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(#120) Introduction to Fluid Mechanics - Lesson 5 · Mechanical Engineering Made Simple

• 0:00
  Welcome back design junkies to Mechanical Engineering Made
• 0:02
  Simple. If you enjoy the podcast, show
• 0:05
  your support with a like a follow or comment.
• 0:08
  Yeah, it's really great to be back for another one.
• 0:10
  So usually when we think about engineering or, I don't know,
• 0:13
  even something like a medical diagnosis, there is this
• 0:16
  expectation of like absolute visible precision.
• 0:20
  Right, people want certainty. Exactly.
• 0:22
  You know, you break your arm, they put you in an X-ray
• 0:25
  machine. The film comes back showing that
• 0:27
  jagged white line, and the doctor just points at it and
• 0:30
  says, there it is. Yeah.
• 0:31
  It's incredibly comforting. You know it.
• 0:34
  Is it's a, it's binary, it's broken or not broken.
• 0:38
  We inherently like things to be visible, discreet, and easily
• 0:42
  categorized. Totally.
• 0:43
  I mean, in solid mechanics, you have a steel i-beam, you have a
• 0:46
  concrete pillar. You can walk right up to it, hit
• 0:48
  it with a hammer, measure its exact length with the tape
• 0:51
  measure right. And then you calculate exactly
• 0:54
  how much weight it can hold before it snaps.
• 0:56
  But what happens when the materials you are building with,
• 0:59
  or, you know, designing for don't stay put?
• 1:01
  Yeah, it's the big question. Right.
• 1:03
  Look what happens when you step into a world where that X-ray
• 1:06
  machine of certainty is just completely broken and the
• 1:09
  physical landscape is constantly flowing and deforming and
• 1:12
  swirling and shifting right beneath your feet.
• 1:14
  It's a completely different ball game.
• 1:16
  It really is. So today, our mission in this
• 1:18
  deep dive is to unhover the hidden underlying rules of the
• 1:22
  most chaotic substances on Earth.
• 1:25
  We are diving into the invisible world of fluid mechanics.
• 1:28
  And it is a wild world once you really get into it.
• 1:31
  Oh. Absolutely.
• 1:32
  We're going to look at how the exact same invisible forces and
• 1:35
  mathematical laws govern everything from a single
• 1:38
  microscopic dewdrop resting perfectly still on a Terra leaf.
• 1:42
  Yeah, all the way up to the chaotic, immense, terrifying
• 1:45
  swirl of a Category 5 hurricane. Which requires a massive shift
• 1:49
  in perspective for any engineer or designer.
• 1:52
  Fluids. And keep in mind this
• 1:54
  encompasses both liquids and gases.
• 1:57
  They demand a completely different conceptual language
• 1:59
  than solids. You can't just measure a block
• 2:01
  of water and expect it to stay a block.
• 2:03
  Exactly. So today we are going to
• 2:05
  translate these heavy, often intimidating concepts into mind
• 2:11
  blowing aha moments. I love those moments.
• 2:13
  Me too. By the time we wrap up, you are
• 2:16
  going to completely change how you look at a simple glass of
• 2:19
  water sitting on your desk or the weather fronts forming
• 2:22
  outside inside your window. Or even the aerodynamic curves
• 2:25
  carved into the bodywork of your car.
• 2:27
  Yes. So I think the most logical
• 2:29
  place to start this journey is at the absolute foundation.
• 2:33
  Makes sense. Where are we starting?
• 2:34
  Before we can even begin to understand how massive bodies of
• 2:37
  water, like oceans or vast weather systems move and
• 2:40
  interact, we first need to define what exactly makes a
• 2:43
  fluid a fluid. Right.
• 2:45
  And perhaps more importantly, why water and air, which are
• 2:48
  both technically fluids, behave so incredibly differently when
• 2:52
  you put them under pressure? Yeah, because if I call air of
• 2:54
  fluid, a lot of people might, you know, tilt their head.
• 2:57
  We instinctively think of fluid as liquid.
• 2:59
  Sure, that's the common everyday definition.
• 3:01
  But the scientific definition divides fluids into two distinct
• 3:04
  categories, liquids and gases, and there is a fundamental
• 3:08
  difference in how they occupy space.
• 3:10
  There is. There's that ancient saying.
• 3:13
  Water takes the shape of the vessel containing it.
• 3:16
  But a liquid also has a very specific boundary.
• 3:19
  It has what engineers call a free surface.
• 3:21
  Right, the free surface is key. If you pour water into a coffee
• 3:25
  mug, it takes the shape of the bottom and the sides of the mug,
• 3:29
  but it stops at a certain height.
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  It creates a flat top. It doesn't magically expand
• 3:34
  upward and outward to fill your entire kitchen.
• 3:36
  Precisely that upper boundary, that flat top resting under the
• 3:41
  air, is the free surface. It is a defining characteristic
• 3:44
  of a liquid. OK, So what about gases?
• 3:47
  Gases, conversely, do not possess a free surface.
• 3:50
  A gas is highly compressible and possesses an inherent kinetic
• 3:54
  energy that causes it to expand indefinitely.
• 3:57
  So it just keeps going. Exactly.
• 3:58
  It will completely fill whatever container you put it in, no
• 4:01
  matter the size. If you release a small
• 4:04
  pressurized tank of helium inside a completely sealed room,
• 4:08
  that helium doesn't just pool on the floor like skilled water.
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  Right, it doesn't just sit there.
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  No. It disperses, diffuses and
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  spreads until it occupies every single cubic centimeter of the
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  available space in that room. So their relationship with space
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  and volume is a massive dividing line.
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  Liquids hold their volume, gases expand their volume.
• 4:28
  That's a good way to put it. Liquids are incredibly hard to
• 4:31
  compress. Gases are famously easy to
• 4:33
  compress, but there is another characteristic that defines a
• 4:37
  fluid and this is where the physics get really interesting,
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  Viscosity. Ah yes, viscosity is the
• 4:43
  absolute key to understanding fluid behavior.
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  Let's break that down. Think about a solid block of
• 4:49
  rubber. A solid shows its elasticity
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  when you subject it to tension by pulling it, or compression by
• 4:54
  squeezing it, or sheer stress by twisting it.
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  It fights back. Exactly.
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  Fights back against all those forces, but a fluid is
• 5:01
  different. A fluid really only pushes back
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  against compression. OK, it offers 0 resistance to
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  being deformed or stretched. However, a fluid does show a
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  very specific type of resistance when 2 internal layers of it try
• 5:14
  to slide over each other. So that's internal friction.
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  Exactly that resistance to sliding layers is what we call
• 5:21
  viscosity. I want to make sure we visualize
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  this properly. Imagine a brand new deck of
• 5:26
  playing cards sitting on a table.
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  OK, I'm picturing it. If I put my hand flat on the top
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  card and slide my hand forward, the top card moves with my hand
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  right, but the friction between the cards means the second card
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  slides forward just a little bit less and the third card even
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  less, all the way down to the bottom card which is stuck to
• 5:45
  the table and doesn't move at all.
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  Yes, you get this slanted staggered profile of cards.
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  That is a brilliant way to visualize it in fluid mechanics.
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  Isaac Newton actually gave us the mathematical definition for
• 5:57
  this exact sliding behavior. Good old Newton.
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  Always showing up right. Instead of sliding cards,
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  imagine sliding layers of water. Newton's lot of viscosity
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  explains the relationship between the force you are
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  applying to slide the fluid and how the fluid reacts.
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  Now, without getting bogged down and reading raw calculus
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  variables, the core concept is a relationship between shear
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  stress and the velocity gradient.
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  Let's break those terms down so they physically make sense to
• 6:24
  you listening. Sheer stress is simply the force
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  per unit area that is trying to slide the fluid layers.
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  So it's my hand pushing on the top card.
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  Yes, and the velocity gradient is a measure of how the speed of
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  the fluid changes as you move further away from the boundary,
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  like the wall of a pipe or the table under your deck of cards.
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  OK, got it. The fluid right against the wall
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  is essentially stationary, but the fluid perfectly in the
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  middle of the pipe is moving the fastest.
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  The change in speed between those two points is the
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  gradient. And the connection between that
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  pushing force and that speed change is the dynamic viscosity,
• 7:00
  essentially the thickness or the stickiness of the fluid?
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  Precisely, and the math actually looks like this.
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  Tau equals MU times the derivative above with respect
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  to. Y where Tau is the sheer stress,
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  right? Right, and MU is the dynamic
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  viscosity. OK, so if a fluid obeys this law
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  perfectly linearly, meaning if you push twice as hard the fluid
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  slides exactly twice as fast, it is called a Newtonian fluid.
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  Which is the ideal scenario for us engineers?
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  Water is our classic Newtonian fluid.
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  Air is also a Newtonian fluid. But nature isn't always that
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  clean, is it? Definitely not.
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  There are rebel fluids out there that refuse to follow Newton's
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  rules. Yes, the non Newtonian fluids.
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  They are endlessly fascinating and honestly notoriously
• 7:45
  difficult to engineer around. Why is that?
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  Because non Newtonian fluids do not have a constant viscosity,
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  their thickness actually changes depending on how much sheer
• 7:54
  stress you apply or how long you apply it.
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  The classic science fair example is Oobleck right?
• 7:59
  That mixture of cornstarch and water.
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  Exactly. Oobleck is a perfect example.
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  If you gently push your hand into a bowl of oobleck, it
• 8:06
  slides in like a thick liquid, right?
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  But if you punch it with your fist, the sudden application of
• 8:11
  intense sheer stress causes the particles to lock together, and
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  it suddenly acts almost like a solid brick.
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  You bounce right off. Yes, that is a sheer thickening
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  fluid, but there are also sheer thinning fluids where applying
• 8:24
  force actually makes them runnier.
