Fluids, Buoyancy, and Archimedes' Principle
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- Опубликовано: 27 авг 2024
- Archimedes is not just the owl from the Sword in the Stone. Although that's a sweet movie if you haven't seen it. He was also an old Greek dude who figured out a bunch of physics way before other people did. Some of this was discovered at bath time, so it has a lot to do with water, but don't get all weird about it, just listen to the old man in the tub. He's smarter than he looks.
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This was extremely well explained and presented. I'm 20+ years out of high school and was curious about this topic. I tried other videos but they are riddled with so much scientific jargon that I can't tell one term from another much less understand the topic at hand. Of course, they left some important things out making it more difficult than it has to be. You made this video understandable for everyone regardless of age or educational background - as it should be! Thank you!
I have to learn this in 6th grade sigh
@@King-fr4bd same lol
different countries different years
Everything i search about on youtube, professor Dave has answers for it. ❤
Exactly😄
@@Ice-tx8kc i love you
Everything?
Right
this teacher is a hero. God bless professor dave.
You all probably dont give a damn but does anybody know a tool to get back into an Instagram account..?
I was dumb lost my password. I appreciate any tips you can give me.
@Elisha Vincenzo instablaster ;)
amen
yes there are enough subscribers but why doesn't anyone like the videos ,so busy on your studies .He is the best teacher till date he should get a million miles per video
I agree but be nicer
You need to control your self my lady find a good doctor before* is too late...
You are right. Him and Organic chemistry tutor
@@Triptocrete bruh you care too much about some commenter in the internet, go get some sunlight. (Dont forget to like the video 😂)
thanks so much for keeping your videos short and to the point! saves so much time when studying :)
My eureka moment came to me when I discovered how to determine if an ant was female or male. It's really quite simple. Drop the ant in water. If it sinks girl ant. If it floats....
Lmaoo
Really? I'm gonna do it
Things that float are boyant
2:14 The ship weigh less than the water it displaces - This is NOT correct. The weight of the water displaced weighs the same as the ship since it floats. Correct?
Yeah I got confused
The water is more dense than the object that is displacing it. They will have equal volume, but not equal weight. That's what creates buoyancy, since the buoyant force is equal in magnitude to the weight of the displaced fluid. It's not equal to the weight of the object.
If they were equal, the ship would sink right up until it was completely submerged
No
Thanks Professor Dave! Appreciate all the great videos.
At the 02:00 the arrows showing the force are not proparlly sized which is an inaccuracy, my teacher got mad at me when i showed this video to the class.
The buoyant force is more than the weight force. This is just an introductory video, so that's all that matters. Your teacher needs to take a chill pill
What a great explanation!!!!
Lifesaver mate. Needed to understand this to teach it to my Year 10s. Now I can properly explain it to them. The only video that made sense to me. Thank you and God bless.
Can always play the video in class too. Everyone loves a video break and visuals
This is a great vid. The only issue I have is the sentences "A floating object displaces fluid based on its mass. A sinking onbject displaces fluid based on its volume". It seems like there are two different 'laws' due to which the floating objects behave differewntly from the sinking objects. Hmmmm....
Think about it like this. An empty water bottle floating in a sink is raising the water level of the sink by a tiny amount proportional to mass of the bottle. If you push it under water the water level increases a lot due to it displacing the entire volume of the water bottle. Now imagine filling the bottle with water from the tap and pouring that water into the sink. The water level will increase exactly the same amount as when the empty bottle was forced under.
1:29 I actually worked in that ship for around 2 years.
Lol 😂
Thanks Professor Dave!!! What a fun name and channel you have
Excellent explanation, thank you very much.
Professor Dave,
I have heard several formulas for calculating buoyant force on an object :
f = mg
f(b) = Volume displaced by object * acceleration of gravity * Density of fluid
f(b) = volume OF the object * acceleration due to gravity * (density of fluid - density of object)
Which equation do you use in what scenario and why? Please Advise. This video was very helpful
The first f(b) is the formula for the buoyant force, and the second f(b) is the sum of the gravitational pull and buoyant force, which is the effective acceleration an object experiences at rest, and it shows how buoyancy 'reduces' the pull of gravity. (note that I said at rest because if the object is moving relative to the fluid, drag and lift forces will also occur)
Sorry this question is probably so basic, but just want to make sure....... 1) The volume of the ball = the volume of the water displaced because the ball was fully submerged? 2) The volume of the water displaced turned into 5000g because you plugged it into Density=M/V?
yes and yes! water is 1.0 g/cm^3
hey I was wondering at 2:11 whether on the force diagram the arrows are equal or not, if the buoyancy force is greater than the weight of the ship wouldn't the ship be "floating" into the air? so when its floating on the surface of the water both opposing forces are equal and therefore the fnety = 0?
