Archimedes principle vs. Bernoulli's Principle
Archimedes' principle, or the law of upthrust, is: "When a solid body is partially or completely immersed in water, the apparent loss in weight will be equal to the weight of the displaced liquid."
In other words, when a body is partially or completely immersed in a liquid, then it experiences an upward buoyant force which is equal to the weight of the fluid displaced by the immersed part of the body.
Bernoulli's Principle states that for an ideal fluid (low speed air is a good approximation), with no work being performed on the fluid, an increase in velocity occurs simultaneously with decrease in pressure or a change in the fluid's gravitational potential energy.
This principle is a simplification of Bernoulli's equation, which states that the sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is the same at any two points in that path. It is named after the Dutch/Swiss mathematician/scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others. In fluid flow with no viscosity, and therefore, one in which a pressure difference is the only accelerating force, the principle is equivalent to Newton's laws of motion.
19 comments:
Archimedes, easily for the win. Even if it were not for his improvements of the catapult, the design of the Syracusia, Claw of Archimedes, burning glass, and so on, I would still give him the nod.
Any principle which can cause a grown man to run through the streets of Syracuse naked yelling "eureka" should never be taken lightly.
I'm going with practicality again, but only because I can't think of anything better today.
Perfect substances don't exist, as we've discussed previously, so Bernoulli wasted his efforts on imaginary materials.
If he had assembled a storyline based on an imaginary world, like J. K. Rowling or J. R. R. Tolkien, he could have done something really worthwhile. I mean, it's hard to beat defeating imaginary evil wizards by orchestrating your own imaginary death, or imaginary miniature people saving an imaginary world by throwing a super-powerful imaginary ring into an imaginary volcano.
Yeah - Archimedes wins, since the only thing he displaced was normal fluids, and he really did it.
Archimedes = boats float.
Bernoulli = airplanes and helicopters fly.
So which wins, aircraft or boats? Well, considering the fact that since World War 2 people stopped building battleships and started building aircraft carriers I think we know the answer to this one. The only thing boats are goo for is carrying the best stuff to where it needs to go. Cage fights are won by the fighters, not by the limo drivers.
Bernoulii for the win!!
tommyp - perfect substances may not exist, but as a "practical" matter we engineers and scientists use these theoretical substances to understand and predict things.
badanswer - I'll grant that Archimedes himself is cooler and more awesome than the man Bernoulli (at least theoretically, I never knew either of them - Archimedes may have been a jerk and a fruad, we don't really know). But the fight here, as I understand it, is between the laws themselves. And given that I think I have made it clear why Bernoulli's Principle kicks Archimedes' principle to the curb.
kit, I am trying to be as objective as I can when I say this, and I mean no disrespect, but you are wrong. Granted, this is a cage match between the principles, not the scientists, so you are not all wrong in your comment. Based on your simplification of Archimedes = boats, and Bernolli = airplanes, historically boats are much more important. But for the sake of brevity I will simply reiterate my first-last point from above: "Any principle which can cause a grown man to run through the streets of Syracuse naked yelling 'eureka' should never be taken lightly."
I will grant that over the course of history Archimedes' Principle has done more for mankind. No question.
But dispite what Hollywood films would have you believe - when yesteryear's legend comes up against today's best...the old guy loses. Records are being broken constantly. The fact that the current world record for a 1-mile run is less than 3 minutes and 45 seconds does not erase or disrespect Roger Bannister's achievement. It just means Bannister would lose the race.
As does Archimedes.
Well, kit, I appreciate that you "engineers" can make up stuff to prove whatever you want, but we all know that it's still made-up.
I mean, magic rings can make you invisible, and a wave of a magic wand can cause your friend to barf slugs, but it doesn't mean that it really happens.
Fantasy is still fantasy, even if people as special as engineers are the ones making stuff up. Besides, I can see lots of practical value in becoming invisible or making my friends barf slugs. I can't see much practical value in carting around imaginary fluids.
tommy, that just shows your lack of understanding.
Working with simplified, idealized, and approximated systems is what allows us to accomplish things without God-like omniscience. Scientists are still working out an understanding of the building-blocks of the universe. But still we are somehow able to make things like boats, cars, airplanes, satellites, paper, medicine, artificial hearts, and the internet. All of those things use, in one way or another; simplification, idealization, or approximation of the real world in their design and creation.
