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B An odd question regarding Bernoulli's Principle

  1. Feb 15, 2017 #1
    I don't know if anyone remembers me. I'm not a physicist but I tend to do pretty well at understanding some of the basic principles of classical physics, and that's recently created food for thought on my part.


    There's a message board I've found that is devoted primarily to debunking popular myths and conspiracy theories, but there's plenty of sensible talk about current topics there too. There's a discussion there about the Oroville Dam incident, and some ideas have been floated regarding what might have led to the failure of the floor of the main spillway. One or two people are suggesting that it was the Bernoulli Effect, where as water flowing over the floor slab of the structure speeds up due to the steepening downward slope, the pressure applied to the slab decreases so much that the slab is lifted from its base by the pressure of non-moving water underneath the slab (and yes, the soils below that slab must be perpetually saturated - there's no way to prevent it). I'm not accepting that the Bernoulli Principle applies in such a case. For what it's worth, I spoke with an engineer who remembers having had a number of classes regarding the design of open structures for water flow, and the Bernoulli Effect was never mentioned in that context. Anyway, I'd like some help either supporting or modifying/disproving some ideas I have for why Bernoulli's Principle was not a cause for this failure.


    My First Reason For Not Believing This:
    Okay, the idea that the slab of the spillway might lift due to increasing the travel speed of the water flowing across it is not too outrageous on the face of things, given that virtually everyone knows that the reason that some kinds of flat roofs on buildings are weighted down with a layer of gravel is to reduce the tendency of the roof to lift due to differential pressure during extreme wind. In fact, one apartment building I lived in had a 50-pound trap door to the roof, held down only by gravity over a set of guide rails, and on one very windy day, that door lifted up and flipped over, hitting the roof with a terrible bang. But I think there's a key point here. In a building, whatever pressure is exerted against the bottom of the roof by still air contained within can expand to maintain that pressure as a section of the roof (or heavy trap door) rises due to the reduction of air pressure on the top side, and due to the rather large amount of reserve volume, the air pressure on the bottom side will remain essentially the same as it does so (the reduction in pressure as that inside air expands very slightly is negligible). Thus, the air in the building essentially "maintains contact" and "keeps applying pressure" as the roof rises. Now, can the same happen with water on the higher-pressure side of a concrete slab? For all practical purposes, water is the same volume at all pressures, and conversely, it has no ability to expand when pressure exerted on it by an outside force is reduced, so even if the pressure applied by flowing water on the top side of the slab were reduced to zero (and even if the slab had no weight of its own), the water beneath the slab would be unable to expand and cause a lifting force. Right? Correct me if I'm wrong.

    My Second Reason For Not Believing This:
    I understand that any fluid being forced through a pipe or hose will experience a reduction in pressure at locations where the cross-sectional area becomes less and the velocity must therefore increase. Though I have long since forgotten how to do the math, I understand that the principle is that the total energy of the moving material cannot change, so if velocity increases, pressure must decrease, and visa versa.

    However, the dam spillway in question is just an open trough, and as such, the pressure exerted by water on the *sides* and *floor* of the vessel is at least in part (and perhaps entirely) a function of the mass of water that is present, and the force applied on that material by gravity. I don't see that simply increasing the speed of the water and changing nothing else can reduce the force applied to the trough because that would be the same as making the water weigh less. Taking this a step further, in this spillway situation, when the water increases speed as the slope becomes steeper (and perhaps due to its downhill acceleration), the volume of flow per unit of time (usually expressed as cubic feet per second in such cases) must remain the same since "what comes in" to any given section of the trough equals "what goes out". With that in mind, if the velocity of the water were to double within a certain section of the trough, the depth of that water would be reduced to half of that prior to the velocity increase, so volume passing per unit of time remains the same.