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  Think of ketchup. You have to smack the bottom of
• 8:29
  the glass bottle to introduce sheer stress, which thins the
• 8:32
  ketchup enough for it to flow out.
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  Oh wow, I never thought of ketchup like that.
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  Yeah, it's a non Newtonian flowed and on an industrial
• 8:39
  scale engineers deal with non Newtonian fluids constantly.
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  Like in what industries? Liquid asphalt.
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  Wet concrete drilling muds in the oil industry, certain high
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  molecular weight polymer solutions, even human blood
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  under certain conditions. Blood.
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  Yep, the entire scientific field of rheology is dedicated solely
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  to studying these complex deformations.
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  It's amazing how complex everyday substances can be, but
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  even if we go back to our standard predictable Newtonian
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  fluids like pure water and air, there is a completely
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  counterintuitive effect when you introduce temperature changes.
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  This is one of my favorite quirks in physics.
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  I always grew up thinking that heat just generally melts
• 9:19
  things. That makes things runnier.
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  But in fluid mechanics that rule entirely depends on whether you
• 9:23
  are dealing with a liquid or a gas.
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  Exactly. If you heat a liquid, it's
• 9:28
  viscosity decreases. It gets thinner and runnier.
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  Right from a molecular standpoint, heating a liquid
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  adds energy. The molecules become more active
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  and spread slightly further apart.
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  OK, this increased distance drops their mutual attraction to
• 9:42
  one another so they can slide past each other much more
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  easily. Think of heating up a jar of
• 9:47
  cold, thick Maple syrup. It goes from a slow, gooey crawl
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  to pouring almost like water. That's a great example.
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  Yeah, but if you heat a gas, the exact opposite happens.
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  And this blows my mind. The viscosity of a gas actually
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  increases as the temperature rises.
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  Heat makes a gas thicker and harder to slide through.
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  It seems like a paradox doesn't? It it really does.
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  But if you think about the kinetic theory of gases, it
• 10:13
  makes perfect sense. In a gas, the molecules are
• 10:16
  already very far apart, right? The internal friction, the
• 10:19
  viscosity, isn't caused by the molecules holding hands and
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  resisting being pulled apart like in a liquid.
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  So what cause is it? In a gas, viscosity is caused by
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  the molecules colliding with each other as they zip around.
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  I love the analogy for this. Imagine a crowded room full of
• 10:34
  people at a networking event. If the room is cool and quiet,
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  everyone is relaxed, maybe slowly strolling around or
• 10:42
  standing still. If you need to walk from one
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  side of the room to the other, you can easily weave your way
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  through the crowd, slipping past people without much resistance.
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  Right, That is a low temperature, low viscosity gas.
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  But then imagine you crank the heat up, yeah, pump high energy
• 10:58
  dance music into the room, and suddenly everyone in the room
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  starts sprinking frantically and completely random direction.
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  That's a real. Chaos.
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  Exactly. They're bouncing off the walls,
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  colliding with each other, crossing paths chaotically.
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  If you try to walk from one side of the room to the other now, it
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  becomes incredibly difficult. Because you're just bumping into
• 11:16
  everyone. Yes, people are constantly
• 11:18
  slamming into you, impeding your forward progress.
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  You're experiencing massive resistance.
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  That chaotic, vigorous molecular movement increases the mixing
• 11:27
  and the internal friction. So high temperature equals high
• 11:29
  viscosity in a gas. Precisely.
• 11:32
  That visualization just makes the invisible world so clear,
• 11:35
  and it highlights something fundamental about the challenges
• 11:38
  engineers face. It really does.
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  A fluid is in reality just an aggregate of billions and
• 11:44
  trillions of individual molecules all bouncing around
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  like those people in the room. But trying to keep track of
• 11:49
  every single molecular collision in a pipe or over a car hood is
• 11:54
  mathematically impossible, even for supercomputers.
• 11:57
  It's way too much data, so engineers rely on a foundational
• 12:01
  assumption. They treat a fluid as a
• 12:04
  continuous isotropic substance. Which means what exactly?
• 12:07
  Because to me it sounds like they are just pretending the
• 12:10
  fluid is a perfectly smooth, uniform block of Jelly rather
• 12:14
  than a microscopic ball pit full of individual plastic spheres.
• 12:18
  Honestly, that is exactly what they're doing.
• 12:21
  It's a vacroscopic approximation, and they can get
• 12:23
  away with this mathematical shortcut because the scale we
• 12:26
  exist on is so vast compared to the molecules.
• 12:29
  How vast? Well, consider the mean free
• 12:31
  path of air. This is the average distance a
• 12:34
  single molecule of air travels before it violently collides
• 12:37
  with another molecule. At normal room temperature and
• 12:40
  atmospheric pressure, that mean free path is roughly 006
• 12:46
  micrometers. That is unimaginably tiny.
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  So tiny that we can't even process.
• 12:51
  It exactly so at any macro scale that a mechanical engineer
• 12:55
  actually cares about whether they are sizing a copper water
• 12:59
  pipe for a house or designing the massive swept wing of a
• 13:03
  commercial airliner, right? Treating the fluid as a
• 13:06
  perfectly continuous medium with no microscopic gaps works
• 13:09
  perfectly. The individual molecular chaos
• 13:12
  averages out into smooth, predictable bulk properties.
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  So what does this all mean for you?
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  Listening. It means that the next time you
• 13:19
  look at a pot of boiling water or feel a hot summer breeze hit
• 13:23
  your face, you'll never experience it the same way.
• 13:26
  No, you won't. You're actually feeling that
• 13:28
  heat fundamentally altering the internal kinetic thickness and
• 13:31
  the friction of the invisible fluids surrounding you.
• 13:33
  It really is a beautiful system, but moving on from the internal
• 13:37
  sliding and friction of fluids, we have to look outward.
• 13:41
  Out to the edges. Right, we have to ask what
• 13:43
  happens at the very edges? What happens at the boundary
• 13:46
  where a body of liquid meets the air, or where it comes into
• 13:49
  contact with a solid wall? This brings us to a fascinating
• 13:52
  topic, the hidden architecture of liquids, the secret forces of
• 13:57
  tension and compression that act at the boundaries.
• 14:00
  Let's start with surface tension.
• 14:02
  Yeah, if you zoom in on the surface of a liquid, it behaves
• 14:06
  exactly like a stretched sheet of rubber that is constantly
• 14:09
  trying to shrink. It really does.
• 14:11
  This is why if you step outside in the early morning and look at
• 14:15
  a dewdrop resting on a leaf, it forms a nearly perfect little
• 14:19
  sphere. It's a marvel of molecular
• 14:21
  physics. Inside the main body of the
• 14:24
  water drop, every water molecule is surrounded by other water
• 14:27
  molecules on all sides. They're being pulled equally in
• 14:31
  every direction by cohesive forces, specifically hydrogen
• 14:34
  bonds, so they are balanced. Right, they're perfectly
• 14:37
  comfortable. But the molecules right at the
• 14:39
  surface don't have water above them, they only have air.
• 14:43
  So they are pulled strongly inward by the water below them,
• 14:46
  and sideways by their neighbors, but not upward.
• 14:49
  So they're getting yanked down. Exactly.
• 14:51
  This creates an unbalanced inward tug, a microscopic
• 14:55
  tension. The liquid is literally pulling
• 14:58
  itself inward, trying to minimize its surface area as
• 15:01
  much as physically possible. And geometrically, the shape
• 15:05
  with the smallest surface area for a given volume is a perfect
• 15:08
  sphere. Precisely.
• 15:10
  What's wild to me is how this tiny microscopic surface tension
• 15:15
  dictates the massive internal pressure of that new drop, or
• 15:18
  the pressure inside a bubble floating in your soda.
• 15:21
  The internal pressure of a spherical droplet is governed by
• 15:25
  a very precise balance of forces.
• 15:26
  And what's the math on that? The mathematical relationship
• 15:29
  states that delta P = 4 * T / d. OK, let's unpack that.
• 15:33
  It means that the increase in internal pressure delta P is
• 15:36
  directly proportional to the surface tension T but inversely
• 15:40
  proportional to the diameter of the drop D.
• 15:43
  Let's focus on that last part because it's crucial.
• 15:45
  The diameter of the drop is the dividing factor.
• 15:48
  This means as the bubble or the droplet gets smaller and
• 15:50
  smaller, the internal pressure skyrockets.
• 15:54
  A large soap bubble has very little internal pressure.
• 15:57
  It's fragile and floppy, but a microscopic bubble when you can
• 16:01
  barely see with the naked eye. It has an exponentially higher
• 16:05
  internal pressure. Because the curvature is so
• 16:08
  tight, the elastic film of the surface tension is wrapped so
• 16:12
  sharply around that tiny volume that it is squeezing the
• 16:15
  interior fluid with immense, almost crushing force.
• 16:18
  Wow. But surface tension doesn't act
• 16:20
  in a vacuum. It frequently battles with other
• 16:22
  forces, specifically adhesive forces, when the fluid touches a
• 16:25
  solid surface. And this battle gives us one of
• 16:28
  my favorite physical phenomena. Capillarity is a perfect example
• 16:33
  of forces competing in plain sight.
• 16:35
  It is the interaction between cohesion, the fluids love for
• 16:38
  itself, and adhesion, the fluids love for a different material.
• 16:42
  So if you take a very fine thin glass tube, open up both ends
• 16:46
  and place it straight down into a cup of water, the water
• 16:49
  doesn't just sit there. No, it doesn't.
• 16:51
  It actually climbs up the inside of the glass tube, entirely
• 16:54
  defying gravity. Exactly.
• 16:56
  And that's because the adhesive force between the water
• 16:58
  molecules and the molecules of the glass wall is stronger than
• 17:01
  the water's own cohesive surface tension.
• 17:04
  So the water essentially wants to stick to the glass more than
• 17:08
  it wants to stick to itself. Yes.
