and container like you mentioned.
Instead what you mean to show is the force exerted by the bottom wall, on the liquid inside. That force is equal to pressure * Area of the bottom. So, you should draw the up arrow originating from the inside bottom.
This might seem like a minor point but it is the main reason people are confused about this paradox. The force on the bottom of the container -- exerted by the water pressure, will be same for all 3 containers. But the force on the bottom of the container exerted by the weight scale will not be the same! One way to visualize this is to divide the "bottom" of the container into two sections. The flat bottom and an infinitesimally thin vertical edge at the bottom. The forces added up by those two sections determine the force exerted on the weight scale and hence the weight. The force exerted by the second thin vertical section is equal to zero in one container shape, downward in the second, and upward in the third.
Great, clear video, thank you!
This directly addresses a point I've been discussing with a friend recently, but still seems puzzling...
Suppose you have a container like the final "upside down T" shaped one, but with the dimensions taken to a greater extreme. The bottom section is very large - the size of a warehouse maybe - and the upper column is very thin and tall - just one square cm, but 100m tall - like a really narrow chimney protruding from our "warehouse" vessel.
By the laws of physics you've confirmed, if you fill only the large lower part with water (using hundreds, maybe thousands of tons of water), you'll create a relatively small amount of pressure for an object on the "floor" of that vessel - let's say that part of the vessel is 5m tall, it would be 1/2 an atmosphere.
But by then pouring in just another 10L (or 10kg) of water, and filling the tall thin section, you can increase the pressure at the bottom to over 10 atmospheres.
This seems completely counter-intuitive, that this tiny bit of extra water could create such massive pressure throughout the huge vessel, but I'm pretty sure it's correct?!
The only caveats I can see are that a) the vessel would need to be very rigid, or it may just flex, expand and allow the column of water to drop into the lower part and b) although the pressure would be very high, it would not be capable of much work - if it started to crush any objects in the lower vessel, the act of doing so would cause the column of water to drop and with it he pressure.
Is the above all correct or is there anything we're missing that means the tiny amount of extra water would not, in fact create the massive pressures?
Everything you said is correct. Someone else asked almost exactly the same question. Did you watch my follow-up video? ua-cam.com/video/JkhufvEHGLc/v-deo.html
Also, look up "Pascal's principle" to see how forcing water through a narrow column applies a huge force in a wide column. This is similar to a lever, in which applying a small force far from the fulcrum results in a large force near the fulcrum.
wow i suck at physics and i slowly starting to understand this! great overview :)
i know right!
You are correct, this is why you can swim down in the ocean, say 10 feet, even though the ocean is a thousand miles wide, you're still only dealing with the pressure at your depth of 10 feet.
I thought about that too
thanks for your explanation,
I have kind of a preoccupation regardind that fact , if pressure always depend on the depth and not the shape why in some exercises using the pressure formula to find it,is useless ,like in case of fluid moving ?
But I could hold back 10liters of water at 1 meter head. But not 100 litres
But, Ocean water is compressible... One cubic inch of ocean water from 3000 feet is more dense than ove square inch of surface water or water that is 6 inches deep.
Some fluids are less compressible than otgers and their shear values increase, by default.
Very helpful video, it breaks it down to the simplest terms possible. The free body diagrams associated with the example at 11:30 were very useful in understanding how the smaller force of water could result in an identical bottom pressure with a large surface area (the upward force of hydrostatic pressure cancels some of the downward force and the stress is handled by the container). Thanks!
Can somebody explain why water acts like this because it wasn't explained in the video. I understand how it works but not exactly why. Like why don't the water molecules push against each other and "crush" eachother. Is it because of the molecular structure that they just repel each other or something like that ?
For slow speed i disliked
For knowledge i took my dislike back...
Thank u sir.. 2 likes
But i request you to make videos short for the sake of time🙏
r/usernamechecksout
watch on 2x, that's what it's for
I still don't understand it. I can't see that it would take as much force to hold back 1 litre of water as it would 1000 litres...