Imaginary fluids aren't around for you to cart around, they are here to make your life better. But if you don't want them, that's fine with me. I just ask that you not use any of the things built using them. Like aircraft, air conditioning, jetskis, internal combustion engines (like in cars), or electricity (since most electrical power plants use methods that involve Bernoulli's "imaginary fluids").
kit - Interesting that you claim God-like omniscience, yet admit that scientists don't yet have an understanding of the building-blocks of the universe. If y'all are so good at making stuff up, you would think you could come up with something interesting for universe building blocks.
Your argument is starting to sound like anti-evolution rhetoric. The idea that you can come up with a substance, the existence of which can't truly be tested, and use it with impunity, is tantamount to claiming the universe was created by a giant marshmallow. The basic premise of Bernoulli's Law is flawed, as it's entirely based on a substance that can't be proven not to exist.
So if you want to believe that the world was created by a giant marshmallow, and that life did not evolve, I would ask you to cease from enjoying the benefits of evolution.
tommyp and kit,
As this discussion continues I would ask you to keep it civil. So far there have been no deaths attributed to my site, and I would like to keep it that way.
tommyp, your claim of scientists not having "come up with something interesting for universe building blocks" shows your ignorance of String Theory. Perhaps I will attempt to rectify this in coming weeks.
kit, if you are requesting us not to use your listed engineering successes, can we still use the failures? You know, the Tacoma Narrows bridge, the Challenger or Columbia, or the Mars Polar Lander; or are those off limits as well?
badanswer: Sorry, I will try to keep the comments here cordial and uplifting. Even when they are addressed to someone that evidently reads "without" as "with".
As far as the failures mentioned please keep in mind these facts. Tacoma Narrows failed because of an unknown, and therefore addressed, factor. The Mars Polar Lander was a communications failure, not a technical failure. Challenger was a combination communications and ethics failure, the technical aspects were understood. Columbia was also a failure due to an unaddressed factor, but in that case it was a factor that probably should have been known and addressed. All of them can be considered engineering failures, but the theories and techniques (based on simplified or ideal laws) were not the point of failure.
I am also only suggesting that those that feel the scientific laws and theories based on simplified or ideal cases are useless give up the benefits based on those principles.
Thinking that one law is better or more useful than another is not the same as thinking something is useless.
For instance, whether I accept a literal reading of Genesis, evolutionary theory, or the myth of the Flying Speghetti Monster; I still feel that evolutionary theory is a useful scientific tool and therefore I'll feel free to enjoy any advantages it gives me.
Perhaps tommyp feels the same about Bernoulli's Principle, but the statements he has made here lead me to think otherwise. If my reading of his comments is flawed I apologize.
kit, Bernoulli allows planes and helicopters to fly in air. The same air that resulted in the friction build up for the Columbia, and in the form of wind accounted for the resonant vibrations of the Tacoma Narrows bridge. This air is also a major contributing factor so events such as hurricanes and tornadoes. All I am saying is that the (mis)application of Bernoulli may blow up in your face (pun intended).
Fair enough. I probably did not stress sufficiently that while simplified and/or ideal laws and principles are useful (and neccesary in many cases), they must be used with a good understanding of thier limitations.
As you point out, misapplying those laws or nor using the correct ones can lead to problems. Tacoma Narrows, for instance, was never analysed for resonant aerodynamics until things started going funny. By not applying the correct set of simplified aerodynamic laws problems were not discovered until it was too late.
Bernoulli's Principle still wins against Archimedes' Principle though.
kit - I was only suggesting that scientists actually pretended to have a God-like omniscience, since they could pretend to have access to whatever else they wanted, as long as it satisfied their whims (or physical/computational inadequacies).
Pretending that something exists not only oversimplifies a scientific principle, it oversimplifies the results of any principle based on this principle.
This is one of the reasons that "accidents" like Columbia, bridge collapses, or other such events occur. Because of science's shortcomings, including simplification by removal of confounding variables (inclusion of "ideal" materials), scientists (and humanity) gain a form of hubris.
This hubris is what allows us to stand on each others' shoulders, pushing the limits of our scientific endeavor further and further, while ignoring the underlying complexities that can often throw a proverbial wrench into so many technological endeavors.
Thus, many people take for granted the advantages these advances provide, forgetting the basic principles that allow their use.
This is even further evidence that Archimedes' principle should have complete dominance over Bernoulli's. Archimedes was making simple observations at the most basic level. Bernoulli's work came about 1500 years later, and obviously stood on the shoulders of previous work. This is particularly true of many of the technological advances you referred to, which combined many principles in complex machinery.
