The discussion revolves around the hydrostatic force exerted by a liquid on the bottom of a container, particularly focusing on whether this force can exceed the weight of the liquid itself. Participants explore the implications of different container shapes, such as funnel-shaped versus cylindrical containers, and the conditions under which equilibrium is maintained.
Participants express differing views on whether the force on the bottom can exceed the weight of the water, with some supporting this idea and others challenging the reasoning behind it. The discussion remains unresolved with multiple competing perspectives.
Participants highlight the importance of equilibrium in understanding the forces involved, but there are unresolved assumptions regarding the nature of forces exerted by the container walls and their role in the overall force balance.
If the fluid is in equilibrium then ##F=mg=\rho h A g##jzwillows said:If so the force could be greater than the weight of water and that defies logic.
An interesting question. What you are basically asking is if we take a funnel shaped container that is wider at the bottom than at the top, can we have more force on the bottom face than the total weight of water? And the answer is yes. The total forces on the water must be zero though. The bottom pushes up with more force than the weight (downward gravitational force), but the sides of the funnel container press partly downward on the water as the water presses (from water pressure) against this surface. Thereby the downward forces from the slanted walls plus gravity will equal (in magnitude) the upward force from the bottom face on the water so that the water is in equilibrium with zero net forces. The force that the bottom face presses upward is the same for a funnel shape as it is for a cylinder shape of the same height that is filled with water. The pressure at the bottom (force per unit area) simply depends on the depth of the water, plus any atmospheric pressure...editing... a follow-on: I believe a hydraulic brake works by a similar arrangement. You apply force (and pressure) at the narrow funnel opening. The pressure balances everywhere, but the bottom face has much larger area, thereby more total force on the brake pad than the force you apply with your foot. Instead of a funnel shape, you could have a somewhat narrow cylinder containing the water, with a wider bottom section, and it requires very little (weight of the) water in the cylinder to cause considerable force on the bottom face.jzwillows said:Is the force from a liquid against the horizontal bottom of a container a function of depth and cross sectional area at the bottom only, i.e., computed by the formula Force=unit weight of water x depth x cross sectional area? If so the force could be greater than the weight of water and that defies logic.
Thanks very much Charles.Charles Link said:An interesting question. What you are basically asking is if we take a funnel shaped container that is wider at the bottom than at the top, can we have more force on the bottom face than the total weight of water? And the answer is yes. The total forces on the water must be zero though. The bottom pushes up with more force than the weight (downward gravitational force), but the sides of the funnel container press partly downward on the water as the water presses (from water pressure) against this surface. Thereby the downward forces from the slanted walls plus gravity will equal (in magnitude) the upward force from the bottom face on the water so that the water is in equilibrium with zero net forces. The force that the bottom face presses upward is the same for a funnel shape as it is for a cylinder shape of the same height that is filled with water. The pressure at the bottom (force per unit area) simply depends on the depth of the water, plus any atmospheric pressure...editing... a follow-on: I believe a hydraulic brake works by a similar arrangement. You apply force (and pressure) at the narrow funnel opening. The pressure balances everywhere, but the bottom face has much larger area, thereby more total force on the brake pad than the force you apply with your foot. Instead of a funnel shape, you could have a somewhat narrow cylinder containing the water, with a wider bottom section, and it requires very little (weight of the) water in the cylinder to cause considerable force on the bottom face.
Charles Link said:An interesting question. What you are basically asking is if we take a funnel shaped container that is wider at the bottom than at the top, can we have more force on the bottom face than the total weight of water? And the answer is yes. The total forces on the water must be zero though. The bottom pushes up with more force than the weight (downward gravitational force), but the sides of the funnel container press partly downward on the water as the water presses (from water pressure) against this surface. Thereby the downward forces from the slanted walls plus gravity will equal (in magnitude) the upward force from the bottom face on the water so that the water is in equilibrium with zero net forces. The force that the bottom face presses upward is the same for a funnel shape as it is for a cylinder shape of the same height that is filled with water. The pressure at the bottom (force per unit area) simply depends on the depth of the water, plus any atmospheric pressure...editing... a follow-on: I believe a hydraulic brake works by a similar arrangement. You apply force (and pressure) at the narrow funnel opening. The pressure balances everywhere, but the bottom face has much larger area, thereby more total force on the brake pad than the force you apply with your foot. Instead of a funnel shape, you could have a somewhat narrow cylinder containing the water, with a wider bottom section, and it requires very little (weight of the) water in the cylinder to cause considerable force on the bottom face.