Are the containers of the same weight? BTW if you use water in the experiment instead of rice it would be really2 convincing...now i am still unconvinced because rice not the same as water...about the 3 different shapes why it is not overflowing i think it's because the water is just enough to fill in that level that's why it the smaller one doesn't overflow...I feel that the diagram is not enough to prove the water pressure just depends on depth....
I think the more the water the more pressure...as it carries more weight..i will test this myself ...i need this theory to help my water pressure.
Does water come in blocks? And if water comes in blocks, then do water blocks bend?And if blocks bend, then is that why the Earth curves? Or is the Earth a level plane?
I conceptually divide the water into sections that I call blocks. There are no actual blocks of water that are separate from each other.
Does this hold good for solids too? Cause I've been thinking that solids kinda act different from liquids and hence the pressure exerted on the bottom would vary if the container is filled with solids.
Solids have different behavior from liquids, as shown by the examples in the video.
If you fill the container with glass marbles, the behavior is somewhere between a single solid block and a liquid, but more like a single solid block due to friction between the marbles.
Badri dont listen To this idiot g chang cause this is totall nonsense his world is based on math and the deluded moron thinks math is reality..
If everything he has vomited In this video then the water towers wich provide water pressure for huge citys wouldnt work 😋 but they do work.
furthermore mixing liquids perticulary water with solids its utterly stupid dissingenious tricks To fool ppl about the reality of the natural world..
The height of the water tower provides the pressure needed to operate the water system of a city. How is this contrary to the video?
@@mentor288 what??????? the fuck is your problem??
The "too long didn't watch" is that the container itself must exert a force to keep the water inside it. That explains why there's pressure even where there's no water directly above
Thank you, this helped solidify my understanding. "The cardboard takes the role of the water above" seemed very arbitrary.
The pull towards the nearest largest mass surely dictates how much pressure is excreted over the object?
What about in a container shape which creates waves as it drains? It seems like it would hav some small effect?
The video applies only to static (non-moving) water in containers.
i'm so thankful, sir
Could you help me wrap my head around this conundrum? If one were to pump water up a certain height, would a vertical pipe exert more force at the bottom compared to a meandering pipe, a hose, to the same height. Will the shape of the curling hose exert less force on the bottom?
No, the shape and path of the container make no difference. The pressure gets transmitted through any type of curly cue path. Note that this is only true for static (at rest, non-flowing) water.
Thank you!
What if you open two holes at the bottom, will pressure decrease or stay the same? Thanks
Same pressure. Note that the whole video is about static (non-flowing) water.
I watched some videos about water pumping with gravity and pressure using a drum, but without electricity. is this true? if it is true, can we pump from 200ft below water with large containers?
so what if you had a long tube, let's say 1500m long and with a diameter of 1m, that is hanging into an empty vessel and then you start to pour down a fluid through the tube into the vessel. the fluid in the vessel fills up until the tube is partially submerged, let's say the vessel is 20m high fully filled and the tube hangs in there 5m from the top of the 20m high vessel. and let's assume there is a lid on the vessel and at the top of the tube. ( i mean sth like this (__I__) not to scale ofc lol.)
what would the pressure be of the fluid in the vessel let's say 10 m from ground? just simply rho x G x z ?
And would this only work when the water in the vessel is connected to the column? I presume so
The pressure is always rho x G x z, where z is the vertical distance to the surface of the water exposed to the open air. If the "lids" are air-tight, there's not enough info to answer the question.
@@graychang99 well, what I actually tried to hint at, was a storage salt cavern. If you google a picture I think you will see what I tried to describe. The well (tube 1500m long) filled with brine or oil. In different concentric tubes. Dwnsitity 1, 2 g/cm3 or 0.83g/cm3.
In the cavern the one tube is suspended almost reaching to the bottom that is filled with brine that reaches a little over the end of the tube. Above that is oil.