You are right. He has it wrong. The ship does NOT weigh less than the water it displaced.
I agree. The ship's weight and the weight of the water it displaces are equal. That's basically Archimedes principle.
I had an exchange with professor Dave on this very comment section a couple of months ago on the subject and he wouldn't admit he was wrong. I guess you could find it. It's worth a read.
If that were true, when you pushed a beach ball into the water, the ball would stand still and not float back to the surface.
If the air was water we could say the ship would float into the air...
Basically:
The force will just stop being applied onto the ship after the ship is out of water
Moral of the story:
Sober up before studying physics
(jk, Dave could explain it better with an animation of interaction between the water particles and the ship )
Your videos are inspiring, Professor
fuck
poo
I don't really get what the meaning of a floating object displaces fluid based on its mass. I do understand a sinking object displaces fluid based on its volume because you know water is pushed out as a result of the object occupying the volume. But can you elaborate why a floating object displaces fluid based on its mass? Thanks
Well, that means that heavier floating objects will displace greater amount of fluid
@@Adecto so?
Elaborate
When an object is floating on the surface of a body of water, the volume of the object below the surface is equal to a volume of water with the same mass as the entire object. For example, if you put a block of wood with a mass of 3 kg in a bucket of water, the volume below the surface will be 3 L (or 3,000 cm^3), because that volume of water has a mass of 3 kg. Now suppose you make the block heavier by putting a 100 g weight on top of it. The block sinks slightly further into the water until it has displaced 3.1 L (or 3,100 cm^3) of water. As long as the weight of the object is equal to the weight of the water it displaces, it will continue to float. If its weight is ever greater than that of the water it displaces (i.e. if it's denser than water), it sinks.
Unfortunately, that is not a robust definition of a fluid. One could absolutely say that a solid can flow and change its shape when it is plastically deformed (or even elastically deformed if we are just talking about shape change). It is even referred to as plastic FLOW and the FLOW stress when we discuss plastic deformation.
The robust definition of a fluid is a substance which will continue to deform limitlessly under a constant shear force.
(I understand perhaps the intended audience of this video is more suited to a more simplistic definition but I think one should still be aware of this.)
In maritime industry they say weight of the vessel and weight of the cargo but they express it in kg and tonnes. In order to calculate momentum of stability we need force × lever, but for force we input mass of the object (in tonnes). Is this because m × g (force) = V × g × density (buoyant force) and since on both sides g is equal we can "pretend to be smart/stupid" and say ship has deadweight of 10000 tonnes and loads weight of 500kg. I was great in high school in physics but when I went at maritime college they just turn my hair gray calling mass weight, and that area of the triangle can be calculated (side a × side b)/2. Teacher said that it is OK to do it like that since side a is very similar to height of c side... I do not care if they are the same in the 10th digit, area of the triangle is height times side divided by 2. I refused to call mass weight and I got low grade. Your opinion? (PS. I am a teacher now and I am working on my own book for students and I want to call it as it is, mass is mass.)
Can you do a video on the conversion maps of organic compounds? Such as how alkanes can alkenes and vice versa?
I tried to understand it but the giant maps of all the different solutions and reactions confused me.
Thanks Prof.
there isn't really too much to say about them, they just list a bunch of possible transformations. it's like someone took a bunch of lecture notes and condensed them into an image. they can definitely seem overwhelming! it just shows you ways to transform different functional groups and what not.
@@ProfessorDaveExplains tnx
2:15 Not true. The forces must have the same value.
Can we also say that the ball is being acted on by a force pushing upwards equal to 5kg? If gravity is assumed to be constant, why use Newtons instead of g or kg?
Kilograms (kg) are a unit of mass while Newtons (kg * m / s^2) are a unit of force. The difference is that a given object always has the same mass, but its weight (the force of gravity) depends on what objects are pulling on it and how far away they are. For instance, if you took a 5 kg object to the moon, it would still have the same mass (5 kg), but only about 1/6 the weight it has here on Earth (8.125 N vs. 49 N).
Mathematically a force is a mass times an acceleration (F = ma). On the surface of the Earth the acceleration due to gravity (g) is approximately 9.8 m / s^2. Multiply that by the mass of an object and you get the force of gravity acting on it in Newtons.