Oh, I misunderstood the question. I thought he was talking about a cylinder.Charles Link said:a funnel shaped container
thank you-that is very interestingbilly_joule said:Pascals barrel is a relevant experiment;
https://en.m.wikipedia.org/wiki/Pascal's_barrel
There's a hole in your logic (although it is textbook). The hole is the explanation that the liquid exerts a force against the that exceeds its weight because the funnel-shaped sides of the container press partly downward on the water as the water presses (from water pressure) against this surface, thereby adding the "additional'" force on the bottom that results in the liquid exerting a force exceeding its weigh. This explanation is flawed because it states the sides of the container exert an additional force, which is is impossible since the force exerted by the walls is a reaction, thus a passive force, and thus equal to the force exerted by the liquid against the walls, and thus being "equal" cannot produce "additional" force. As for the hydraulic brake explanation, although textbook, it is flawed because there is no vehicle to allow the force exerted by the brake pad to exceed that applied. The only "vehicles" which would permit this for a liquid a constant temperature would be an increase in density or expansion (as a gas), neither of which is possible for a liquid.Charles Link said:An interesting question. What you are basically asking is if we take a funnel shaped container that is wider at the bottom than at the top, can we have more force on the bottom face than the total weight of water? And the answer is yes. The total forces on the water must be zero though. The bottom pushes up with more force than the weight (downward gravitational force), but the sides of the funnel container press partly downward on the water as the water presses (from water pressure) against this surface. Thereby the downward forces from the slanted walls plus gravity will equal (in magnitude) the upward force from the bottom face on the water so that the water is in equilibrium with zero net forces. The force that the bottom face presses upward is the same for a funnel shape as it is for a cylinder shape of the same height that is filled with water. The pressure at the bottom (force per unit area) simply depends on the depth of the water, plus any atmospheric pressure...editing... a follow-on: I believe a hydraulic brake works by a similar arrangement. You apply force (and pressure) at the narrow funnel opening. The pressure balances everywhere, but the bottom face has much larger area, thereby more total force on the brake pad than the force you apply with your foot. Instead of a funnel shape, you could have a somewhat narrow cylinder containing the water, with a wider bottom section, and it requires very little (weight of the) water in the cylinder to cause considerable force on the bottom face.
Actually Pascal's Barrel is an anecdote-based, qualitative rather than quantitative, experiment/demonstration, as are all demonstrations "confirming" the principle that the force exerted by a liquid against the walls of the container is a function of the hydrostatic pressure rather than being based on mass.jzwillows said:thank you-that is very interesting
Actually the flaw in logic is yours and not @Charles Link's. When you have an action-reaction pair between two bodies A and B, if you are doing a force balance on A, you only include the force exerted by B on A (not the force that A exerts on B), and, if you are doing a force balance on B, you only include the force exerted by A on B (not the force that B exerts on A). Didn't they teach you that in your course. If they diden't, shame on them.jzwillows said:There's a hole in your logic (although it is textbook). The hole is the explanation that the liquid exerts a force against the that exceeds its weight because the funnel-shaped sides of the container press partly downward on the water as the water presses (from water pressure) against this surface, thereby adding the "additional'" force on the bottom that results in the liquid exerting a force exceeding its weigh. This explanation is flawed because it states the sides of the container exert an additional force, which is is impossible since the force exerted by the walls is a reaction, thus a passive force, and thus equal to the force exerted by the liquid against the walls, and thus being "equal" cannot produce "additional" force.
@Charles Link, in post #3, provided a perfect explanation of all this, without reference to hydraulic presses and jacks.OldYat47 said:The total force on the bottom for any liquid is (density X gravity X height X area of the bottom). The total force on the bottom can be much greater than the weight of the liquid. This may be counter intuitive but that's the way it works. It's all hydraulics. There are good articles about how things like hydraulic presses and jacks work that should clear up any confusion.
It appears my comment went over your head. Look a little closer. Try evaluating the logic of my statement.Chestermiller said:Actually the flaw in logic is yours and not @Charles Link's. When you have an action-reaction pair between two bodies A and B, if you are doing a force balance on A, you only include the force exerted by B on A (not the force that A exerts on B), and, if you are doing a force balance on B, you only include the force exerted by A on B (not the force that B exerts on A). Didn't they teach you that in your course. If they diden't, shame on them.