• 17:09
  So it reaches up, grabs the glass and pulls itself upward
• 17:14
  until the weight of the water column finally balances out the
• 17:17
  pulling force. But here is where it gets really
• 17:19
  interesting. If you take that exact same
• 17:22
  glass tube, wipe it clean and place it into a pool of liquid
• 17:27
  mercury, the exact opposite phenomenon occurs.
• 17:31
  Mercury is fascinating. The mercury doesn't climb.
• 17:33
  It is actually pushed down inside the tube, ending up lower
• 17:37
  than the surrounding pool right, and the surface of the mercury
• 17:40
  inside the tube forms a convex meniscus.
• 17:43
  It domes upward in the middle, curving away from the glass
• 17:46
  walls. It's like the mercury is
• 17:47
  actively repelled by the glass. In a sense, it is.
• 17:50
  This occurs because the cohesive force of the mercury atoms
• 17:53
  holding onto each other is massively stronger than any
• 17:56
  adhesive attraction they might have to the glass.
• 17:58
  The contact angle of mercury to a glass wall is incredibly
• 18:01
  steep, between 1:30 and 150°. So it wants nothing to do with
• 18:05
  the glass. Nothing at it, so it pulls
• 18:06
  inward on itself, depressing the level inside the narrow tube.
• 18:09
  So we've got fluids stretching like rubber sticking to walls
• 18:13
  and repelling materials. But what about squeezing?
• 18:16
  Ah, compression. Earlier we said a defining treat
• 18:19
  of liquids is that they are incredibly hard to compress, and
• 18:23
  honestly, almost every engineering textbook will
• 18:25
  plainly state that water is an incompressible fluid.
• 18:29
  They will say that yes. But wait, stop right there.
• 18:32
  I know that in reality, engineers constantly use
• 18:35
  simplified models like the perfect fluid or the ideal gas.
• 18:40
  These are models that don't actually exist in the physical
• 18:42
  universe, they are just used to make the math workable on a
• 18:45
  chalkboard. Are you telling me that calling
• 18:47
  water incompressible is just one of those convenient lies?
• 18:50
  You are absolutely right to call that out.
• 18:52
  Calling water purely incompressible is absolutely an
• 18:55
  engineering approximation. It is a very useful, very
• 18:58
  convenient lie I. Knew it.
• 19:00
  In the physical reality of our universe, under extreme
• 19:03
  pressure, water absolutely does yield its squishes.
• 19:06
  OK, so it has a limit. Right.
• 19:08
  It has what physicists call a bulk modulus, which is a measure
• 19:12
  of a substance's resistance to uniform compression.
• 19:15
  However, it takes a truly massive amount of force to see
• 19:18
  it. How massive?
• 19:19
  If you take a volume of water at a normal room temperature and
• 19:23
  you increase the surrounding pressure by a full standard
• 19:25
  atmosphere, which is roughly 14.7 lbs of force per square
• 19:28
  inch, the entire weight of the sky pressing down on us, right?
• 19:32
  One atmosphere. The water's volume only shrinks
• 19:34
  by about .0005%. That is a tiny microscopic
• 19:39
  fraction. Almost negligible.
• 19:41
  So if you are designing a municipal plumbing system or the
• 19:44
  water lines for a new house, assuming the water doesn't
• 19:46
  compress makes your math infinitely easier.
• 19:49
  Oh, massively easy. And that .005% variance is never
• 19:53
  going to burst a pipe or ruin your final design.
• 19:55
  Exactly. But it makes me wonder if water
• 19:58
  really is slightly compressible. Does that tiny fraction ever
• 20:02
  actually matter in the real world, or is it just a trivia
• 20:04
  fact for physicists? Oh, it matters immensely.
• 20:07
  It is fundamentally responsible for life and communication in
• 20:10
  the oceans. Wait, really?
• 20:12
  Yes, if water were perfectly purely incompressible, exactly
• 20:17
  as the simplified engineering models suggest, the entire field
• 20:20
  underwater acoustics simply wouldn't exist.
• 20:23
  How does compressibility relate to sound?
• 20:26
  Think about what a sound wave actually is.
• 20:29
  Sound is not a physical object, it is a mechanical pressure wave
• 20:33
  propagating through a medium. Right, like ripples in a pond.
• 20:36
  Exactly. It requires the molecules of
• 20:38
  that medium to bump into each other, compressed together
• 20:41
  slightly, and then spring apart, passing the energy down the
• 20:44
  line. Oh, I see where this is going.
• 20:46
  The speed of sound in any fluid relies entirely on this slight
• 20:50
  compressibility. What's the formula for that?
• 20:53
  A physical relationship dictates that velocity equals the square
• 20:56
  root of K divided by rho. OK, let's translate that.
• 20:59
  Velocity is the speed of sound, K is the fluids bulk modulus.
• 21:02
  It's resistance to compression and rho is its density.
• 21:06
  Let me wrap my head around that. The bulk modulus is the
• 21:09
  resistance to compression. So if a perfect fluid is purely
• 21:12
  incompressible, its bulk modulus would technically be infinite.
• 21:15
  Yes, theoretically. Which means, according to that
• 21:18
  math, the speed of sound in that perfect incompressible fluid
• 21:22
  would also be infinite, right? The sound wave would travel
• 21:25
  instantly from one side of the ocean to the other, which
• 21:28
  completely breaks the laws of physics.
• 21:30
  It would violate relativity, yes.
• 21:31
  So without that tiny .0005 percent yield, a submarine sonar
• 21:37
  system wouldn't function. Whale songs couldn't travel for
• 21:40
  hundreds of miles. Because the pressure waves
• 21:43
  wouldn't have any squish to travel.
• 21:45
  Through the entire ocean would be completely deaf and silent.
• 21:48
  Exactly. The gap between pure simplified
• 21:51
  math and complex physical reality is where all the most
• 21:54
  beautiful and interesting phenomena live.
• 21:57
  That's incredible. That microscopic, almost
• 21:59
  negligible slight squishiness of water is the only reason marine
• 22:03
  mammals can communicate over vast distances in the dark.
• 22:07
  That is such a great aha moment. OK, so we've looked at the
• 22:10
  microscopic scale, the tiny view drops, the climbing capillary
• 22:13
  tubes, the microscopic compression of sound waves.
• 22:15
  Let's scale up. Let's look at millions of
• 22:18
  gallons of water. This brings us to fluid statics,
• 22:21
  the crushing, massive reality of Stillwater.
• 22:25
  What happens when we take massive amounts of fluid and
• 22:28
  stack it up against a wall like a hydroelectric dam?
• 22:32
  To understand the sheer power of fluid statics, we first have to
• 22:35
  go back to the 17th century and understand Pascal's law.
• 22:39
  Please Pascal, right? Yes, Pascal was a brilliant
• 22:42
  French mathematician and physicist.
• 22:45
  He realized a fundamental truth about confined fluids.
• 22:48
  If you apply pressure to a fluid that is totally enclosed in a
• 22:51
  vessel, that pressure is transmitted equally and
• 22:54
  undiminished to every single part of the fluid into the walls
• 22:57
  of the vessel. Meaning the fluid doesn't absorb
• 22:59
  the pressure in one spot, it instantly shares it everywhere.
• 23:02
  Exactly. This is the absolute magic
• 23:05
  behind the hydraulic press. Let's visualize a closed system
• 23:08
  with two Pistons, essentially 2 plungers, pushing into a sealed
• 23:12
  fluid reservoir. One plunger is very small, maybe
• 23:15
  an inch across. The other plunger is massive,
• 23:17
  maybe a few feet across. Right now pressure is defined as
• 23:20
  force divided by area. So if you push down on the small
• 23:23
  plunger with a small amount of force, say 10 lbs, you create a
• 23:28
  specific amount of pressure in the fluid because that small
• 23:32
  force is concentrated on a small area.
• 23:33
  But because of Pascal's law, that exact same pressure is
• 23:37
  instantly transmitted through the fluid to the large plunger,
• 23:40
  yes? And the math for this is F2
• 23:43
  equals F1 multiplied by a 2 / a one.
• 23:47
  So force 2 equals Force One times the ratio of their areas.
• 23:50
  Exactly. And since pressure equals force
• 23:53
  divided by area, if the area of the second plunger is massive,
• 23:57
  the resulting outward force must also be massive to keep the
• 23:59
  equation balanced. The force is amplified
• 24:02
  exponentially based on the ratio of the areas.
• 24:04
  You can literally lift a two ton car off the ground by simply
• 24:08
  pushing down on a small lever with your bare arm.
• 24:11
  Feels like you are cheating the universe creating energy out of
• 24:14
  nowhere. It really does.
• 24:16
  But you aren't. It's simply the beautiful
• 24:17
  geometry of fluid statics. You have to push the small
• 24:20
  plunger down a very long distance to move the big plunger
• 24:23
  up just a tiny bit so the work balances out.
• 24:26
  That's in a closed, artificially A pressurized man made system.
• 24:30
  But in the natural world, like a deep lake or the Mariana Trench,
• 24:33
  pressure isn't created by a plunger.
• 24:35
  No, it's not. It's created purely by gravity
• 24:37
  pulling down on the immense weight of the fluid itself, and
• 24:41
  in a liquid pressure increases linearly with depth.
• 24:44
  Yes, the formula is P = P zero plus rho times G * H.
• 24:50
  So P is the total pressure, P0 is the atmospheric pressure
• 24:54
  pushing down on the surface of the lake, and then you add rho,
• 24:58
  the density of the liquid multiplied by G, gravity
• 25:01
  multiplied by H, which is your depth.
• 25:03
  Because water's density is incredibly constant, remember
• 25:06
  that tiny .005% compressibility doesn't really change its
• 25:10
  density much. The pressure goes up in a
• 25:12
  perfectly straight linear line as you dive deeper.