The unit of Newtons are introduced, in order to make Newton's second law equation work elegantly and simply. Fnet = m*a. Since acceleration has the units of meters/second^2, and mass has the units of kilograms, then Fnet needs a unit of kilogram-meters/second^2, which we define as the Newton.
Since Earth's gravitational field is not equal to 1 m/s^2, an object's weight in Newtons is not equal to its mass in kilograms. When kilograms and grams are informally used as weight or force units, they refer to weight in Earth's gravitational field. 1 kg-force is defined as 9.80665 Newtons, and 1 gram-force is a thousandth of this value. The value of 9.80665 N/kg is used, because this is a representative average of Earth's gravitational field.
I need stuff like this explained on a kindergarten level. His explanations give me enough to understand the principle without the specific scientific speak. Good enough for guberment work.
A liquid X of density 3.36g/cm^3 is poured in a u tube in right arm with height 10cm,which contains mercury.another liquid Y is poured in left arm with height 8 cm.upper levels of X and Y are same.what is the density of Y??
well you said: The buoyant force will support the object IF the OBJECT IS LESS DENSE than the fluid (ρ object < ρ fluid) because the weight of the object < weight of the fluid (with the same volume). And about the ship floats you said: w ship < F buoyancy. The ship weighs less than the weight of the water it displaces, so it floats. HOWEVER, isn't it supposed to be W ship EQUALS to the F buoyancy (if they float??) or all my years in school I have been taught the wrong thing? It's equal because the weight of the ship has to be canceled out by the Fa and so we can calculate this: ρf.Vfdisplaced = ρobject.Vtotalobject
How do you calculate waterline if the object has non uniform density?
Well, this video alone was my eureka moment for me for understanding this principle.
@gurman lall Seriously, I'm a physics student who kept studying a lot to principles and the concept of buency never I had a grasp for, until this video.
and what if the ball was filled with cement to equal 40N, the buoyant force would only be 4N until it found equilibrium and had 40N of buoyancy for the 40N weight.
I love ships and buoyant force is something that really puzzles me, I just cant comprehend how strong it can make a ship of tons of weight to float in the sea
ah, the way of the university student is to look for answers with Prof Dave. He is absolutely helping me get my degree
I understand everything it really helps
That's right, the explanation is very easy to understand
Wasn’t Archimedes testing whether or not the Kings crown with gold or not using water displacement? That’s why he said Eureka.
While he did develop a test to determine the volume of an object of any shape by measuring the water it displaces, his "eureka" moment was when he figured out that the same principle (the displacement of water) causes objects to float. A floating object displaces a volume of water with a mass equal to its weight.
you are the best man.keep up.thanks
For a seconds I thought I was watching a kiddie show. Intro Music Kills it.
but then you got to all the amazing knowledge and you couldn't believe it, right?
Oh yeah! Thanks! wish you could make one about bernoulli
Sir What about Current electricity? Would you upload videos on Current electricity?
those are coming soon!
Short and sharp video
I never knew Q from Impractical Jokers knew so much about physics
Thanks sir
What if half object sinks?
Matter can also take on a fourth state called plasma...
thank you
If a object is hydrophobic and is technically not touching water, is the object stil buoyant?
Yes. The buoyant force (like all contact forces) is caused in large part by molecules repelling one another. A hydrophobic substance repels water more strongly than most other substances.
@@wizardsuth ah ok thank you for the explanation
thanks!
Hey do you have a podcast??
I did but nobody listened to it so I stopped!
@@ProfessorDaveExplains whaaat! I never knew about the podcast... maybe it was not advertised enough 😑☹️
Thanks a lot
If we take a ball of same weight and volume. The buoyancy and weight will be balanced so if we put the ball on height 'h' from top then will it go up (float), or it will go down (sink) OR it will be on 'h' height only (as it is not practically possible that an object stays the place where it was)
If you take a neutrally buoyant ball that is equal in density to water and completely rigid, and immerse it in incompressible water, then it will neither float nor sink. It will remain at the initial position you placed it, and if you give it an initial velocity, it will move at a constant velocity, since the forces add up to zero.
