Fluid has so much to bend the mind. Soliton waves, shocks, expansions, critical transition phenomena (besides phase transition)
Look at froude number and planning hulls, the purpose of chines, steps, etc. in a high speed hull to manage skin friction vs wave drag. Wave Dispersion, wave superposition, etc. the free surface itself means if you are solving for flow, flow then determines the free surface which then determines the flow.. add infinitum. It’s nonlinear like a baby general relativity in that way. The shallow water equations are hyperbolic so you get shocks etc. deep water, long wavelength waves act in linear fashion so you get superposition effects. On and on. Fun times.
I took the introductory fluids course at my university but eventually gave up as I could never figure out the right approximations to take and I couldn’t build the intuition. It didn’t help that I was paired with a guy I didn’t like for homework.
Some of my friends did like it though (one got to explain how he spent his summer in the maths department learning about fingering.)
After I graduated, I returned to visit some friends doing master’s degrees and it was only at this point that I learned there was a moderately large laboratory under the maths department doing real physical experiments with actual fluids.
Fluid mechanics is a standard course in many undergraduate engineering curriculum. A quick Google search reveals lots of open-source and downloadable pdfs of printed texts.
Mr_overalls has the overview idea covered. I might add that if you start with the Reynolds transport theorem, you can’t go wrong, but that might be the wrong-math-way-around for you.
Are there particular aspects you are interested in?
E.g.
Computational methods
Turbulence
Topology / geometry
Shocks and expansions
Superposition, radiation/diffraction, added mass
Analogues with other systems
Some of this stuff involves simplifying assumptions. Sometimes those reveal neat corners of behavior. (E.g. the superposition business)
Some of it might be better introduced qualitatively at first, like say turbulence. It all depends where you are.
By the way, I don’t know some great amount of this stuff at some expert level. I may be able to guide you in some direction of interest is all.
I wish I knew of an overview which scanned across all this funny behavior but some is pretty widely separated.
Naval architecture text books focus on the linear aspects, and the free surface of course.
Cfd (computational fluid dynamics) just about has to deal with “everything else”
except the topology and “geometry of” (physics, mechanics, fluids, etc) which kind of lives the hermit life, like the quaternions or geometric algebra or something.
There must be a few general equations that capture all these behaviors in fluids right? That is, aren’t all these just “emergent” aspects of some fundamental physics?
There are additional aspects that may or may not be lumped in somebody’s exposition - such as the transport of heat and coupling of the energy equation in the compressible Navier-Stokes equations.
I'm building a system for measuring levels in water tanks using submersible pressure sensors (triggered by living in a dry area and being totally dependant on our tanks).
Quality sensors cost a lot - too much for domestic purposes. Much cheaper ones can be bought from China, so I've been looking for some way to test them, without actually altering the level in a gigantic water tank.
It occurred to me I should be able to just use a thin vertical pipe. But as you say, this seems counter intuitive, especially if the pipe is barely wider than the sensor itself. Just doesn't... Feel right.
I've been using ohm/square for decades. I know the math. I've measured it. It works. I know it's true. But my mind refuses to accept that ohms/square can possibly be a unit. Every single time my mind is like, "ohms per square what?"
My understanding of that is that it's using "square" as in aspect ratio like how screens are 16:9 or whatever, while "square" in units is more commonly used as in `exp(n, 2)`. And that terminology mismatch is why it often doesn't seem to make sense.
It’s called head - and it’s a key calculation in if a dam is worthwhile. The pipe feeding the turbine can be quite small for a lot of power if the head is large.
You could also use a small pressure vessel/sealed tank, and pump in water with a hand pump. You could simulate nearly any sized tank that way too.
Hey, also, why not just find the height of the water level by attaching something ultrasonic to the inspection hatch (or whatever). https://www.adafruit.com/product/4664
Not accurate enough. I want to be able to quantify e.g how much water was used to water the garden. In a 25K litre tank, that's a very small change in level.
Its basically the Bernoulli's equation. Its because pressure is force over area and the mass of the body of water above it is area times height time density so the area cancels out. You can add velocity into the equation and its a conservation of energy equation. Similarly there is a continuity equation which is a conservation of mass. These two are the backbone of a beginning fluid mechanics course in engineering.