• 25:14
  So for every 33 feet you go down in the ocean, the pressure
• 25:18
  increases by one full atmosphere.
• 25:20
  It is relentless, predictable and crushing.
• 25:22
  But gases again play by different.
• 25:24
  Rules. Of course they do.
• 25:25
  We live at the very bottom of an ocean of air.
• 25:28
  Atmosphere pressure changes as you climb a mountain, but it
• 25:31
  does not change linearly because air is highly compressible.
• 25:34
  Its density thins out dramatically with altitude.
• 25:37
  Exactly the lower layer of Earth's atmosphere, the
• 25:40
  troposphere, is a great example. As you climb up through the
• 25:43
  troposphere, the temperature drops about .65°C for every 100
• 25:48
  meters you ascend. That it doesn't keep dropping
• 25:50
  forever. No.
• 25:51
  It eventually hits a boundary around 10:50 kilometers up.
• 25:56
  The temperature caps out at a brutally constant -50.5°C.
• 26:01
  Which, not coincidentally, is precisely the altitude that
• 26:05
  commercial airliners choose to fly at, right?
• 26:07
  They cruise in that extremely cold, incredibly thin, low
• 26:10
  density air where the pressure is a fraction of what it is down
• 26:14
  at sea level. That thin air dramatically
• 26:16
  reduces the friction and aerodynamic drag on the
• 26:19
  aircraft, saving thousands of gallons of jet fuel.
• 26:22
  So knowing how crucial pressure is, how do engineers actually
• 26:25
  measure it? You can't just look at water and
• 26:27
  know it's pressure. Obviously not.
• 26:29
  The field has developed several incredibly clever, purely
• 26:34
  mechanical devices. Historically, the most reliable
• 26:38
  are manometers. Manometers.
• 26:40
  Yes. These use literal columns of
• 26:43
  liquid to balance and measure the invisible pressure.
• 26:46
  Let's explain the YouTube manometer.
• 26:47
  It is exactly what it sounds like, a glass tube bent into the
• 26:51
  shape of a U. You fill the bottom of EU with a
• 26:54
  dense liquid like mercury. You connect one top end of the
• 26:58
  tube to the pressurized pipe you want to measure, and you leave
• 27:02
  the other top end open to the room air right?
• 27:04
  The pressure from the pipe pushes down on the mercury on
• 27:07
  its side, forcing the mercury on the open side to rise up.
• 27:10
  Yes, you literally just hold a roller up to the glass tube and
• 27:14
  measure the height difference between the two columns of
• 27:16
  mercury. That height difference tells you
• 27:18
  the exact pressure. It is beautifully simple.
• 27:20
  But what if you were trying to measure minute fluctuations in
• 27:23
  pressure? A change so small the mercury
• 27:26
  might only move a millimeter. Too hard to read accurately.
• 27:28
  Exactly. O engineers develop the inclined
• 27:31
  manometer. Instead of a vertical U, they
• 27:33
  take the measuring glass tube and tilt it at a very shallow
• 27:37
  angle, almost horizontal. OK, I see.
• 27:40
  Because of the tilt, a tiny vertical change in pressure
• 27:43
  forces the liquid to travel a very long horizontal distance
• 27:47
  along the glass tube just to gain that millimeter of height.
• 27:51
  Oh, that's clever. It physically magnifies the
• 27:53
  reading across a long scale so it can be easily and accurately
• 27:57
  read by the human eye. It's stretching out the data
• 28:00
  physically. I love that.
• 28:02
  And then there's my absolute favorite pressure gauge, the
• 28:05
  Borden tube. A classic.
• 28:07
  I love the mechanical elegance of this device.
• 28:09
  It was invented by Eugene Borden in the 1800s.
• 28:13
  If you walk into any industrial plant or look at an air
• 28:15
  compressor in a garage, you'll see these analog pressure gauges
• 28:18
  with a little needle on a dial. Right inside that gauge is a
• 28:21
  Borden tube. Let's walk through how it works,
• 28:23
  because it relies on a brilliant geometric trick.
• 28:26
  OK, lay it out. Inside the gauge is a curved
• 28:29
  metallic tube. It's bent into AC shape, but the
• 28:33
  secret is that the tube doesn't have a perfectly round cross
• 28:35
  section like a garden hose. It has an elliptical flattened
• 28:39
  cross section. 1 end of the C shaped tube is fixed in place
• 28:43
  and connected to the pressurized fluid.
• 28:45
  The other end is sealed shut and free to move.
• 28:48
  So when pressurized fluid enters that hollow tube, Pascal's law
• 28:52
  tells us, the pressure pushes outward equally in all
• 28:55
  directions against the interior walls.
• 28:58
  Because the tube is flattened into an ellipse, the pressure
• 29:01
  tries to force the walls outward to maximize the internal volume.
• 29:05
  It tries to force the flatten the lifts to become a perfect
• 29:08
  inflated circle. And here's the genius part.
• 29:10
  As the cross section tries to bulge from an ellipse into a
• 29:13
  circle, it forces the entire C shaped curve of the tube to
• 29:17
  straighten out slightly. It uncurls.
• 29:19
  Exactly. It uncurls just like a paper
• 29:21
  party blowout toy when you blow into.
• 29:22
  It that's a great visual. That tiny physical uncurling
• 29:26
  motion at the free end is attached to a tiny gear.
• 29:30
  As it uncurls, curls, it turns the gear, which spins the needle
• 29:33
  on the dial. The higher the pressure, the
• 29:35
  more it tries to become a circle, the more it uncurls, and
• 29:38
  the higher the needle points. It translates invisible fluid
• 29:41
  pressure into purely mechanical rotational motion.
• 29:45
  It is brilliant and if we pull back and connect this deep
• 29:48
  understanding of pressures to the bigger picture, mastering
• 29:51
  these calculations is exactly what allows us to build
• 29:53
  monumental landscape altering structures safely.
• 29:57
  Like dams? Consider the terrifying
• 30:00
  engineering problem of designing a massive hydroelectric dam, or
• 30:04
  the steel sluice gates that hold the water back.
• 30:06
  You are dealing with a wall of water where the pressure is 0
• 30:09
  right at the very surface, but it becomes absolutely crushing
• 30:12
  at the bottom of the dam. Right.
• 30:13
  And this leads to a great Riddle for you listening at home.
• 30:16
  I want you to visualize this. Let's hear it.
• 30:18
  Imagine you are the engineer designing a large rectangular
• 30:21
  steel underwater door, a sluice gate built right into the flat
• 30:26
  vertical face of a dam. The water pressure is pushing
• 30:29
  massively against it. You need to put a hinge and a
• 30:32
  robotic arm on the back of this door to hold it shut.
• 30:35
  So you need to find the absolute center of that pressure.
• 30:38
  The point of balance. Right.
• 30:40
  Where is the single point on that door where all that varying
• 30:44
  force effectively balances out? Naturally, human intuition
• 30:48
  screams it's a rectangle. It's symmetrical, so the center
• 30:50
  of pressure must be dead center, right in the geometric middle.
• 30:54
  But if you build the hinge in the geometric middle, the door
• 30:58
  will fail catastrophically. Why?
• 31:00
  Because the center of pressure is always lower than the
• 31:02
  physical geometric center. Because of the depth.
• 31:04
  Exactly. Remember, pressure in a liquid
• 31:07
  increases linearly with depth. That means the water pushing
• 31:11
  against the bottom half of your rectangular door is
• 31:14
  significantly deeper than the water push against the top half.
• 31:17
  Therefore, the bottom half is experiencing significantly more
• 31:20
  force. It's a lopsided load.
• 31:23
  The aggregate force is physically shifted downward.
• 31:25
  Exactly, to find the exact location of that shifted point,
• 31:30
  engineers have to use a concept called the geometrical moment of
• 31:33
  inertia. Which is tricky math.
• 31:35
  Finding the total overall force on the wall is relatively easy,
• 31:40
  it's just the pressure at the geometric center multiplied by
• 31:43
  the total area. But to find where that force
• 31:46
  actually acts, the exact coordinate where you must attach
• 31:49
  your hinge so the door doesn't twist, you have to calculate the
• 31:52
  moment of inertia for the shape of the gate.
• 31:54
  Right, which involves integrating the increasing
• 31:57
  pressure over every square inch of the area.
• 32:00
  And that math proves that the action point is shifted below
• 32:03
  the center. If engineers blindly trusted
• 32:06
  their intuition and didn't account for this downward shift,
• 32:09
  the unbalanced torque from the deeper water would literally RIP
• 32:12
  the hinges right off the steel gate.
• 32:14
  It is a perfect, sobering example of how our human
• 32:17
  intuition fails us, but the rigorous math of fluid mechanics
• 32:21
  saves the day and keeps the dam intact.
• 32:23
  So we've spent a lot of time looking at how static water
• 32:26
  crushes inward and pushes sideways against walls, but we
• 32:29
  have to flip that around. What do you mean?
• 32:31
  How does that exact same pressure network suddenly create
• 32:34
  an upward lifting force? How does water hold things up?
• 32:38
  And what happens when a still body body of water interacts
• 32:41
  with a moving object or is suddenly violently accelerated?
• 32:45
  To answer that, we have to go back to ancient Greece around
• 32:48
  287 BC and look at the genius of Archimedes.
• 32:52
  Archimedes. He wasn't just an abstract
• 32:54
  philosopher, he's very practical engineer.
• 32:57
  He invented the Archimedes screw, a massive rotating spiral
• 33:01
  used for pumping water out of the holes of sinking ships, and
• 33:04
  he studied centers of gravity extensively.
• 33:06
  But his most famous and lasting legacy in fluid mechanics is of
• 33:10
  course, Archimedes principle. We all know the legend of him
• 33:14
  shouting Eureka in the bathtub, realizing that his body
• 33:17
  displaced an exact volume of water.
• 33:20
  But the principle he derived from that is foundational.