In reality, no object is infinitely rigid, and water isn't perfectly incompressible. If the solid object is more flexible than the water in its ability to change volume under pressure, then this will be an unstable equilibrium. If the object descends, then it will experience more water pressure and compress, thus becoming denser than water, which will cause it to sink. If it rises, then it will experience less water pressure and decompress, thus becoming lighter than water and floating. This is the working principle of Cartesian divers, where you can compress a water bottle and make the divers descend. And counteracting this instability is a major design challenge for making a submarine neutrally buoyant, so it can hover in water.
By contrast, if the object is more rigid than the fluid, then the equilibrium will be a stable equilibrium. As it descends, it experiences a denser fluid that causes it to float, and as it rises, it experiences a sparser fluid that lets it sink. This is why objects that are buoyant in air, will naturally rise to a cruising altitude, where they experience a stable equilibrium, because air is a lot less uniform in density than its liquid counterparts. So blimps and balloons have no trouble achieving a stable flight in air, unlike submarines in water.
@@carultch oh damn thanks, that was really helpful
i actually died watching this
f
I don't get it sir were did you get 9.8n/kg
It's a constant of this planet. It is the Earth's gravitational field strength.
Perfect teacher just perfect👌👏
Brilliant teacher
I kind of feel ashamed that I had to look up this topic because "a certain group of people" would bring up density and buoyancy in their arguments to disprove gravity but I lacked the knowledge to refute them...
@@traversniemi5342 No friend, it is you who need think things through more carefully.
Cool!
Thank you.
1:27 So has Dave hired a Finnish (or Swedish) graphic designer lately, since the Stockholm-Helsinki ferry shows up all of a sudden? 😅
buoyancy isn't a force though.... do you mean upthrust?
The buoyant force is a reactionary force to gravity.
1:42 I don't know how you get to that from Archimedes' principle.
My guy just saved my chemistry test
After watching like 8 useless videos I finally figured it out on my own: the water isnt exerting any special force on the floating object. Instead whats happening is gravity is pulling down harder on the water than the boat because the water is more dense. This extra downward pull on the water forces the boat out of the way because of displacement. This is what causes the boat to float.
Its like the water and the boat are competing to see who can get get to the bottom. The most dense object wins and because 2 objects cannot occupy the same space the boat gets forced upward by default, because its not heavy enough to beat the water for the bottom.
Buoyancy does not work in a weightless environment. Its gravity that gives boats their magic.
that's a great to way to think of it! except you must see that there is indeed a force being exerted, the buoyant force, in the same sense that a chair exerts a force on your body, the normal force. but your conceptualization is indeed sound.
Only in the sense that the electrons of any object repel the electrons of any other object. There is nothing inherently special about boats or water or buoyancy in general.
Explaining it as its own unique force is very confusing. There is only gravity and electron repulsion at work. The resulting "buoyancy force" is merely a side effect of gravity pulling harder on the water than on the boat.
I'm trying to give you constructive feedback and also help everyone else who might be reading. I looked through a whole bunch of buoyancy explanations and they never once mentioned this. They just say "boats float because of the buoyancy force" and never explain what that is or where it comes from or how this even works. They all make sure to mention the boat must weigh less than the water or it will sink, but not why this is important.
well yes, but in this way all the forces we discuss in classical physics are actually just other forces in disguise. the frictional force is a manifestation of the electromagnetic force. centripetal force, normal force, the tension of a string, none of these are fundamental forces. but they are excellent descriptors of phenomena, so we still use these terms.
His comments aren't ridiculous in the slightest.
He's right; a boat's flotation is entirely due to gravity acting more greatly on the more dense water than the less-dense boat thus displacing the boat upwards to a point of equilibrium.
@@Anon-gx6ih I think you've got the concept. If an object displaces some of the molecules in a fluid, others are effectively pushed upwards against gravity, and this causes them to push back with equal force. Although buoyancy is caused by countless molecules interacting via electrical forces, in physics we tend to simplify our models by looking at the net effect, which is an upward force exerted on the object by the fluid. Indeed, Archimedes figured this out before anyone knew anything about electrical forces or the internal structure of matter. One clever fellow, that.
Why do we take acceleration due to gravity in calculating upward buoyant force? Please reply
Because the buoyant force is a reactionary force to gravity.
@@ProfessorDaveExplains thank you so much, for prompt reply 😊 you're doing great work 💯
@@itsmrbrightside179 Buoyancy works like an inverted Atwood's machine. There is coupled motion between the displaced parcel of fluid equal in volume the volume of the object immersed, and the object itself. But instead of interacting through tension in an overhead string, like the coupled motion between the masses in Atwood's machine, an object in water interacts through the differential hydrostatic pressure of the water nearby, and the displaced water also experiences buoyancy from the rest of the water body. Instead of the pulley in Atwood's machine, you have the pressure on the water from the bottom of the container, that supports the entire body of water.