That's interesting because it seems perfectly intuitive to me.
Both in terms of understanding the physics (weight of water above the column divided by the area of that column, and then any water around the column just has to have the same pressure to contain that column) and just plain practical experience from e.g. dipping underwater in the ocean and not getting crushed like a bug.
It is very counterintuitive when you reason in terms of weight though. If you imagine a pile of rocks for instance, it makes sense that the strain on the base of a pyramid is lower than on the base of a column of the same height and base area.
You have to visualize the atmospheric air pressure to reconcile the result with intuition.
I mean it's perfectly intuitive to me that a pyramid of rocks isn't going to collapse, so you don't need a container to hold it in. The closer analogue would be pouring sand in to a tube vs. pouring it in to a bottle that widens below the neck - it's intuitive to me that the bottle would be under enormous strain to hold the sand in. (And, incidentally, the part of the bottle where it widens would be applying extra "weight" to the sand below it)
This is one of those physics phenomenon where I feel like they are a software bug. Bell's Theorem and a lot of quantum entanglement stuff is like that as well.
It’s actually quite intuitive, as the force is distributed over a larger area. So although the pressure gradient isn’t affected by the discontinuity in the container size, if you compare forces exerted by the pressure on a plate in either section of the chamber you’ll observe that the force on the wider plate would be reduced to compensate for the increased area in the presence of the same pressure.
I'm not sure why you're being down-voted. If you double the size of a water column, you of course double the total weight pressing down. But you've also doubled the cross-sectional area, so the weight-per-unit-area (pressure) remains the same. This is pretty intuitive if you understand what pressure is.
Perhaps because the explanation (and indeed concept) isn’t that intuitive so the comment may be read as dismissive?
If you see pressure as coming from the weight of the fluid above and now replace fluids with solids for a mental model, it obviously doesn’t work: imagine two parallel rigid plates connected by some rigid structure. The top plate will represent the (fluid) boundary between the top of the barrel and the tube and the bottom plate the bottom of the barrel. If you put a narrow column of metal on the top of the top plate, then the pressure exerted by the bottom plate is, say, p. If you make that column much wider, increasing the weight above, the pressure is say 10p.
I think the problem is that this intuitive model of pressure is just wrong but if it doesn’t come from the weight of the water above, it is hard to intuitively see where it does come from.
Your example is completely different though. Considering neighboring water columns isn't like adding more to the top of the plate, it's like setting up an entirely different plate next door. Which of course doesn't affect the first instance at all.
The point is that the way people typically think of the problem leads to examples like mine, and this is why the concept is unintuitive. It doesn’t matter whether the model is correct—the whole point is that it is the incorrect model many people will have or start with.
Pressure is force per area, the area doesn't matter by definition. Similarly to how we measure rainfall in millimetres: volume / area = length.
Whereas if you were to place a bucket of water on your head, the area of the bucket would surely make a big difference to the force you feel, all else being equal.
A fun thought experiment is to realize that if the earths atmosphere were totally removed except for a cylinder that encircled your house and went into space, you would feel physically the same. Just like in the water, in some sense the only thing air pressure cares about is how much air is directly on top of your head.
On those oddly shaped reservoirs, the walls compensate for the lack of a water column above the places where it widens. The actual force on the water is the same as would be in a cylinder.
why is it counter intuitive for you? It is not to me at all. Gravity pulls down. There is essentially no lateral component to gravity. Height is measured in the verticle dimension, the same as gravity. Now imagine water column as a stack of pennies. The more pennies are added to the stack the more pressure is on the lower pennies. It does not matter how many stacks are in front of or behind or to side of the stack you are looking at.
> There is essentially no lateral component to gravity
Yet you can distribute the weight of a structure on larger bases. If you put two columns on pennies on a steel plate, the pressure under the plate will be higher than if you put only one column.
It is easy to imagine the bottom vessel as similar to such a plate.