• 33:23
  It states that the upward buoyancy force exerted on
• 33:25
  anybody completely or partially immersed in the fluid is exactly
• 33:29
  equal to the weight of the fluid that the body displaces.
• 33:31
  Let's trace the logic of that. If you take a solid heavy block
• 33:35
  of raw steel and drop it into a pool, it sinks straight to the
• 33:37
  bottom. Right, obviously.
• 33:39
  Why? The steel block displaces a
• 33:42
  certain volume of water, a volume exactly equal to its own
• 33:45
  size. The Archimedes upward buoyancy
• 33:48
  force pushing back on the steel is equal to the weight of that
• 33:52
  specific cube of displaced water.
• 33:54
  But because steel is physically much denser than water, that
• 33:57
  small cube of displaced water weighs far less than the heavy
• 34:01
  steel block. Gravity winds, the downward
• 34:04
  force is greater, and the block sinks.
• 34:06
  But if you take that exact same weight of steel, melt it down,
• 34:09
  and forge it into the shape of a large hollow boat hull, you
• 34:13
  change everything. You're spreading the weight out.
• 34:15
  Exactly. When you place the boat in the
• 34:17
  water, it displaces a massive volume of water because of its
• 34:20
  wide, hollow shape. The weight of all that displaced
• 34:23
  water is immense, generating a massive upward buoyancy force
• 34:27
  that easily counteracts the downward weight of the steel.
• 34:29
  The downward pull of gravity and the upward push of buoyancy
• 34:32
  perfectly cancel each other out and the ship floats.
• 34:35
  It's an elegant balance, but making a ship float is honestly
• 34:38
  only half the battle for a marine engineer.
• 34:40
  What's the other half? The much harder half is making
• 34:43
  sure the ship stays upright when the ocean gets rough.
• 34:45
  Ship stability is a constant, delicate and mathematically
• 34:48
  complex dance between two invisible points, the center of
• 34:52
  gravity, which we'll call G, and the center of buoyancy, which
• 34:55
  we'll call C. OK, let's unpack this invisible
• 34:57
  dance. The center of gravity, G is the
• 35:00
  balance point of the ship's actual mass.
• 35:03
  All the steel, the engines, the cargo, the crew, Right?
• 35:06
  Unless you are actively moving heavy cargo around on the deck,
• 35:09
  Point G is relatively fixed in space relative to the ship.
• 35:13
  Yes, but the center of buoyancy C is the center of the displaced
• 35:18
  waters volume under the hull. And here is the trick that
• 35:21
  messes with people's heads. As a ship rolls to the side in a
• 35:25
  wave, leaning heavily to starboard, the actual physical
• 35:29
  shape of the underwater portion of the hull changes.
• 35:31
  Because the water level shifts relative to the boat.
• 35:34
  Exactly. One side dips deeper, the other
• 35:36
  side lifts out of the water because the underwater volume
• 35:39
  changes shape. The center of that, the center
• 35:41
  of buoyancy C physically moves out to the side.
• 35:44
  It shifts laterally to the side the ship is leaning, and this
• 35:47
  lateral movement is what dictates survival or disaster.
• 35:51
  You now have the downward pull of gravity acting straight down
• 35:54
  from G and the upward push of buoyancy acting straight up from
• 35:58
  the new shifted C Because they are no longer perfectly lined up
• 36:01
  vertically, these two forces create a rotational couple, a
• 36:05
  torque. And to figure out which way that
• 36:07
  torque is going to twist the ship, engineers find a third
• 36:11
  magical point. The meta center.
• 36:12
  Right. They draw a vertical line
• 36:15
  straight up from the new shifted buoyancy center.
• 36:17
  The exact point where that upward line intersects the
• 36:19
  ship's original vertical center line is called meta center or M.
• 36:23
  The location of the meta center is everything.
• 36:25
  It is the ultimate arbiter of stability.
• 36:27
  How so? If the meta center M is located
• 36:30
  high up above the center of gravity G, the ship is
• 36:33
  considered stable. The rotational torque created by
• 36:36
  the forces will act as a writing moment.
• 36:38
  It will forcefully twist the ship back to an upright level
• 36:41
  position. But if you mess up the design or
• 36:44
  load too much heavy cargo on the top deck, raising the center of
• 36:46
  gravity. Then you have a problem.
• 36:48
  Yeah, if M ever falls below G, it is a catastrophic disaster.
• 36:52
  The forces align in the opposite direction, creating an
• 36:55
  overturning moment. The ship's own buoyancy works
• 36:58
  against it, pushing the ship further over until it completely
• 37:01
  capsizes. Exactly, and naval architects
• 37:04
  meticulously manipulate the distance between G&M, known as
• 37:08
  the metacentric height, depending on what the ship is
• 37:10
  designed to do. So they customize it.
• 37:12
  They do. They don't just want a stable
• 37:15
  ship, they want the right kind of stability, right?
• 37:17
  For a military warship like a destroyer, you need an
• 37:19
  incredibly stable, rigid platform for firing weapons
• 37:23
  accurately, right? So you design the hull with a
• 37:26
  very large metacentric height, generally 0.8 to 1.2 meters.
• 37:31
  Which means if a massive Rogue Wave hits the site of a warship
• 37:35
  and rolls it over, the riding force is immense and the ship
• 37:38
  snaps back to an upright position very aggressively and
• 37:41
  violently. It's safe, but it's a brutal
• 37:43
  ride. Extremely brutal, but you
• 37:45
  absolutely do not want that on a luxury cruise ship.
• 37:47
  Definitely not if a massive 15 story passenger ship snapped
• 37:52
  back violently every time a wave hit it.
• 37:54
  Plates would fly off tables, people would be thrown into
• 37:58
  walls, and everyone on board would be violently seasick,
• 38:01
  throwing up over the railings. It would be a nightmare.
• 38:03
  So large passenger ships are intentionally designed with a
• 38:06
  much smaller metacentric height, usually sitting at a gentle .3
• 38:11
  to .7 meters. They are still perfectly safe
• 38:14
  and will right themselves, but they have a much slower, softer,
• 38:17
  more gentle sweeping roll. The torque is lower, which keeps
• 38:20
  the passengers comfortable and completely unaware of the
• 38:24
  massive fluid forces battling beneath their feet.
• 38:26
  It's a brilliant, highly tuned application of statics.
• 38:30
  But we don't just deal with fluids resting in massive oceans
• 38:33
  or static tanks. What happens when we take a tank
• 38:35
  of fluid and violently put it into motion?
• 38:38
  This leads us to a concept called relatively stationary
• 38:40
  states. Let's visualize this.
• 38:43
  Imagine you are sitting in the passenger seat of a sports car
• 38:45
  and you're holding a completely full, open cup of coffee.
• 38:49
  A risky move? Very risky.
• 38:51
  The car is stopped at a red light.
• 38:53
  The surface of the coffee is perfectly flat and level with
• 38:56
  the Earth, but the light turns green and the driver stomps on
• 39:00
  the gas pedal, accelerating hard in a straight line.
• 39:03
  The coffee violently sloshes backward toward you.
• 39:06
  Exactly. And then, as long as the
• 39:08
  acceleration remains constant, the surface of the coffee
• 39:11
  stabilizes, but it's no longer flat.
• 39:14
  It's locked at a tilted angle, rising up the back of the cup.
• 39:17
  Yes, the fluid surface adapts to the combination of gravity
• 39:20
  pulling down and the inertial force pushing back, and the
• 39:23
  mathematics give us the exact formula for that final resting
• 39:26
  angle. What's the math?
• 39:27
  It's elegantly simple. Tan Theta equals a / g.
• 39:31
  So the tangent of the angle of the fluid surface equals the
• 39:34
  car's horizontal acceleration a divided by the vertical
• 39:38
  acceleration of gravity. G exactly.
• 39:40
  So if you know gravity is a constant, the only only variable
• 39:43
  dictating that angle is the car's acceleration.
• 39:45
  That means the tilted fluid surface is literally acting as a
• 39:49
  physical, highly accurate accelerometer.
• 39:53
  You can mathematically calculate the exact zero to 60 speed of
• 39:57
  that sports car just by looking at a photograph of the angle of
• 40:00
  your coffee. It's a beautiful physical
• 40:02
  relationship, and it gets even more visually striking and
• 40:05
  mathematically complex if you introduce rotation.
• 40:08
  Oh, like spinning? Right.
• 40:10
  Instead of driving in a straight line, imagine you take a
• 40:12
  cylindrical glass vessel filled with liquid, place it on a
• 40:16
  motorized turntable and spin it rapidly around its central
• 40:19
  vertical axis. Just like stirring a cup of tea
• 40:21
  really fast. Exactly as it spins, centrifugal
• 40:25
  force pushes the liquid outward against the glass walls.
• 40:28
  The surface of the liquid dips down deep in the dead center and
• 40:31
  rises high up on the outer edges.
• 40:33
  It forms a perfectly smooth, sweeping concave bowl shape.
• 40:36
  OK. In mathematics, this is known as
• 40:39
  a rotating parabolic curve. And again, the math perfectly
• 40:42
  predicts reality. There is a precise equation that
• 40:45
  plots exactly how deep the center will dip and how high the
• 40:48
  edges will rise. Yes, the formula is Z -, H zero
• 40:53
  equals Omega squared times r ^2 / 2 * g.
• 40:57
  Which basically means the curve is based solely on the angular
• 41:00
  velocity at how fast you are spinning the turntable and the
• 41:03
  radius. You can plot the entire
• 41:05
  parabolic bull shape on a graph before you ever turn the motor
• 41:08
  on. What is truly fascinating to me
• 41:10
  about both of these examples, the straight line accelerating
• 41:13
  car and the spinning cylindrical bucket, is how fluid engineers
• 41:17
  actually handle them mathematically to keep their
• 41:19
  sanity. What do they do?