To find the upward force of the water don't you have to find the real weight which is the weight when it's not in water-the apparent weight which is the weight in the water?
hmm, well the weight of an object should not matter whether it is in water or on land, as weight is simply determined by the mass of the object and the strength of the gravitational field
so, it doesnt matter what the different weights are in a situation. you just have to find the mass and times that by 9.8
yes mass times g is how you calculate weight in any scenario
ok, but why in other videos they say to times the volume times the density then times by g to find this buyont force
or to take away different weights
nice video!
can you explain pascal principle.
can u pls explain in more simplified terms?
If p(object) < p(fluid), the object, will float. If p(object) > p(fluid), the object will sink. The volume of water displaced by a sinking object is equal to the volume of that object.
This means:
Fb = pgv
Where:
Fb = buoyant force
p = density
g = gravity
v = volume of displaced fluid
Yo i went through like 13 videos on why ships float and pebbles sink even though ships weigh more than a pebble. This is the only video which explains Archimedes principle of buoyancy with clear explanation. Cheers Dave
Sir please take a video on Pascal law
thank u man!!!!
is this the same as isostasy?
Can anyone tell me what does the phrase "displaced water" mean here? It's really confusing 😭
I upvoted your comment! Yay!
Fill a bucket with water up to the brim, then stick your arm in all the way to the bottom. The displaced water is what sloshes over the sides. To put your arm in the water, you have to displace (push aside) a volume of water equal to the volume of the part of your arm that's under the water. If the bucket isn't full, the water level rises as you put your arm in. Making the water move upwards like that requires you to exert a force, and the water pushes back with equal force.
Thanks Dave - my professor is a little wonky, but when you teach me the same things she does I know it must be legit
Love you from India 🇮🇳 🇮🇳
arnav is is you?
Aren't there five forms of matter: solid liquid gas plasma and BEC?
yes, but the latter two are not really of interest unless discussing particle physics
Yes. And there are buoyant forces in plasmas as well. If you were an astrophysicist studying the sun, you would be calculating buoyant forces in plasma as the surrounding fluid.
However, introductory examples tend to stick to situations that most students can easily relate to here on Earth, and therefore stick to buoyancy in liquids and gasses. There are ways you can make buoyancy occur in solids, and Bruce Yeany has experiments that show it occurring in agitated sand.
Oh no
simple
ZOMG, no!!! The ship weighs THE SAME as the water it displaces. But the water, being denser than the mostly hollow vessel, takes up LESS VOLUME, so a bouyant ship remains only PARTIALLY submerged below the surface until it displaces enough water that the ship's weight, and the displaced water's weight, are the same.
Everything you said was true except the statement in the yellow box which also appeared on the thumbnail.
No, that's correct.
If the ship weighs less than the water it displaces, how much less? Surely it's the same.
@@captainoates7236 I don't know how much less. It's an imaginary ship. But it weighs less than the water. That's how it floats. If it weighed more, it would sink.
Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
The statement above is a description of the Archimedes principle copied and pasted directly from the wikipedia article on buoyancy.
I apologise for trying to correct you as you are far more qualified than I and I know wikipedia is not completely reliable but the operative word here is 'equal' and not 'less' whether the body is floating or not.
@@captainoates7236 If you are having trouble comprehending the sentence you just pasted, I suggest watching this classical physics series from the start.
Incomplete question 😢
Is archimedes principle the same as buoyancy?
Nooo
Archimedes principle is the method for calculating the buoyant force in a situation of fluid statics. Buoyancy or the buoyant force, is the upward force an object experiences by virtue of being immersed in a fluid.
Where did he get the 9.8 from?
it's a constant, acceleration due to gravity on earth.
Professor Dave rocks
Solids can be fluids
They cannot.
Archimedes was not onboard the Titanic.
Good thing.
Greetings and Salutations
I thought #Lift & #Accuracy makes #motorboat base arks float
I posted on Facebook that's what brought me here
But why is buoyant force acting in the first place? Is it because of newtons 3rd law?
Since the buoyant force is proportional to the water displaced, is it that the water is trying to counter act the constant displacement done by the objects mass and acceleration due to gravity?
It isn't due to Newton's third law, but otherwise you're right.