In one case you have provided, airplanes do draw some of their operation from the principle described by Bernoulli, but not as much as has been previously assumed - Evidence from NASA website. Note that the mix-up to which you are attributing aircraft lift is also due to an over-simplification based on both Bernoulli and Newton's equations (second to last paragraph on the page).
OK, I didn't want to pull Navier-Stokes into it but here goes.
There is no current work that actually accounts for everything in aerodynamics, because it would involve (like most everything else) getting down into sub=atomic particles. But as i mentioned to badanswer, selectively ignoring certain elements gets you answers that are more than good enough to do the work.
For instance, matter travelling through the air creates friction and therefore heat. But at speeds below Mach 1 the heating aspect is so small that it makes no effective difference, so we ignore it. This continues on and on until you rach the point where things actually matter for the accuracy you need.
Here's an example. Say you give me a basic mission for a helicopter (size, weight, distance, etc). in less than an hour I can give you the size or the rotor, engine power req'd, and most of the other basic of the helicopter. I do this with all kind of simplifications, including pretending the rotor is a magic disk that moves air rather than individual blades. *poof*
You can then spend a million dollars and 3 years designing the helicopter for that mission to much greater detail. And my 1-hour numbers will be within 10% or so of the final helicopter's. Now if you want a full helicopter you are going to need to spend more than an hour on it. But an hour is more than enough time to tell you whether your helicopter will fit on your boat.
Now when the time comes to figure out how to get that last 0.5% efficiency out of the rotor, you may want to pull out the full Navier-Stokes equations and your CFD (Computational Fluid Dynamics) program and let your computer chew on it for a day or two. And then run your second case, for a day or two. 3 weeks later you might have an answer. Assuming you set it up correctly.
I'm sure by now you realize that my background involves aerodynamics. (Which might have something to do with my passionate defense of Bernoulli) :) Should you care to divulge your field of expertise, I'm sure I can find an example of using simplified/ideal equations being a good idea.
As a general example, let me guess that when figuring out how long it will take to get somewhere you do not pull out the relativity equations and calculate your time dilation.
HOW DARE YOU BRING NAVIER-STOKES INTO THIS FORAY!!!
I have memories from fluids I am trying to repress. One more outburst like that and you will be banned. Assuming I can figure out how to do that. I am sure a little simplification of the problem can make it much easier.
Now you're taking all the fun out of my arbitrary selection system. I study chiropteran habitat ecology in forest ecosystems. Bats in the woods.
So technically, I should actually side with you, because without the principles involved, my favorite organisms would not exist.
But this isn't about what's true or not - if it was, our illustrius blog captain badanswer would have no way to peddle his "information".
I do have to admit however, that I have learned more on basic physical principles over the last few weeks than I've learned in a long time ;)
Back to the issue at hand - deterministic computer models are only capable of handling so much stochasticity. They only model it, based on probabilities. Problems arise through user error, certainly, but occasionally there are design flaws that shouldn't exist, but do.
That 10% difference you mentioned could (not will, but might) be the cause of a catastrophic failure. That's where our lack of understanding can cause us issues.
The fact that many of the basic equations that even computers use are based on non-deterministic information allows for stochastic events to occasionally surprize us.
I oversimplified this for laughs, laughed, then kept reading. Did you check my link? Bernoulli's principle really isn't as big a part of aircraft lift as generally taught, unless I misunderstood the NASA article.
I have been silently observing the discussion at hand and have found that the time has arrived for me to comment. I do choose Archimedes as the winner in this particular battle. My reasoning is listed below:
"Legend describes how Archimedes uncovered a fraud against King Hieron II of Syracuse using his principle of buoyancy. The king suspected that a solid gold crown he ordered was partly made of silver. Archimedes took two pieces of pure gold and of pure silver that had weights identical to the weight of the crown. He then successively immerses the gold, the silver, and the crown in a container filled to the brim with water and measured the volume of water that overflowed with each material. He found that the crown displaced more water than the gold but less than the silver, thereby proving that the crown contained some other metal which was less dense than gold." http://www.juliantrubin.com/bigten/archimedesprinciple.html
How cool is that? C'mon, when did Bernoulli fix a King's crown or have any sort of association or audience with royalty? Never, that's when.
Easy win for Archimedes.
Post a Comment