At the brine oil interface the pressure should be identical.... But now I am confused.. As the brine is under the oil, is it still only rho g z or do I have to add the pressure of the oil too? Because it is similar to a column where there are different fluids with different densities atop one another
Another probably stupid question. Same scenario. Let's say there is no oil above the brine and there is air above the brine. The only reason there is pressure in/on the brine is the column? Is there a pressure directed upwards from the brine to the air or just to the outside walls?
The more general principle is that the CHANGE in pressure with z is rho x G x z. If you have nonzero pressure at the top, you just add that value.
oh, for some reason it didn't really click until the last figure showing all three systems connected. Thank you for including that last image :)
wtf that was great explanation ,thanks dude
The last diagram helps and is good. But I'm still imagining me being able to hold back a pint of water with beer mat but not a saucepan with a magazine
Thankyou so much bud for this video. There are a lot of videos but this is the only one which has explained the best way. Again thankuou
I like! Keep it up!
Maybe I'm too dumb to understand:')
But I don't get the last part. If water can't transmit the force, how does the force of 18N was transmitted downwards, making it total 30N? Thank you so much for this great video too.
See if this supplementary video helps: ua-cam.com/video/JkhufvEHGLc/v-deo.html
At 13:53, is it Hydraulic mechanical Advantage, similar to Hydraulic Jack?
Very thanks I have no words to say for ur awesome concept contents..This small difficulty was restricting my study of fluid mechanics..
As we are never taught how liquid behaviors
you are really helping people with this
an amazing substance, water!
I don't know if you still answer these or not, but, you originally based that the pressure at the bottom was 3kPa. You got this number by considering the weight of the water. The weight of the water does matter on the shape of the container. Now, if you had started with a different shape and said that the total weight of the water was 20N, but same surface area at the bottom, wouldnt you have obtained a different pressure at the bottom? Very interesting video.
No, the total weight of the water is not related the pressure at the bottom. Remember that a solid object puts its entire weight on the bottom, whereas a liquid distributes its weight against all container surfaces, including sideways and upward, depending on the container shape.
i would like to thank you .
you did a great job 🙂
شكرا لك
So what changes from different container shapes? I mean the smaller they are at the bottom if you place them on your hand they feel more painful, where if it is big it doesn't hurt that much? Force? I know it is not mass as it can be the same.
The bigger container carries a larger mass, but the force on the bottom is exactly the same as in the other containers. The extra weight presses against the sloping sides, not the bottom.
very well explained, thanks
So let’s say I put a straw 1000 yards long and 1 atom thick filled with water into a pool of water. Would the pressure of the pool now be the same if I was 1000 yards in the ocean???
No. If the tall straw were a reasonable width, the water would drain into the pool. However, if you capped the pool to trap the water, then the 1000 yards of depth in the straw would indeed increase the pressure in the pool to the same as 1000 yards deep in the ocean (assuming equally salty/dense water).
@@graychang99 That's actually pretty scary
The pic at the end realy did the trick. Thanks!
Very helpfull
Thanks
Why the sideways force is also 0.4?
The force of the liquid goes in all directions: up, sideways, and down equally.
Hello. I am farmer from Punjab. Neither engineer nor scientist. I have seen many things around me and I am trying to break physics law of perpetual motion. I know it's impossible theory but it doesn't mean that we can't try. But problem is this that I have seen many things but without perfect tool and scientist , I am handicap.
This is a fare better explanation than other videos.
14:39 flat earth
Bottom line, head determines the pressure.....
Pascal’s principle
Absolute legend
Thank you so much
Water *thinks* it has water in its surrounding.
A block of water sounds like Minecraft
Best video ever
Excellent explanation. Would the same thing hold true for a container of coffee beans? Could you approximate coffee beans as a fluid? Or are friction forces at play?
Friction forces are at play.
Your rice experiment does not hold. The rice is hold by the of carton exerting a side force to stay vertical.