The water has weight due to gravity. If you displace some of it, the volume you displace is forced upwards against gravity. The displaced water pushes back with a force equal to its weight. We call this upward force buoyancy.
The buoyant force occurs because of the pressure gradient in the fluid. Pressure (relative to surface atmospheric pressure) is proportional to depth below the surface, for a fluid of uniform density. This causes a stronger force of fluid pressure at the bottom of an immersed object and a weaker force at the top. The difference between the two pressure forces on the object, yields a buoyant force.
@@carultch Wow Thanks! I've always wondered why buoyant force acted in the first place. You have answered 28 year long life question. XD
@@jomarico1770 No problem, glad I could help.
Another way to think about it, is that buoyancy works like an inverted Atwood machine. It's coupled motion between the immersed solid, and the displaced fluid, because the displaced fluid has to move in exactly the opposite direction as the solid. And they both interact through the buoyant force, that maintains this coupled motion.
Mass 1 is the displaced fluid, and mass 2 is the immersed solid. Except instead of a pulley, we have the bottom of the container pushing up on the entire fluid medium, and instead of the tension in the string, we have the fluid pressure as it interacts with the immersed object.
Great teacher ❤
Nice explained
Thank you Physics Jesus
Sir kindly answer my question
what question
Um, answer to what?
@@ProfessorDaveExplains he made another comment with the question
Sir try to explain at molecular level as why and how it happens .as anon say evrbody explain boat nobody telll a how
Thanks, it was educating
Excuse me, Sir. I have one question. How buoyant force behave in microgravity where there are no up and down?
It doesn't. Water tends to coalesce into a sphere due to the electrical attraction between water molecules. Objects don't have any particular tendency to float or sink in it.
Professor, will there be any more videos on circular motion like torque, moment, angular moment?
unfortunately no that was the last stuff for motion, i'm moving on to thermodynamics, but feel free to email me with questions!
oh no! Torque is a very important topic in classical physics, please try making just one video if you can manage time.....People may wonder how the rotation of engine shaft/ turbine has changed the world so far and things would get more clear with your knack of explaining things simply!
oh i did release a video about angular motion and torque yesterday, did you see that one? i thought you were asking if i would do more on that subject on top of that tutorial.
uh-oh... sorry professor, I didn't notice! you already posted a video on torque... thanks as always
NICE
science jesus
don't get it, far too much jargon
The ship weighs exactly as much as the water it displaces; not less.
you are very right
The volume of water displaced is denser than the equal volume of the ship in the water, therefore the displaced water weighs more. That's what's holding the ship afloat. Think of it like a big, steel beach ball full of air.
@@cc_snipergirl
Nope; the water is pushing up exactly the same as the ship is pushing down.
The weight of the water being displaced is exactly the same as the weight of the ship; provided the ship is floating.
That is buoyancy.
The total volume of the ship is not relevant; as long as it is at least the volume of the water necessary to weigh as much as the ship is displaced.
@@michaelpcoffee The volume of the water displaced is determined by the volume of the object displacing it. The density of the object displacing the water determines if the object sinks or floats. The formula for the buoyant force is density of the object*volume of fluid*gravity.
@@cc_snipergirl
The volume of the water displaced by a floating object is determined by the weight of the object.
The guy that discovered that said 'ureka'.
You explained it, but you did not explain what caused it 😅
I did. It's the reactionary force to gravity.
Professor. I want to ask, is there any relation between buoyant force and hydrostatic pressure?
Yes, as a matter of fact there is. Consider a cubic meter box, immersed in a deep lake, with water pressure on all sides of it. To make the math easy, assume water's density is exactly 1000 kg/m^3, g is exactly 10 N/kg, and the ambient pressure at the top of the lake is exactly 100 kPa. Place the top of the box 10 m below the surface. This will mean that the top experiences 200 kPa of static pressure, and the bottom experiences 210 kPa of static pressure. The force on the top of the box is therefore 200 kN downward, and the force on the bottom of the box is 210 kN upward. The net force from the water thus far, is therefore 10 kN.
Do we need to consider the sides? Well, there will be hydrostatic pressure on the sides of the box, but any pressure on the left side, will experience equal and opposite pressure on the right side. Same with the front and back sides. So pressure on vertical surfaces will add up to zero. This allows us to conclude that the net buoyant force is 10 kN.
According to Archimedes principle, it should also equal the weight of 1 cubic meter of water. 1000 kg/m^3 * 10 N/kg = 10 kN. And look at that, both methods agree and get the same answer.
Ty sir!!