I think the key to make this intuitive is to realize a few things:
- pressure in liquids are transmitted differently
- water is actually very slightly compressible
- atmospheric pressure is also an important part of the system
The intuition with the columns of pennies over a plate doesn't translate because in the plate case the surface is fixed (the surface of the plate) so the pressure depends on how much weight you put on it. In the case of multiple columns of water, the pressure you're looking at is the pressure on the combined surface of both columns, which remains constant because both the weight AND the surface are increasing proportionally, keeping the ratio (that gives you the pressure) constant.
> Yet you can distribute the weight of a structure on larger bases.
In the case of solid objects, indeed. This is because in solids atoms are bonded together and so the weight can distribute. An easy and extreme case of this last statement is to imagine standing on a bridge. Your weight is supported not just by the part of the bridge underneath you, but, via transmission, by the two end points attached to land.
In liquids, the atoms are not bonded, so the same distribution cannot happen.
Nobody is saying this fact about liquids isn’t true. We all know it’s true, so proving it doesn’t change anything.
It is counter intuitive though precisely because the pennies analogy doesn’t work.
If I put a 1m stack of quarters on a pressure gauge, then I put one quarter on the gauge and a stack of pennies on top of it up to 1m high, I get two different readings. Conversely if I measure the pressure at the bottom of two bottles the same shape as the stacks of coins, I get the same readings.
If you measure the pressure at the bottom of two bottles containing different density liquids the same shape as the two stacks of different coins you get two different pressure readings.
In case it was not clear in my analogy a "penny" (it can be anything solid and incompressible) is representative of a water molecule. If you want to compare the pressures of stacks of pennies and quarters because for some reason you are fixated in these specific physical coins rather than what they represent then I will make it explicit. Imagine pennies represent water and quarters represent mercury. Two different liquids, two different coins, two different pressures. I don't get what you guys don't get.
Can you explain to me why you think it is intuitive that the downward pressure of a liquid at the bottom of a container should vary for equal depths but different volumes? E.g. you seem to intuitively think that if you have a big pan filled with 1 inch of water the water pressure at the bottom of the pan is greater than the pressure at the bottom of a 50 ml flask also filled with one inch of water. This is false but I am interested as to why you and the others think it is "intuitive?" Where does the additional force come from to increase the pressure in the bigger pan? Gravity pulls straight down.
In my case, the difference in intuitiveness is that I am used to things crushing because of weight/force but not because of pressure.
If you have a bottle of 1 kg of water and put it on a plank between two stools, what matters to know if the plank will break is the total weight (and torque) of the bottle and the surface of contact. The shape of the bottle is irrelevant.
When you have that image in mind and someone suddenly tells you that actually no, 1 kg of water on a 50 meters high column can actually break things 1kg of water in a bucket can't, it is very counterintuitive.
And the stack of pennies is really unhelpful I feel. Make an inverse pyramid with 1000 pennies, all of them resting on one at the bottom tip, or make a column of these, the force exerted on the bottom one will be the same. The force per area as well. Not so with water.
The difference is that the water molecules move until they find an equilibrium in which there is a gradient of pressure and where molecules push back in every direction equally. Pennies do not, they are content exerting "pressure" in a single direction
Water exerts pressure in a single direction too: down. There is no PSI gradient in the lateral direction. This is intuitive because there is no force acting in that direction. I do not believe water molecules ever find a topological equilibrium in a liquid phase. Because then they would be a solid or a crystal. Water as a liquid can flow but it still only exerts pressure in the downward direction. To my analogy, pennies can slide or move from one stack to another (e.g. waves). The only thing affecting the pressure on the bottom penny of a given stack at a given instant is the number of pennies in that same stack resting on top of it. What is going on in the adjacent stacks does not matter, because gravity only pulls down.
Actually, yours is not such a great explanation, since a stack of quarters would manifest greater pressure than a stack of pennies. Whereas, a fluid column would manifest the same pressure no matter the diameter.
No, a stack of pennies would manifest a greater force, but the pressure would be the same. Pressure is force per area, which means that the increased weight from a wider column is exactly cancelled by the increased area that the force is distributed over.
Ok, yes, this holds true if the support surface increases the same. But the parallels still do not hold too well. Imagine sort of a funnel holding water, no matter the thickness of the base or top, the fluid pressure at the base is the same. Whereas with coins it does not work the same.