    Now, here's what I'm thinking. I don't know if there might be other ways in which the pressure of the water might be reduced when its velocity in an open trough increases, but there should be pressure (or some component of the total pressure if things are more complex than I know) applied to the floor of the trough no matter what happens, and that pressure should be the weight of the water per unit of floor area. For example, if water weighs roughly 62 pounds per cubic foot, a six-foot thickness of flowing water will apply a pressure to the floor of 372 pounds per square foot, and if the velocity were to double so that the thickness of the flowing water were cut in half, the pressure applied to the floor would be 186 pounds per square foot (for simplicity, I'm ignoring the fact that the normal force applied to the slab is not vertical, and thus is somewhat less than the full gravitational weight of the material). Is that correct? If so, it seems to me that there would be no way to reduce the pressure applied by flowing water to the floor of the spillway to less than that which is due to the water's actual weight. Further, recalling Reason #1 above, the water beneath the slab would never be able to "push back" to lift the floor in the first place, since all it can do (assisted of course by the soil who's pore space the water occupies) is support the force of the slab that is due to gravity, whereby any reduction in that applied weight (such as mechanical lifting of the slab by some outside force) will simply result in an equal reduction in applied force from below, the same as what happens if you don't apply all your body weight to your bathroom scale.

    So, am I totally wrong in my assessment of this problem, or am I missing something? Thank you.
     
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  3. Feb 15, 2017 #2

    boneh3ad

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    It has nothing to do with the Bernoulli effect (which isn't even technically the name of any principle of fluid dynamics). Or at least, it has nothing to do with it in the way you've described. Bernoulli's equation does have a term in it related to gravitational potential energy, so in that sense, it plays into what happened in this situation. The water flowed downhill, so it exchanged gravitational potential energy for kinetic energy. In reality, the average static pressure in the water would be the same at the top and at the bottom.

    The real issue is shear stress. You have this massive quantity of water rushing down the slope at a high rate of speed, but at the surfaces, the velocity has to be zero (the no-slip condition). This means there is a pretty sharp velocity gradient right at the surface, which means very high shearing stress. That stress will slowly tend to pull loose bits of the concrete away, leading to erosion. Compounding the matter is that any time the surface has a defect (such as one caused by a bit of concrete flaking away), it can form vortices and recirculating regions that would amplify the erosion. Effectively, once the process starts, it will tend to accelerate.

    Then, once you open up large enough cracks and chips in the surface, water can penetrate and even lift up larger chunks of concrete.
     
  4. Feb 15, 2017 #3

    Simon Bridge

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    [I got beaten to the punch...]
    ... if you do not intend to cite it, then there is no point even mentioning it.
    ... you mean this thing? https://en.wikipedia.org/wiki/Oroville_Dam#2017_spillway_failure
    OK. I get that.

    The reason I'm being a bit nit-picky about your description there is that you say this discussion site concerns debunking popular myths. This is an area I have a lot of experience in. There is a standard of evidence for these discussions to have merit and your description here fails at the most rudimentary of them. If you want to be effective, you need to up your game.

    ... well the default position is to withhold belief - it is up to the people proposing the idea to defend it, you can then concentrate on discussing the arguments.

    The first thing you need is a proper articulation of the claim.
    For instance, in fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. There's none of that stuff about pressure from other fluids, or anything. Someone is adding another effect into the description without saying so.

    Bernoulli's principle certainly applies - it is the law of conservation of energy basically - but it won't be the only thing that applies.
    The argument is that there is a pressure difference between the top and bottom of the slab that is sufficient to lift the slab (and redirect the flow of water above it)... and that this pressure difference is due to the speed that the water flows.

    I'd have asked how they ruled out other effects.

    The proponents are probably not arguing that Bernoulli's principle is the only thing that is important here, just that the mechanism described is the largest and most important contributor. You do not need to argue that it does not apply at all, which you seem to be trying to do, to refute the argument.

    You have argued that water does not expand, so the proponents have to explain where the extra volume of water (appearing under the raising slab) comes from. That is a valid point, how do they answer that?