• 41:20
  They use a conceptual trick called gyrostatics.
• 41:23
  I want to break this down because it sounds incredibly
• 41:25
  intimidating. Gyrostatics.
• 41:27
  It sounds complex, but it's really a shift in perspective.
• 41:30
  If an engineer tries to calculate the complex floshing,
• 41:34
  swirling in forces of that fluid relative to the solid earth
• 41:37
  outside the car, the math is a nightmare.
• 41:40
  It's a dynamic moving system. So how do they fix it?
• 41:43
  Rather than doing that, the engineer simply shifts their
• 41:46
  coordinate system. They attach their imaginary XY
• 41:50
  and Z grid lines directly to the moving car or the skidding
• 41:53
  bucket itself. It's like when you were riding
• 41:55
  on a smoothly accelerating high speed train.
• 41:58
  If you look out the window, the world is flying by at 200 miles
• 42:01
  an hour. It's chaotic, right?
• 42:03
  But if you close the blinds and just look at the tray table in
• 42:05
  front of you, everything inside the train feels completely
• 42:09
  stationary. You just feel a slight invisible
• 42:12
  force pressing you back into your seat.
• 42:14
  That is the perfect analogy. By shifting their frame of
• 42:17
  reference to the moving vehicle, the engineers can treat this
• 42:21
  dynamically accelerating sloshing fluid as if it were
• 42:24
  perfectly peacefully at rest. So.
• 42:27
  Clever. They just invent a fake gravity
• 42:29
  force pointing backward to account for the acceleration.
• 42:32
  It's a mathematical sleight of hand that magically transforms a
• 42:35
  mind bending dynamic problem right back into a simple
• 42:39
  solvable static problem. I love that.
• 42:41
  Work smarter, not harder. Just change your perspective
• 42:44
  until the math gets easy. But as brilliant as gyrostatics
• 42:47
  is, eventually engineers have to face the music.
• 42:51
  We can't always pretend the fluid is sitting perfectly still
• 42:53
  in a cup. No, we can't.
• 42:55
  Up to this point in our deep dive, we've looked at fluids at
• 42:58
  rest or moving uniformly as a single solid block.
• 43:02
  But what happens when the fluid truly breaks loose?
• 43:04
  When it flows? When it begins to flow, mix to
• 43:06
  form, and tear itself apart? How do we even begin to track
• 43:10
  1,000,000 molecules moving in a million different directions?
• 43:13
  That is the transition from statics to dynamics.
• 43:17
  When you have billions of fluid particles moving independently
• 43:20
  through a pipe or around an airplane wing, you need a highly
• 43:23
  organized framework to observe them.
• 43:25
  OK, historically in the study of kinematics, there are two main
• 43:29
  methods to chart the flow. The first is the Lagrangian
• 43:32
  method. It's a Lagrangian method.
• 43:34
  Let's define this. The Lagrangian method involves
• 43:37
  picking a single specific fluid particle, giving it a
• 43:40
  theoretical name tag, and following it on its entire
• 43:43
  convoluted journey through space and time.
• 43:46
  You tracked everything about it. You track its exact position,
• 43:49
  it's kaleidoscopic changes in velocity and its acceleration at
• 43:52
  every single second. Here is my analogy for the
• 43:55
  Lagrangian method. To really ground it, imagine you
• 43:58
  want to understand the morning rush hour traffic flow in a
• 44:02
  massive city like Los Angeles. Good luck with that.
• 44:04
  Right. The Lagrangian method is like
• 44:07
  secretly placing a GPS tracker on the bumper of one specific
• 44:11
  car, let's say, or a red Honda Civic, and obsessively tracking
• 44:15
  everywhere that single car goes. OK, you get a perfect, highly
• 44:19
  detailed record of that one car specific experience.
• 44:22
  You know exactly how long it sat at every stoplight, every
• 44:25
  traffic jam it hit, every brief Hwy.
• 44:27
  Sprint it made. But the flaw in that method is
• 44:30
  obvious, right? You know everything about the
• 44:32
  red Honda Civic, but you know absolutely nothing about the
• 44:36
  thousands of other cars around it.
• 44:38
  You don't know if a traffic jam was caused by an accident or
• 44:41
  just heavy volume. You lack the big picture.
• 44:44
  And that severe limitation is why modern fluid mechanics
• 44:47
  overwhelmingly prefers the second framework, the Eulerian
• 44:51
  method. In the Eulerian method, you
• 44:53
  don't follow the particles, you let the particles come to you.
• 44:55
  How does that work? Rather than following a specific
• 44:58
  red Honda Civic, you pick fixed coordinates in space, A specific
• 45:04
  XY location. You simly sit there and watch
• 45:07
  whatever fluid haens to flow AST that exact point overtime.
• 45:10
  Going back to the Los Angeles traffic in alley, the Eulerian
• 45:14
  method is standing on a highway overpass above a massive 10 lane
• 45:18
  freeway with a radar gun and a clicker.
• 45:21
  You don't care where any specific car came from, and you
• 45:24
  don't care where it's going after it passes you.
• 45:25
  You are just standing at that specific coordinate measuring
• 45:28
  the average speed and density of every single car that passes
• 45:32
  your exact location right now. Which is much more useful data.
• 45:35
  By placing engineers with radar guns at multiple overpasses all
• 45:39
  over the city, you build a macroscopic real time map of the
• 45:43
  entire higher systems behavior. It is vastly more useful for
• 45:46
  engineering. If you are designing a pipe, you
• 45:49
  don't care about the journey of 1 water molecule, you care about
• 45:52
  the pressure and velocity of the water hitting the specific bend
• 45:54
  in your pipe. Right?
• 45:55
  But even with the Eulerian framework, visually
• 45:58
  understanding how the fluid actually moves and deforms is
• 46:01
  tricky. So we use three distinct visual
• 46:04
  concepts, streamlines, streak lines and path lines.
• 46:08
  Let's break these down so we can see them in our mind's eye.
• 46:11
  A streamline is essentially A theoretical curve drawn on
• 46:14
  paper. Drawn mathematically, yes.
• 46:16
  It's drawn so that it is always perfectly tangent to the
• 46:19
  velocity vector of the fluid particles at that exact instant.
• 46:23
  Because of this definition, fluid can never cross a
• 46:25
  streamline, it always flows parallel to it.
• 46:28
  How would you visualize that physically?
• 46:30
  If you sprinkle fine aluminum powder on the surface of moving
• 46:33
  water and snap a photo with a slow shutter speed, the tiny
• 46:37
  smeared blurs of the powder show you the streamlines.
• 46:40
  That's a great way to put it. Then there are streak lines.
• 46:43
  The streak line is a bit more physical.
• 46:44
  What's the difference? It is formed by continuously
• 46:47
  injecting a dye into water or a stream of smoke into the air at
• 46:51
  a single fixed point in the flow.
• 46:54
  As the fluid moves, it carries the dye with it, creating a
• 46:58
  continuous visible line of all the particles that have
• 47:01
  historically passed through that specific injection point.
• 47:04
  Like the classic images of cars in wind tunnels with the white
• 47:07
  smoke blowing over the hood. Those are streak lines.
• 47:10
  Exactly. And finally we have a path line,
• 47:12
  which is essentially the physical real world recording of
• 47:15
  the Lagrangian method we talked about earlier.
• 47:18
  It's the actual recorded path of one specific particle, tracked
• 47:22
  over time. Like a balloon.
• 47:23
  Yeah, like releasing a single brightly colored weather balloon
• 47:26
  into a storm and tracing its exact, squiggly, unpredictable
• 47:30
  line across the sky on a map. Now, there is a crucial
• 47:33
  distinction here regarding how these lines behave.
• 47:35
  If a fluid flow is steady, meaning the velocity and
• 47:38
  pressure at any given point never change overtime, like
• 47:41
  water flowing smoothly out of a hose, then streamline, streak
• 47:44
  lines and path lines are all perfectly identical.
• 47:47
  They overlap exactly. The weather balloon will
• 47:50
  perfectly follow the smoke trail.
• 47:52
  But if the flow is unsteady, like a violently gusting wind or
• 47:57
  water from a tap, you are actively turning on and off
• 48:00
  rapidly. Those 3 lines completely diverge
• 48:03
  from one another. The balloon goes wildly off the
• 48:06
  smoke trail. The streamline shift and the
• 48:08
  math required to track it becomes monstrously complex.
• 48:12
  This intense complexity is why dimensionality is so important
• 48:15
  in engineering. Real fluid flows in the real
• 48:18
  world are always fully 3 dimensional.
• 48:21
  They have velocity components moving up and down, left and
• 48:23
  right, forward and backward. But dealing with complete 3D
• 48:26
  calculus for every single junction in a massive municipal
• 48:30
  water system would take a supercomputer forever.
• 48:32
  Nobody has time for that. So engineers do what engineers
• 48:35
  do best. They simplify.
• 48:37
  They assume a flow is 2 dimensional if it's very wide in
• 48:39
  uniform, ignoring the slave friction on the side walls.
• 48:42
  Or they simplify it all the way down to 1 dimensional flow if
• 48:44
  they just need to know the bulk average velocity of water moving
• 48:47
  straight through a simple pipe. They intentionally ignore the
• 48:51
  microscopic 3D complexity to make the mathematics solvable on
• 48:54
  a practical deadline. There is a critical point where
• 48:58
  that mathematical simplification fails spectacularly.
• 49:02
  Where ignoring the complexity is no longer an option.
• 49:04
  Exactly. If you are standing on that
• 49:07
  Eulerian overpass watching your Highway Traffic, you might
• 49:11
  notice the traffic usually flows in smooth, straight, predictable
• 49:15
  lines. People stay in their lanes.