Yes, what you said is correct. The cardboard divider exerts a side force. But I don't understand why the experiment "does not hold."
Which container has the largest pressure at the bottom? If they have different shapes and they carry different amounts of water????
The containers have the SAME pressure at the bottom. The only thing that matters is the depth, not the amount of water or the shape of the container. The video tries to explain why this is true.
Although the forces on the BOTTOMS of the 3 containers are exactly the same, the TOTAL net vertical forces on the container are equal to the weight of the water. The water in the wide container exerts additional downward forces on the two diagonal sides. The upside-down "T" shaped container exerts UPWARD forces on the container -- the downward forces are partially canceled by the upward forces, which allows the force on the bottom to exceed the weight of the water. See the follow up video, ua-cam.com/video/JkhufvEHGLc/v-deo.html
Is gravity and pressure married?
Yes
I was searching for a way to get the water level of a tank by measuring psi! Is this possible?
Yes. If the top of the tank is open to the atmosphere, then the height of the water above the point where you take the pressure reading is about 10 cm per 1 kPa (about 2 feet per 1 psi).
This was very helpful
I was extremely confused by this concept, but now I understand! Thanks!
So the container shape wont have an effect, but does de bottom area has an effect on it? Great video!
It does because pressure is equal to force/ area. Which means the larger the area the lower the pressure and the smaller the area the higher the pressure
Tnx
Is this considered hydrostatic equilibrium?
Yes
Thank you for this
wonderfukly explaied
Very helpful, thank you
Would it be correct to refer to the counterbalance force as contact force between the surface of the container and the water?
Yes.
Good explanation!
Hello Sir - I am not an engineer but I think mechanically and am extremely curious! I am not very clear on this example...if I am in the ocean at at depth of 100' standing on the bottom, the only force is on top of my head? There is no side pressure at all?
The pressure is spread all over your body, perpendicular to your skin surface: DOWN on the top of your head, UP on the soles of your feet, SIDEWAYS on your chest, and so on. Your whole body is being squeezed, like a boa constrictor around a mouse.
Mike Earls..search about Pascal Law..
Nice video.thanks.
How are you trying to explain this and continuing to add new weights of measurement the whole time?? I am sure with a little thought you can make this more clear for all.
I used metric units for the general global audience, and for U.S. science and engineering students. For the U.S. general audience, here are some approximate conversions: 10 newtons = 2 pounds, 7 kilopascals = 1 pound per square inch, 1 liter = 1 quart, 10 cm = 4 inches.
Why is that 4+4 =6
That was helpful. Thank you!
What will happen if the water is in motion towards gravity? or the water is having a velocity with respect to gravity
Water in motion is not in an equilibrium state and therefore does not follow the neat level pressure profiles shown in the video.
For example, in a slow smoothly moving stream, the lines of constant pressure are slanted downward in the direction of flow.
This is the clearest and easiest way to understand. Very well explained. Gifted presentation.
Well thank you! I'm happy to hear that you found it useful.
Thanks for making things clear
Thanks for clearing my doubt
These three bottwes at the beginning have the same bottom lenght. What if it was different for each bottle. Would it affect the pressure in the bottom?
No, the pressure depends only on depth, so the size of the bottom has no effect on pressure. However, the total force (pressure x area) would be different.
@@graychang99 thanks!! I figured it out.. I had to solve an exercise for today's lesson
@@graychang99 then can we say that the pressure is independent of weight of liquid above it
Pascal says pressure is same all directions and you say presure is more in depth. Please clarify my confusion
The pressure is the same in all directions (up, down, left, right) for both liquids and gases.
For a gas, the difference in pressure in a container due to depth is
negligible because the gas is so light. The gas fills the whole
container and pushes against all the walls and top.
A liquid fills a container from the bottom up. The pressure is zero (relative to the atmosphere) at the top and increases linearly with depth. Again, the pressure acts in all directions (up, down, left, right).