It appears you don't seem to understand our inputs on this. The thread was a year old, and it took an effort to read through the comments that we made a year ago, (Edit: Upon seeing @russ_watters post, I looked more closely at the date=yes, it is two years ago), but upon re-reading them, I think they give a very satisfactory answer to the problem.jzwillows said:It appears my comment went over your head. Look a little closer. Try evaluating the logic of my statement.
There are three forces acting on the water in the container:jzwillows said:It appears my comment went over your head. Look a little closer. Try evaluating the logic of my statement.
I am familiar with all you state - I initially acknowledged that which I am debating as textbook. As for the hydraulic jack, its principle is based on the principle that the applied force is transferred as a pressure, not force, a principle that has yet to be verified quantitatively.OldYat47 said:The total force on the bottom for any liquid is (density X gravity X height X area of the bottom). The total force on the bottom can be much greater than the weight of the liquid. This may be counter intuitive but that's the way it works. It's all hydraulics. There are good articles about how things like hydraulic presses and jacks work that should clear up any confusion.
I would add that the forces said to be exerted by the container differ from the forces exerted by the water in that they are passive forces. There is also the lateral force exerted by the water resisted by the container.Chestermiller said:There are three forces acting on the water in the container:
1. The downward gravitational force
2. The upward pressure force exerted by the bottom of the container
3. The the downward pressure force exerted by the slanted side(s) of the container.
Do you disagree with any of this? If so, which part.
There is no such thing as a passive force. There is no such thing as an active force. There is no such thing as an action force. There is no such thing as a reaction force. There are only forces. They come in pairs.jzwillows said:I would add that the forces said to be exerted by the container differ from the forces exerted by the water in that they are passive forces. There is also the lateral force exerted by the water resisted by the container.
I was asking only about the forces acting on the water. Was that not clear?jzwillows said:I would add that the forces said to be exerted by the container differ from the forces exerted by the water in that they are passive forces.
Like I said, I am asking only about the forces acting on the water. There are indeed lateral forces acting on the water by the walls of the container, but, if the system is in equilibrium, these cancel out. And, in our discussion here, I wish to focus only on the components of the forces in the vertical direction (since we are interested in the vertical force from the bottom of the container). Is this OK with you?There is also the lateral force exerted by the water resisted by the container.
No need to get testy, but there is a need to pay better attention to what you are being told.jzwillows said:It appears my comment went over your head. Look a little closer. Try evaluating the logic of my statement.
As for you being clear but not completely correct. I am fine with focusing on vertical direction.Chestermiller said:I was asking only about the forces acting on the water. Was that not clear?
Like I said, I am asking only about the forces acting on the water. There are indeed lateral forces acting on the water by the walls of the container, but, if the system is in equilibrium, these cancel out. And, in our discussion here, I wish to focus only on the components of the forces in the vertical direction (since we are interested in the vertical force from the bottom of the container). Is this OK with you?
This distinction is physically unjustified. It is a distinction without a difference.jzwillows said:TWhen a force is applied to a stationary object as opposed to the application of two opposing forces, the force being applied is active. The resisting force is passive. And while they are equal in one sense (magnitude) the are not in another since one is being applied and the other a reaction.
My attention is on correcting the misinformation presented. I have performed experiments sufficient to prove my points.russ_watters said:No need to get testy, but there is a need to pay better attention to what you are being told.
Or: it's been two years. At this point, why don't you just build yourself a test rig for this? Here's how:
Take a clear, flexible, rubber or plastic tube and attach it to a yardstick. Mount the cap of a 3 liter soda bottle to a board, with legs. Drill a hole in the cap and attach the tube. Cut the bottom off the soda bottle and screw the rest into the cap. fill completely with water. Note the height of the water in the tube. squeeze the bottle from the "bottom", making a flat wedge shape. Note that the water height doesn't change.
It should take you less than an hour! (if you have the parts)
Huh? What does this mean? Do you agree or don't you agree with the three vertical forces I identified in post #15?jzwillows said:As for you being clear but not completely correct.
Here is the reality of the situation: You have two Physics Forums mentors, a Physics Forums science advisor, and a Physics Forums homework helper (with over 75 years of experience between them) all arguing one way, and then there's little ol' you (with no identified credentials) arguing against them and accusing them of spreading misinformation. Their position is that it is you, not them, that is on the verge of spreading misinformation. Understand that spreading misinformation on Physics Forums is likely to result in infraction points and possibly a ban from Physics Forums. So please be careful and tread lightly.jzwillows said:My attention is on correcting the misinformation presented.