Hmmm ... reinforces my counter-intuition. The stack of pennies might explain why the bottom of the jar would explode, but not the sides, area not below the stack of pennies.
My intuition (wrong here) is that the extra surface not beneath the stack of pennies (your analogy) would in fact distribute the pressure and therefore represent a lower PSI on all sides of the jar.
I guess I translated "pennies" into "little bags of water". The little bag of water at the bottom only gets pressurized from the little bags of water above it.
And so the bottom bag's "pushing" outward from compression would be affected only by those above it.
Usually some very fine abrasive particles are added to water-jet cutters because the water alone doesn’t cut so quickly if at all. Similarly, the depth of a cut can be limited as it only really works if the water goes all the way through (otherwise the pool slows down and redirects the force from the jet)
The Wright brothers, in trying to figure out how to design an airscrew (propeller), assumed it would work like a ship's screw, and went looking for the theory behind it.
There was no theory, ship's screws were designed by trial and error.
So the Wrights invented the first propeller mathematical theory. It produced propellers that were 90% efficient, about double the efficiency of other experimenters' ad hoc propellers.
Double the efficiency meant the Wrights needed half the horsepower to get into the air.
>There was no theory, ship's screws were designed by trial and error.
The early marine propeller designs consisted of an Archimedes-type screw with multiple full turns. During tests of one such design on a small boat in the Paddington Canal in London, half of the propeller broke off. The broken propeller (with only one turn) turned out to be able to propel the boat twice as fast. [0]
The inventor, Francis Smith, amended the patent to describe either a single-turn screw propeller or one with two screw threads each describing half a turn (essentially a two-bladed propeller).
The propeller efficiency aspect is why I don't believe all the other "first powered flight" claims. The Wright Flyer had barely enough power to get airborne, and that's with the double-efficiency propeller.
Attempts to build flying replicas of the other claimants' machines don't impress me because they don't address the power needed to get those contraptions into the air with the engines available at the time. (The Wrights couldn't find an engine with the power/weight needed, and had to design/build their own powerplant.)
That is mostly because you only get to be famous as a hull designer if you make "beautiful" hulls (ie for yaghts and stuff), and beauty is very difficult to express mathematically. The people designing containers ships don't draw their lines by hand but rely on large amounts of computing power to compute hull stresses and squeeze every last bit of storage space out of their designs.
As an interesting anecdote, when I was still working for the (Dutch) navy they had a project going on to use constraint solvers to generate new submarine designs. The design team would generate 10 designs every week, take them to the sub guys who would spot new problems ("there is no bathroom close to the command deck" for example) and then go back and translate all the problems into new constraints for the solver. Later iterations even had VR models so they could "walk" through the virtual ship.
I can relate. I wrote a constraint solver as a pre-processor for my curve and surface generator. Never quite made a “beautiful” hull…. Probably an issue with my objective function and graduation constraints ;)
Have you ever tried to model a sailboat hull in AutoCAD, SketchUp?
I remember trying out all the"new" cad software in the 80/90's, it was impossible.
I still think it extremely difficult. What you can do by hand is easy, conceptually and practically. Software is there now, but still extremely complicated.
Not a single bit of straight line, anywhere, in any direction!
I've not tried, but I'm familiar enough with modern CAD software to know how I might approach the problem. Basically you draw your cross-sections as NURBS curves, then let Catmull-Clark subdivision make a smooth surface.
Naval architecture is a fascinating and beautiful discipline. This post does it justice.
It's too bad there aren't many naval architecture careers in the US. We hardly design or build any ships here anymore. The one exception is military ships. So if you have a naval architecture degree your main employer options are a) government or b) government contractor.
It depends on what you mean by "deeply" and how you wish to go about it.
If you want to try and pick it up on your own, start with the book "Introduction to Naval Architecture" by Thomas Gillmer and Bruce Johnson, from the US Naval Institute. From there, if you're still interested, probably "Applied Naval Architecture" by Robert Zubaly or something from SNAME (Society for Naval Architects and Marine Engineers).