Crummy examples literally
I have a couple of questions, but one of them is why do we always talk about pressure when talking about forces exerted by gases or liquids Why not refer to the push by fluids as simply force?
Pressure is force per unit area. We are concerned about pressure because the force that the water exerts (both the direction and magnitude) depends on the size and shape of the container.
I understand the concept, but I can't wrap my mind around it. So if I had a steel fuel tank and we filled it full and welded a very tall fill pipe on it. If we filled the tank and pipe with fuel that would increase the pressure on all bottom surfaces of the tank?
Yes, absolutely. Just the small weight of the fuel in the skinny pipe on top increases the pressure in the rest of the vessel. Re-watch the part about the upside-down-T-shaped container for the explanation.
Also, look up "pascal principle hydraulic jack" to understand how a small force applied to a narrow channel of fluid results in a large force in a wide channel of the same fluid. This is like a lever and fulcrum, which converts a small force applied over a long distance to a large force over a short distance.
@@graychang99 I understand the hydraulic jack, but the smaller piston has to move a farther distance to move the bigger piston.
Nice explanation
*So theoretically we could build a wall to hold out the ocean regardless of volume?* Proven by the Netherlands?
Yes. The pressure at a depth of 3 meters is the same, whether you are holding back the whole ocean or just a wall of water 1 cm thick. Only the depth matters, not the amount of water.
I thought this guy was a little... 'slow', but then he said, "water SEEKS its level" and now I know why. Water doesn't 'seek' anything, that's just something someone said and certain people think it sounds good so they keep repeating it.
If water 'seeks its level', why does it curve up on the sides of a container? Here another good question, why is there air pressure in the atmosphere at all? It's almost like there's a force pulling things toward earth, with more dense things closer to earth and less dense things naturally stacking atop, producing weight...
Water is fluid, so the air pressure (caused by gravity) causes it to move to the path of least resistance, which is determined by the pull of gravity on the water. Water is more dense than air so it displaces air until the forces are balanced.
If there was a vacuum at one end, the water would not "seek level" as he states, it would seek a counterbalancing pressure, which would be air, in this case. It would empty the other container easily. You're right, that phrase is not appropriate, really.
Can i get your email? I have question for you?
Go ahead and post your question as a comment.
G Chang i’m not good in english to ask question to you..if you don’t mind to contact me through email azwanakhbar85@gmail.com
His question is how to plant bomb 💣 🤣🤣
Amazing explanation
Great thanks
While the internal pressure at the bottom is the same in each, your explanation (and everyone else's) falls apart with the third container since for the lesser of volume of water to exert the same pressure on the bottom as the cylinder of same depth it would be exerting a force that exceed the force based on its mass - its weight - and that can be accomplished by only two ways, through expansion or increase in density, neither of which is possible with a liquid. Simply stated, a given weight of water in the third container cannot exert a force on the bottom greater than its weight (thus the pressure against the bottom is limited to that based upon its weight). I explain this in detail in a video titled Elementary Hydrostatics on my channel.
Did you watch the whole video? The apparent paradox of 12 N of water exerting a force of 30 N on the bottom of the container is explained by the opposing vertical forces inside the container. The extra 18 N of downward force comes from the inside of the container itself, pushing down on the water to balance the upward pressure of the water against the horizontal surface inside the container. Start watching at the 11:28 mark for the detailed explanation.