• 49:17
  Usually. But occasionally someone slams
• 49:19
  on their brakes or swerves, and the smooth flow erupts into
• 49:23
  total, unpredictable chaos. Cars are weaving, braking,
• 49:27
  cutting each other off. And what's that called in
• 49:29
  fluids? In fluid dynamics, this sudden,
• 49:32
  violent leap from smooth order to chaotic mixing is known as
• 49:36
  the transition to turbulence. And this transition brings us to
• 49:39
  one of the most famous and important experiments in all of
• 49:41
  engineering history, the work of Osborne Reynolds and the
• 49:44
  transition to chaos. It's a classic experiment.
• 49:47
  In 1883, Osborne Reynolds set up a brilliant, exquisitely simple
• 49:51
  apparatus in his laboratory. He had a long straight glass
• 49:54
  tube connected to a large tank of Stillwater.
• 49:57
  He allowed the water to flow slowly down the tube and right
• 50:01
  at the entrance, directly in the center of the flow, he
• 50:03
  continuously injected a single razor thin thread of brightly
• 50:08
  colored dye. At very low speeds, the visual
• 50:11
  result was beautiful. The thin thread of dye traveled
• 50:13
  straight down the center of the glass tube, perfectly intact.
• 50:17
  It looked like a solid colored string suspended in glass.
• 50:20
  It never mingled with the surrounding Clearwater.
• 50:22
  Never. The fluid was sliding perfectly
• 50:25
  in parallel, distinct layers like our deck of cards from
• 50:28
  earlier. Reynolds classified this smooth,
• 50:31
  orderly behavior as laminar flow.
• 50:34
  But as Reynolds slowly open the valve at the end of the pipe,
• 50:37
  increasing the velocity of the water, he hit a tipping point.
• 50:40
  The critical velocity. Suddenly, instantly, without
• 50:43
  warning, the perfect straight thread of dye violently
• 50:47
  shattered. It whipped around, curling,
• 50:49
  twisting and mixing furiously until the entire glass tube was
• 50:52
  clouded with uniform color. The orderly layers were gone.
• 50:56
  The fluid was tearing itself apart internally, creating
• 50:58
  microscopic eddies and whirlpools.
• 51:00
  He classified this chaotic state as turbulent flow.
• 51:04
  What made Reynolds a genius was that he didn't just observe the
• 51:07
  chaos, he decoded it. He discarded.
• 51:10
  This violent transition from laminar to turbulent wasn't just
• 51:14
  determined by the raw speed of the fluid.
• 51:16
  It was a highly complex interaction of multiple
• 51:18
  variables battling against each other.
• 51:20
  And he managed to distill this complex battle into a single,
• 51:24
  elegant, dimensionless number, which engineers worldwide now
• 51:28
  honorably call the Reynolds number.
• 51:30
  Let's talk about the physical meaning behind the Reynolds
• 51:32
  number. Because it's legendary, we won't
• 51:34
  just list the variables we need to understand the tug of war
• 51:37
  happening inside the pipe. Yes.
• 51:39
  Let's break it down. The Reynolds number is a
• 51:41
  mathematical fraction. The formula is RE equals rho
• 51:45
  times v * d divided by MU. OK, so on the top of the
• 51:48
  fraction you have the inertial forces, you have rho the density
• 51:51
  of the fluid, V its velocity, and D the physical diameter of
• 51:55
  the pipe it's flowing through. Think about what those top
• 51:58
  factors represent. Density and speed create
• 52:01
  momentum. A dense fluid moving fast has a
• 52:04
  lot of momentum. These are the chaotic tearing
• 52:07
  forces. Right.
• 52:08
  They are the forces trying to push the fluid forward blindly,
• 52:12
  trying to RIP the smooth layers apart into turbulent chaos.
• 52:15
  Exactly, but on the bottom of the fraction acting as the
• 52:19
  divisor, you have must our old friend from the beginning of the
• 52:22
  episode dynamic viscosity. Viscosity is the stickiness, the
• 52:27
  internal friction of the fluid holding the molecules together.
• 52:31
  So the Reynolds number is literally just a mathematical
• 52:33
  ratio of the chaotic tearing inertial forces to the smooth,
• 52:37
  sticky viscous forces. It's a tug of war.
• 52:40
  Exactly. If the Reynolds number
• 52:41
  calculates out to a low value, it means the viscosity is
• 52:44
  winning, the fluid is thick and sticky enough to suppress the
• 52:48
  chaos, and the flow remains smooth and laminar.
• 52:50
  But if it's high. If the Reynolds number is very
• 52:53
  high, it means momentum is winning.
• 52:55
  The speed and density overpower the stickiness, tearing the
• 52:58
  fluid into violent, chaotic turbulence.
• 53:00
  Reynolds meticulously tested this and found that the critical
• 53:03
  number, the point where flow inside a pipe, almost always
• 53:06
  remains safely laminar regardless of how much you shake
• 53:08
  or agitate the supply tank, is around 2320.
• 53:11
  What's incredible about dimensionless numbers like the
• 53:14
  Reynolds number is that they act like the ultimate cheat codes of
• 53:17
  the universe. Cheat codes, I love that.
• 53:20
  Because it's a ratio, all the specific units of measurement
• 53:23
  cancel each other out. You aren't left with feet per
• 53:26
  second or gallons per minute. You're just left with pure
• 53:30
  physics. So it scales perfectly.
• 53:32
  Yes, it proves that a tiny half inch glass tube of water in an
• 53:37
  1883 laboratory and a massive 48 inch steel crude oil pipeline
• 53:43
  running hundreds of miles across the freezing Alaskan tundra are
• 53:46
  governed by the exact same mathematical destiny.
• 53:49
  That's. Why?
• 53:50
  If you plug in their respective densities, speeds and
• 53:52
  viscosities and their calculated Reynolds numbers match, their
• 53:56
  flows will behave identically. Which is exactly what allows
• 53:59
  modern engineering to exist. It allows us to build a tiny
• 54:02
  scale model of a new fighter jet wing, put it in a small highly
• 54:05
  controlled wind tunnel, match the Reynolds number by tweaking
• 54:09
  the air density or speed, and no, with absolute mathematical
• 54:13
  certainty, exactly how the massive full size jet will
• 54:17
  handle turbulence when it flies through the real atmosphere.
• 54:21
  It is the bedrock of aerodynamics.
• 54:23
  It's incredible, and I have to take a brief second to talk
• 54:25
  about Osborne Reynolds, the man, because he wasn't just a stoic
• 54:28
  mathematician. No, he was a character.
• 54:31
  The historical accounts paint a picture of a wildly eccentric,
• 54:34
  fascinating genius. He was an engineering professor
• 54:37
  at Owens College in Manchester, and beyond turbulence, he
• 54:40
  actually discovered the destructive phenomena of
• 54:42
  cavitation, those microscopic, violently imploding vapor
• 54:46
  bubbles that eat away steel ship propellers.
• 54:49
  But despite his genius, his teaching style was famously,
• 54:52
  hilariously chaotic. Yes, the historical accounts of
• 54:55
  his lectures are amazing. He would apparently often turn
• 54:58
  his back entirely on his students, standing at the
• 55:00
  chalkboard mumbling to himself as he attempted to derive
• 55:04
  massive, incredibly complex thermodynamic equations
• 55:07
  completely from scratch, just from his own memory.
• 55:09
  He would write out this huge sprawling derivation covering
• 55:13
  the entire board, step back, stare at it, suddenly shout no
• 55:17
  that's wrong, and aggressively rub the whole thing out.
• 55:19
  Which I'm sure was great for the students taking notes.
• 55:21
  Oh, I'm sure they loved it. He'd start over on a completely
• 55:24
  new track, do it all again, and ultimately conclude out loud
• 55:27
  that his predecessor, the famous Professor Rankin, was right all
• 55:30
  along. That's so funny.
• 55:32
  He famously refused to blindly trust any scholars view, even
• 55:36
  massive historical authorities, without proving it himself from
• 55:39
  absolute first principles. That intense, almost stubborn
• 55:43
  skepticism is exactly what led him to see the hidden
• 55:46
  mathematical patterns and turbulence that everyone else
• 55:49
  had completely missed. It's a great reminder that true
• 55:52
  science is an active, messy, deeply human process, not just a
• 55:56
  clean list of facts to memorize out of a book.
• 55:59
  Completely agree. And Speaking of messy processes,
• 56:02
  understanding turbulence introduces us to our final major
• 56:04
  topic, the macro structures of chaos, vortices, swirls, and
• 56:09
  circulation. Turbulence itself is
• 56:11
  characterized by pure, unadulterated, microscopic
• 56:15
  chaos. But sometimes flowing fluids
• 56:18
  organize that energy. They create vast, highly
• 56:21
  organized, swirling structures that have enough concentrated
• 56:25
  power to RIP roofs off houses and level entire cities.
• 56:29
  Yeah, we have to look at how fluid deforms.
• 56:31
  As fluid particles flow along, they don't just move forward in
• 56:34
  a straight line. They deform, they stretch out,
• 56:36
  and they spin. This introduces the concept of
• 56:39
  vorticity. And clued mechanics breaks
• 56:41
  massive rotational flows into two distinct categories that
• 56:45
  honestly sound totally backwards and contradictory when you first
• 56:48
  hear them, the force vortex and the free vortex.
• 56:51
  Let's define them very carefully, because distinction
• 56:54
  is beautiful. A forced vortex is what
• 56:56
  engineers call a rotational. Flow.
• 56:58
  This goes back to the spinning cylindrical bucket of water we
• 57:00
  talked about earlier. Yeah, you put a bucket of water
• 57:02
  on a motorized turntable and you physically force it to spin,
• 57:05
  right? The fluid rotates around the
• 57:07
  center of the bucket, and the velocity of the water actually
• 57:10
  increases as you move outward toward the edge, just like the
• 57:13
  outer edge of a vinyl record moves faster than the inside
• 57:15
  track. But here is the key defining
• 57:18
  feature of the forced rotational vortex.