If you want to go to school and you don't want to get a degree in it, you can study something similar; but, related. (I majored in Ocean Engineering, which included a number of naval architecture courses.)
If you can afford it, go ahead! At least aeronautical engineering is a solid (and not easy) full time degree program. Embry-Riddle is one well known school, and they may be doing online classes/have some coverage.
Some hull shapes are inherently unstable. The slightest deviation from pristine vertical balance will make the ship flip. However, even hull shapes that are initially stable at some angle reach their limits. All of these examples assume the deck is perfectly sealed and that water doesn’t get into the hull.
Loosely related: here is a video of the German Maritime Search and Rescue Service (DGzRS) trying to 'sink' one of their (then new) smaller rescue lifeboats which has self-righting capabilities:
Yeah, this is a fantastic blog post but is a little inaccurate in some edge cases.
In solo around the world races like Vendee Globe, the boats are required to be fully buoyant and self righting no matter how they end up. The most common approach to achieving this is to rig a canting keel with a device that when the boat capsizes, lets the keel swing to one side, creating a weight imbalance that rights the boat. They're quite serious about it too: you don't get to race the boat unless you demonstrate it works that way at the pier.
There are hull forms (without the canting keels I mentioned) that have positive righting moment through 180 degrees. Life rafts are universally designed this way. For boats it's just not that necessary ultimately, as capsize is pretty dang rare on keel boats as a baseline. Vendee Globe et all are hardasses about it because they know if the worst happens, there's no rescue possible on a short timeline.
This page is so well done. All physical and mechanical problems should be taught this way. I just loved playing with the sliders. I felt like I didn't even need to read the text to understand the concepts. This could be a great alternative teaching style for bored kids.
I am just fascinated by the amount of work and effort that goes into this. A simple view-source shows tens of thousands of lines of code... for a free blog. Incredible
Bravo. As usual, Ciechanowski makes extremely easy to understand, graphical expressions of complex ideas. Highly recommend this site and his other topics.
Nice visualizations! Next how about response amplitude operators and statistical response in a random wavy sea? Spectra of Motion, force, etc are really compact tools for design analysis. The linear theory is quite beautiful in my opinion. Not Maxwell’s equations beautiful, but up there.
Speaking (indirectly) of the equations of motion, I didn’t see added-mass as I scanned through. Could be fun to talk about as well as diffraction radiation.
Somehow the above are more fun sounding to me than Navier Stokes. I dunno. My burnout shifts with time.
{ // Start of block statement.
const foo = "a" + 2; // Only available inside block statement.
console.log(foo); // "a2"
} // End of block statement.
console.log(foo); // Uncaught ReferenceError: foo is not defined
Expanding on that question, does anyone know of a place where work like this gets discussed? I was unaware of his stuff, which is indeed wonderful, and if there is a way to meet with others who are interested in this kind of thing, and in doing it for ourselves, I'd sure like to be there.
Reminds of something my father, a sailor in the British Merchant Marine, told me. He was recounting a ridiculous North Sea gale, basically hurricane force winds. The ship plunged into the trough and then topped the waves, the screws coming well out of the water every time. "It gave me a new respect for naval architects", he said.
Very intuitive. I wish there was a list of exemplar visualizations for different subject matters. It's 2021, there's still a lot of bad textbooks out there, emphasis on books.
> at the scales we’re interested in we can assume its value doesn’t change.
The reason submarines can be neutrally buoyant at specific depths is because water is compressible, and water's density changes with depth. Adjust the submarine's density to match the water's density at a certain depth, and the sub will be neutrally buoyant at that depth.
No it isn't. Submarines can be neutrally buoyant at any depth because they have the ability to control their density. The fact that water is slightly compressible has no effect on submarines' operation.
No, WalterBright wasn't the one who worded it badly. Seems you still need to think about it some more: How does adjusting the density of the submarine help change its neutral-buoyancy depth... Unless the density of the surrounding water also varies with the depth? And how does that vary, unless water actually is (albeit very slightly, I imagine) compressible?
To go silent while being depth-charged, they'll want to sit at neutral buoyancy with the propulsion off. They don't want to sink to crush depth or surface.
