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(#119) Introduction to Fluid Mechanics - Lesson 4 · Mechanical Engineering Made Simple

• 0:00
  Welcome back design jockey so mechanical engineering made
• 0:02
  simple. If you enjoy the podcast, show
• 0:05
  your support with a like, a follow or a comment.
• 0:07
  Absolutely. Today we are inviting you into a
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  very special master class. It's a deep dive into the hidden
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  rules that govern, well, almost everything around you.
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  Yeah, it really is everything. And looking at our sources for
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  today, we've compiled a massive stack of historical engineering
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  texts, flu dynamics research papers, and real world case
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  studies. But our mission today isn't just
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  to read you some math. No, definitely not.
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  Our mission is to build a mental toolkit.
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  We want to permanently change how you look at the physical
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  world, and I want to start by painting a picture for you.
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  Go for it. OK, imagine the massive steel
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  propeller of a modern ocean freighter.
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  Right, this things are huge. Massive.
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  It's a solid piece of meticulously cast metal.
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  It weighs tons, and it's designed to push millions of
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  pounds of cargo across the Pacific Ocean.
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  But when shipbuilders pull these propellers out of the water
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  after a few years, they often find the solid steel looks like
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  it's been eaten away by acid. It's.
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  Completely destroyed. It's pitted, scarred, ruined.
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  You might think it's, I don't know, chemical rust.
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  Or maybe it hit some rocks on the ocean floor.
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  Which would be a good guess, right?
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  But it's an either that solid steel was destroyed by
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  microscopic bubbles of water. What's fascinating here is that
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  the sheer destructive power of a collapsing water bubble is one
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  of the most extreme mind bending phenomena in the physical world.
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  It really is. And the craziest part is that
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  the physics dictating how those microscopic bubbles destroy
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  steel. They're the exact same physics
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  dictating how a curveball drops over home plate, or how the
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  Romans designed aqueducts thousands of years.
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  Oh wow. Or even just why a garden hose
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  behaves the way it does when you put your thumb over.
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  It, I mean, fluids seem inherently chaotic, right?
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  They're constantly shifting, swirling, deforming.
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  Exactly. They look like pure chaos, but
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  beneath that apparent chaos is a shockingly elegant set of rules.
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  And we are going to map out exactly why fluids behave the
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  way they do. Today we are just going to list
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  off intimidating mathematical formula.
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  Yeah, we are going to unpack the underlying logic.
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  So here's the syllabus for our deep dive today.
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  We've got 4 main modules, Module one right, module one.
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  We're going to start by looking at an impossible perfect
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  universe where fluids have no friction, just to understand the
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  foundational rules of energy. The.
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  Ideal world? Yep.
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  Then Module 2, we're going to drag that pristine math into the
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  messy, sticky reality of our world to understand turbulence.
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  Where things get complicated. Very complicated.
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  From there, module 3, we will RIP the roof off our pipes and
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  look at how gravity drives open rivers.
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  Open channel flow. Exactly.
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  And finally, Module 4 will flip the camera entirely.
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  We'll look at what happens when solid objects like airplanes,
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  golf balls and those ship propellers try to force their
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  way through the fluid. You know, the path we are taking
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  today actually mirrors the historical journey of human
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  understanding. Oh, really?
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  How so? Well, the earliest physicists
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  had to pretend fluids were perfect and frictionless.
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  They had to just to get their equations to work.
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  Oh, I see. But nature, as we know, is never
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  perfectly frictionless. Right, far from it.
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  The monumental breakthroughs that gave us modern aviation,
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  advanced plumbing and global shipping, they all came from
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  finally embracing the friction and understanding the chaos.
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  I love that. OK, so let's start in that
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  perfect ideal world, because before we could possibly
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  understand the complex, swirling 3 dimensional chaos of a
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  hurricane. Or the chaotic wake behind a
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  semi truck on the highway. Right, exactly.
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  We have to master the rules of a simplified universe first.