• 57:21
  Each individual microscopic fluid particle is actually
• 57:25
  spinning on its own central axis.
• 57:28
  How do we visualize that? If you want to visualize this,
• 57:31
  imagine dropping a tiny rectangular wood chip into that
• 57:34
  spinning bucket. The wood chip will travel in a
• 57:37
  large sweeping circle around the bucket, but the chip itself will
• 57:40
  also rotate 360° as it travels. OK, so it's rotating
• 57:45
  macroscopically around the bucket and rotating
• 57:47
  microscopically on its own axis. Exactly.
• 57:50
  In contrast, a free vortex is categorized mathematically as an
• 57:53
  irrotational flow. Which sounds wrong.
• 57:56
  It really does. This is the classic everyday
• 57:58
  example of water draining out of a bathtub or Whirlpool forming
• 58:02
  in a river. The fluid is swirling rapidly in
• 58:05
  a circle around around to central point, but unlike the
• 58:08
  spinning bucket, the velocity profile is reversed.
• 58:11
  The water is actually moving the fastest right near the center
• 58:14
  hole, and the speed drops off inversely proportional to the
• 58:18
  radius as you move outward. OK, wait, stop right there.
• 58:20
  I have to push back on this terminology because this is
• 58:23
  where the math feels like a prank.
• 58:25
  You are calling a free vortex where water is literally
• 58:28
  swirling around a bathtub drain in a massive circle.
• 58:32
  Yeah. You are calling that
• 58:34
  irrotational? Yeah.
• 58:35
  That's what it's. That makes absolutely no sense
• 58:37
  to me. I'm literally standing over the
• 58:39
  bathtub watching the water rotate in a giant circle right
• 58:42
  in front of my eyes. How is that irritational?
• 58:44
  It is the most common point of confusion in fluid kinematics.
• 58:47
  The key to unlocking it is separating the macroscopic path
• 58:51
  of the bulb fluid from the microscopic state of the
• 58:53
  individual fluid molecules. OK, explain.
• 58:56
  Yes, the water as a whole mass is traveling in a large circular
• 58:59
  path around the drain, but the microscoic fluid elements do not
• 59:03
  rotate on their own internal axis.
• 59:05
  OK, so let's use the wood chip test again.
• 59:07
  If I drop my tiny rectangular wood chip into the bathtub drain
• 59:11
  vortex, what happens? If you drop the wood chip in, it
• 59:15
  will absolutely travel in a large circle around the drain,
• 59:19
  but the chip itself will always point in the exact same compass
• 59:22
  direction. If the painted tip of the wood
• 59:24
  chip is pointing perfectly N when you drop it in, the tip
• 59:28
  will continue pointing perfectly N for the entire 360° circular
• 59:33
  journey around the drain. It never spins on its own axis,
• 59:36
  it just translates in a circle. That complete lack of
• 59:39
  microscopic internal spin is what makes the flow
• 59:42
  mathematically strictly irritational.
• 59:45
  That is a brilliant distinction, the macroscopic circular path
• 59:48
  versus the microscopic internal spin.
• 59:51
  That completely solves the paradox.
• 59:53
  And what's truly terrifying is when nature decides to combine
• 59:56
  the 2. Like 1.
• 59:57
  Natural phenomena like massive hurricanes and tornadoes are
• 1:00:01
  incredibly complex combinations of both vortex types.
• 1:00:04
  They feature a deadly high speed forced rotational vortex right
• 1:00:08
  at their very core, the eyewall surrounded by a massive
• 1:00:11
  sprawling free irritational vortex on their outer periphery.
• 1:00:15
  And engineers have to find a way to quantify these massive
• 1:00:19
  swirling motions, not just to understand weather, but to build
• 1:00:22
  the machines that power our world.
• 1:00:25
  They use the mathematical concepts of circulation and
• 1:00:27
  Stokes theorem. Stokes theorem sounds incredibly
• 1:00:30
  intimidating. It involves clothesline
• 1:00:32
  integrals, but physically it's it's just a way of adding up the
• 1:00:35
  rotation. Yes, the math states that gamma
• 1:00:39
  equals the closed line integral of VS with respect to DS.
• 1:00:43
  Or in other words, if you take the surface integral of the
• 1:00:46
  vorticity over an area, it is exactly equal to the total
• 1:00:49
  circulation around the closed curve boundary of that area.
• 1:00:53
  So practically speaking, if I want to find the total
• 1:00:55
  circulation, I just trace a closed loop, a big circle inside
• 1:00:59
  the moving fluid, and I mathematically add up every
• 1:01:02
  single velocity vector that is pointing along path.
• 1:01:05
  It gives me a master number for the swirling power of that area.
• 1:01:08
  Exactly. And this isn't just abstract
• 1:01:10
  chalkboard math. Stokes theorem is the
• 1:01:12
  foundational mathematical blueprint used to design
• 1:01:15
  incredibly complex machinery. It is how engineers shape the
• 1:01:18
  beautifully curved metal impellers inside the water pumps
• 1:01:21
  keeping your car engine cool, or the massive spiraling
• 1:01:25
  centrifugal blowers pushing air through skyscraper HVAC systems.
• 1:01:30
  Oh, so they use the circulation math to design the blades?
• 1:01:32
  Exactly. By calculating the exact
• 1:01:35
  mathematical circulation of the fluid, they can sculpt the metal
• 1:01:38
  blades to slice into the water, capture that rotational energy,
• 1:01:42
  and move the maximum amount of fluid while burning the absolute
• 1:01:45
  minimum amount of electrical energy.
• 1:01:47
  It's just astonishing how these invisible mathematical rules
• 1:01:50
  dictate absolutely everything around us.
• 1:01:52
  It's like seeing the matrix. It really is.
• 1:01:54
  We've gone from understanding the microscopic elastic surface
• 1:01:57
  tension of a morning dewdrop to realizing the slight .005%
• 1:02:03
  compressibility of water is the only thing allowing whale songs
• 1:02:07
  to travel across the oceans. We've covered a lot of ground.
• 1:02:10
  We really have. We visualize the chaotic
• 1:02:13
  Reynolds transition shattering a smooth flow of dye in a glass
• 1:02:16
  pipe, and we've decoded the swirling dual vortex mathematics
• 1:02:20
  powering a Category 5 hurricane. And that is the true grand take
• 1:02:25
  away here these concepts. Viscosity, buoyancy, the
• 1:02:29
  Reynolds number, Stokes theorem. They aren't just arcane
• 1:02:33
  equations scrawled on a chalkboard by an eccentric,
• 1:02:36
  mumbling professor. No, they're everywhere.
• 1:02:38
  They are the fundamental governing rules of physical
• 1:02:41
  reality. The exact same principles of
• 1:02:44
  fluid mechanics that dictate the crushing torque on a massive
• 1:02:48
  concrete hydroelectric dam also dictate the exact pressure of
• 1:02:53
  the blood pumping through the veins in your neck.
• 1:02:55
  Right now. It's incredible.
• 1:02:56
  They govern the chaotic weather fronts forming outside your
• 1:02:59
  window, and they dictate the aerodynamic drag on the car
• 1:03:02
  sitting in your driveway. It connects absolutely
• 1:03:04
  everything. You can't Unsee it once you
• 1:03:06
  learn it. And as we wrap up, I want to
• 1:03:08
  leave you, the listener with a final highly provocative
• 1:03:11
  thought, something that you on that builds entirely on what
• 1:03:13
  we've learned today. What is it?
• 1:03:14
  Think back to Osborne Reynolds. Think about that Reynolds number
• 1:03:17
  and that violent, chaotic transition from smooth, easy
• 1:03:21
  laminar flow to turbulent chaos. Turbulence creates massive
• 1:03:25
  parasitic amounts of aerodynamic drag and friction.
• 1:03:29
  It is the ultimate enemy of mechanical efficiency.
• 1:03:32
  Exactly. Now, what if modern aeronautical
• 1:03:35
  engineers could find a way to actively, perfectly control that
• 1:03:40
  boundary layer of air flowing over a commercial airplane wing
• 1:03:43
  in real time? That would be amazing.
• 1:03:45
  Right. What if, using millions of
• 1:03:48
  microscopic sensors and tiny active physical adjustments on
• 1:03:51
  the wing surface, they could artificially suppress the
• 1:03:54
  Reynolds transition? Delay the turbulence.
• 1:03:57
  Exactly. If they could delay turbulence
• 1:03:59
  at will, forcing the air to remain in that smooth,
• 1:04:02
  frictionless laminar state across the entire width of the
• 1:04:06
  wing, regardless of how fast the plane is flying, the energy
• 1:04:09
  savings would be astronomical. It would completely
• 1:04:12
  revolutionize global travel. It really would.
• 1:04:14
  It would slash aviation fuel consumption by incredible
• 1:04:17
  margins and fundamentally alter our carbon impact on the
• 1:04:19
  planet's atmosphere. It is considered the Holy Grail
• 1:04:23
  of fluid dynamics, and achieving it relies on mastering the very
• 1:04:26
  equations we just spent the last hour discussing.
• 1:04:29
  Just something to ponder the next time you're sitting in a
• 1:04:31
  window seat at 30,000 feet, looking out of the wing,
• 1:04:34
  watching the invisible, chaotic air rush by.
• 1:04:36
  It perfectly reminds us that there is always more to learn.
• 1:04:40
  The universe is incredibly complex and the rigorous
• 1:04:43
  application of this knowledge can literally change the world.
• 1:04:46
  That's exactly why we do this. We started by looking at a tiny
• 1:04:50
  dewdrop and a massive hurricane and realized they are speaking
• 1:04:54
  the exact same mathematical language.
• 1:04:56
  If you haven't already, give us a like and follow and please
• 1:04:58
  leave us a comment if you enjoy the podcast.
• 1:05:00
  We love to hear from the folks who make this possible.