No that's not at all how it works. No one really uses free fall depth charges any more. A submarine under attack won't just sit there because it would be easier to target with active sonar; instead they will usually maneuver at low, quiet speed to escape or gain a firing position.
Really nice explanations and visualizations. The discussion about ship stability and the moment arm between center of gravity and center of buoyancy gave me flashbacks of my undergrad aircraft stability and control classes (where the moment arms between CG and center of lift on the wings determines static stability).
The discussion about propeller design is also very similar to aircraft as well - not just aircraft propellers but also compressors in turbofan engines.
The fact that there's a ton of similarity between the disciplines isn't too surprising, but the great visuals in this blog post made that connection seem particularly satisfying.
There is an excellent book by Elting Morison that includes a chapter on naval architecture, and the ways it was held back at the behest of naval commanders who wanted to preserve the culture of sailors that would be destroyed by the introduction of more powerful engines and faster hulls.
My first job out of college was as a junior engineering officer on a ship. I had taken naval architecture and the daily draft report was part of my job. The fuel king had a spreadsheet where the engineering watch input all the tank levels overnight. I added a sheet that took that data and solved all the tank problems, bouncy, incline, etc, and printed the report. So instead of two hours of number crunching, or one of my enlisted guys doing what he did (which was basically copy forward and subtract an inch a day), the report was completely automated, with fore, aft, and center draft. With zero human effort.
Apparently the guy who took my job when I left had a nervous breakdown. I feel a little bad about that, but not really. He should have paid attention in class.
Playing the game From the Depths (if you like games like kerbal space program I highly recommend it) taught me a lot about naval architecture and hull design.
I already knew some about it since I already liked playing Naval games, but it took at least 12 hours or learning and experimenting before I could design a hull design which didnt sink or roll over, or other odd behavior. This is all despite the game not modeling some of the other aspects like water pressure, and being simpler compared to real life.
Basically, there is a lot more to designing ships that meets the eye.
I've always thought that metacentric height would make the perfect try-at-home in your bath tube experiment against Flat Earth. If the center of buoyancy and the center of gravity were indeed the same, every ship would be rolling like a log and there weren't any differences in types of ships and hull shapes at all.
However, I guess, those adhering to said fancy model must not be bothered by such complexity of thought…
These are so well done. I gave my 4 year old the internal combustion engine page to play around with, thinking that he’d just find the animations fun to play around with. He ended up with a pretty good (4 year old level) understanding of how different parts of an engine work.
>> It turns out it’s a proper scientific discipline dedicated to the engineering of ships.
No. It is about the engineering of all sorts of things. Ships are a subset. I'd say that it covers all things that float, but that wouldn't include docks, cranes and other things that integrate with ships.
>>As containers are added the ship will sink a little and increase its draft – the distance between the bottom of the hull and the waterline.
This is the wikipedia answer. In the real world "draft" is the lowest part of the ship, which might be something other than the hull. Sailboats especially measure draft from the bottom of their keel, a thing lower than the hull. The "hull" is the watertight body and doesn't include things like keels and rudders which, while uncommon on large vessels, normally extend well below the hull's depth.
It's amazing what different people take from articles. That someone would read through this page and instead of appreciating the effort and craft their response would be an absolute textbook example of tedious internet pedantry.
Or someone who has to spend too much time around navy people who obsess about these definitions, people for whom small errors can lead to poorly loaded holds or vessels hitting rocks because they didn't know their draft from their hull depth.
I live in a recreation state, and to provide some numbers there are well over three times as many registered boats in my home state than there are naval O-6 rank ship captains. Just in one state.
Admittedly "beaching" a nuclear air craft carrier is more important to the USA than a local bubba beaching his fish trawler on a sandbar; but to bubba as an individual, its more important not to beach his fishing boat as avoidance of beaching his fishing boat is actionable for bubba, whereas watching TV reports of a naval accident are not.
How did I not know this? It's so counter intuitive that a thin column of water can cause the same pressure as a wide one.
The video they link shows this in action: https://www.youtube.com/watch?v=EJHrr21UvY8
One mind bending fact she shares in the video is that a thin layer of water, touching the damn wall, is the same pressure as an entire lake.