    You have argued that the derivation for Bernoullis principle involves a closed pipe, so maybe it does not apply to an open trough.
    You will want to check with rivers here - clearly water flows faster through the narrower parts of the river, but is the pressure in these parts lower? I think this is something you aught to be able to look up.

    Lets say it is - isn't that water slower at the top than at the bottom? Wouldn't this mean there is a difference in pressure between the top and bottom ends of the slab? Could that produce a torque that may lift the bottom end of the slab? The extra water needed would come from above the slab, pushing or being sucked under it. Has that argument come up?

    [Like boneh3ad points out - not actually true but it is intreguing that this is not thought of]

    I'd be more concerned the Bernoulli applies to laminar flow, and the flow here is far from.
    I'd also wonder why the slab did not lift prior to this - according to the argument as stated, the slab should have lifted pretty much right away?

    I am not finding anybody else talking about an individual slab lifting from the spillway ... reports talk about large holes. The discussion sounds more like speculation on how slabs of concrete may fall from a spillway surface. This is why it is important to get a clear statement of the claim.

    ** Spillways can take a hammering over a long time - the surface slabs can become loose from constant pummelling, and the material beneath gets saturated ... it expands irregularly, turning the slabs so they are more vulnerable to damage. Eventually some slabs fall out like bricks fall out of a wall.

    You may want to examine the physics of how water moves in stream or river.
    http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/RiverViscosity.htm
    Also: discussion involving bernoulli in a river:
    https://www.physicsforums.com/threads/bernoulli-and-flow-in-a-flooding-river.451818/
     
  5. Feb 16, 2017 #4

    russ_watters

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    Bernoulli's Principle does apply here, but in order for the water to be able to lift the concrete, it would require negative pressure above the spillway -- meaning the water would be pulling the spillway up. Obviously, water cannot apply negative pressure.

    This isn't like lift on an airplane where you have a baseline of positive pressure above and below the wing when the wing is stationary. For the dam spillway, there is no positive pressure baseline either above or below it to reduce with motion.

    The simple explanation is best: Cracks -> erosion
     
  6. Feb 16, 2017 #5
    Thank you all. Briefly:

    The name of the site where such discussion is occurring is metabunk.org. The proposition that the slab was being lifted was not one of the myths being busted there, but it was an earnest belief of one of the contributors to the discussion. He actually provided about a page-and-a-half of calculations backing up his idea that a truly enormous lifting force was being exerted by the rushing water, but since the idea that the water on the slab could somehow do that didn't make sense to me in the first place, so I didn't try to wade through his mathematical reasoning. The nature of the site is such that I don't want to get into an argument with the guy who proposed this idea, and though I did reply to him at one point I just thought that if a simple way becomes apparent for pointing out some clear flaw in his argument, I may mention that.

    I appreciate the detailed reply of Simon. Just to respond to a few items that can't be lumped into what I said in the previous paragraph, yes, rivers have zones of faster flow, but I haven't found evidence that the pressure is affected by much more than just how much water is "stacked" above the point of measurement (gravity again), but then, it's not a topic which lends itself to easy internet searches. As to the person's response to my idea that the water below the slab cannot "push up" from below as the slab rises is something that he did not address in his reply. Perhaps that's a good reason to just let it go, and I probably will, but I thought it would still be fun to find out whether someone might come up with some insight that would make this "click" a little better for me. And, yes, I'll check out the links Simon provided.

    As to the remarks about actual cause of the failure, I wasn't actually looking for that but I don't mind hearing ideas. It's actually a subject I am familiar with since my area of expertise (at least in my work life) is soils and foundations, and there are a number of factors involving the native existing bedrock which most likely are involved, beyond the fact that the slab "takes a beating".

    I welcome any additional comments regarding this magical slab-lifting phenomenon.
     
  7. Feb 16, 2017 #6

    russ_watters

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    Consider this: if you punch a hole in the spillway, does water flow down through the hole or does air get sacked up into the water?

    Or; is the spillway supported by the hillside or held down (kept from flying away?) by the hillside? Can dirt hold tension?
     
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