Thank you for responding. I did watch your explanation and I am thoroughly familiar with the detailed explanation as I debunk it in my paper: it is the textbook explanation, the so-called hydrostatic paradox. It is based on the presumption that a liquid acts as a gas in that the pressure exerted by the liquid is a function of the internal pressure which in the case of a liquid, as we know, is a function only of depth. Your explanation which I acknowledge, is the accepted explanation, is is based on this presumption. First your statement that the extra force comes from the inside of the container itself is inaccurate in two ways, 1) the reaction from the container is just that, a reaction, a passive force (no different than the reaction of the ground to you standing on it or to the building if you leaned on it, and as such is equal and opposite to the force applied on it, therefore, cannot exert a net downward force, and 2) the drawing used to explain the source of the force is a free body diagram , which by definition, is an illustration of forces acting on objects rather than an explanation of the sources of the forces. And this returns to my comment which is why the stated physics taking place is impossible: it is impossible for water to exert a force greater than that based upon its weight, which is why no one has ever explained the physics of how that is accomplished (as I stated, the only way for water to accomplish that is through expanding as a gas or increasing in density - this has to be pondered). This accepted hydrostatics was accepted without scrutiny 4 centuries ago. Again, with a gas the pressure exerted is the same as the internal pressure because of the characteristic of compressibility - as more molecules are added to a container of a gas it tries to expand resulting in the increase in pressure exerted by the gas against its borders reflecting the internal pressure. A liquid cannot; therefore the pressure exerted by a liquid is tied to its mass instead of internal pressure.
I see that you still have difficulty understanding how water can exert a force greater than its weight. Let me see if I can convince you otherwise. For your objection #1 (a balanced force cannot exert a net downward force), imagine that your 100-pound nephew stands on a scale, and you press down on his head, and hold it with a force of 10 pounds. This is a balanced static force -- you press down with a force of 10 pounds and his head presses back on your hand with a force of 10 pounds. Yet the scale now reads 110 pounds. The force is transmitted through his body to the scale at the bottom.
Your objection #2 is valid for a solid material, but not a liquid. The important property of a liquid (like a gas) is that it exerts its pressure forces in ALL directions, not just downward. So for the upside-down T-shaped container in my video, the NET force on the container is exactly its weight, 12 newtons, but this force is not just a single downward at the bottom; it is 30 newtons downward on the bottom and 18 newtons upward on the two horizontal surfaces on the legs of the "T": 30 N - 18 N = 12 N of net downward force.
Alternatively, consider compressing two iron springs and placing them (compressed vertically) inside the two lower sections of the "T" of the container, without any water. You can see that the force of the springs on the bottom can far exceed the weight of the springs, because they are pressing against the horizontal surfaces of the legs of the "T". This is exactly what happens when you put water in the container.
Thanks a lot.
by changing shape can we increase velocity like in water jet machine
Yes, that's true for water in motion. However, this video is about static water (water at rest, not moving).
Respected sir ,
Suppose for example if there is inverted cone shape structure of 3 meter diameter and 7 meter height and water is flowing downwards and another of same height and diameter which is of cylindrical shape at the bottom for both the shapes pressure will be same or different ? (if the fluid is dynamic)
Respected sir ,
Suppose for example if there is inverted cone shape structure of 3 meter diameter and 7 meter height and water is flowing downwards and another of same height and diameter which is of cylindrical shape at the bottom for both the shapes pressure will be same or different ? (if the fluid is dynamic)
Let's assume that the hole at the bottom of the cone-shaped and cylindrical containers is the same size, and plugged with a cork. The pressure on the plug is exactly the same. Then you unplug the cork, and the water flows out of the hole. Which one flows out faster?
I don't know for sure, but I would guess the cylindrical container would be slightly faster because the water surrounding hole (left and right of the hole) deeper and at a higher pressure than the water above the hole in the cone-shaped container. On the other hand, the water turns a corner to flow out, instead of straight down, which could affect the pressure profile.
But when you consider the concept of a submarine, it has a definite "shape", and that shape has "weight", which you have to take into account in order to avoid crush depth. All that water on top of the sub creating pressure exponentially as it descends lower, and lower. Yet, I'm still amazed at how whales can survive without all that heavy metallic material that protects all the sailors from certain death. Perhaps it's the fat in their bodies, but that would not explain other creatures that have no fat, perhaps their miniscule size plays a role, who knows for sure, but God. It's all interesting though.
Bad
Thank you Lord Jesus Allah Muhammad Buddha Ganesh and everyone else in the universe. I’ve pondered this question for over a decade and have never found the answer. Thank you!