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  So picture A1 dimensional universe where we only look at
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  the average straight line velocity of a fluid moving
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  through a pipe. OK, so to do this we imagine a
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  theoretical fluid. It doesn't stick to the walls of
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  the pipe, it doesn't heat up, and crucially, it doesn't lose a
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  single drop of energy to friction.
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  It's perfectly smooth. Perfectly smooth.
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  Physicists call this an ideal or invisid fluid.
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  Invisic. Got it.
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  And in this incredibly simplified sandbox, the fluid is
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  ruled by a few absolute unbreakable laws of physics.
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  OK, lay the first one. The first of these is the
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  conservation of mass. In the realm of fluid mechanics.
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  This is mathematically expressed as the continuity equation.
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  OK, continuity equation sounds like something out of a graduate
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  level textbook. It does sound intimidating,
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  yeah. But the underlying concept from
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  our sources is beautifully simple.
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  It just means what goes in must come out.
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  Exactly. If you have a solid steel pipe
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  and you aren't adding any extra fluid through a side valve.
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  And the pipe hasn't sprung any leaks.
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  Right, no leaks then. The absolute mass of the fluid
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  flowing into the entrance has to equal the mass flowing out of
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  the exit in that exact same amount of time.
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  You can't magically create or destroy water inside the pipe.
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  Right when you write that out mathematically, you say that the
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  mass flow rate is constant everywhere in the system.
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  OK, so how do we calculate that? The mass flow rate is calculated
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  by multiplying 3 specific variables together, which are
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  the density of the fluid, the the cross-sectional area of the
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  pipe, and the mean velocity of the flow.
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  So density one times area one times velocity one at the
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  entrance must perfectly equal density 2 times area 2 times
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  velocity 2 at the exit. I follow you, but let's bring
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  this down to earth and talk about liquid water, because that
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  allows us to cheat the math a little bit, right?
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  He does, yes. Because water is for all
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  practical, everyday purposes and incompressible fluid.
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  Right, it doesn't squish. Yeah, you can put it in a
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  hydraulic press and squeeze it with thousands of pounds of
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  force, but its density isn't really going to change.
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  A gallon of water is a gallon of water.
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  Exactly. So if the density the entrance
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  is the exact same as the density at the exit, we could just cross
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  density out of the equation entirely, right?
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  That is the crucial simplification.
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  Once you cross out density, you are left with something
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  incredibly elegant, which is area times velocity is a
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  constant. Area one times velocity 1 equals
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  area 2 times velocity 2. OK.
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  And this mathematical statement area times velocity is constant.
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  Constant is something I guarantee every single person
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  listening has experienced intuitively.
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  It's the classic backyard trick. You know, putting your thumb
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  over the opening of the garden hose.
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  The perfect example. Right.
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  You're out in the yard, the hose is running, and the water is
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  just sort of lazily spilling out onto the grass.
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  The hose has a certain circular area and the water has a certain
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  lazy velocity. But then you want to spray your
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  friend who is standing 10 feet away.
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  As you do. As you do so, without even
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  thinking about the physics, you clamp your thumb over half of
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  the opening. Think about what you are
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  physically doing in that moment. You are dramatically reducing
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  the cross-sectional area that the water has available to flow
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  through. OK, but remember the continuity
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  equation. Area times velocity must remain
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  constant, right? Because the spigot attached to
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  your house is still pushing the exact same mass of water into
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  the hose every single second. The water has nowhere else to
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  go. Exactly.
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  If you cut the area in half, the velocity has absolutely no
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  choice but to double to maintain that mathematical balance.
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  The area goes down, the velocity skyrockets and suddenly you have
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  a high speed jet of water hitting your target.
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  I love this because my entire life I thought I was increasing
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  the pressure of the hose with my thumb.
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  That's what it physically feels like when the water pushes back
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  against your skin. It does feel like that.
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  But I'm not changing the pressure from the city waterline
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  at all. I am just manually trading area
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  for velocity. I'm forcing the same amount of
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  traffic through fewer lanes so the cars have to speed up to get
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  through. That traffic analogy is spot on,
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  and the idea of trading one property for another brings us
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  to the second unbreakable rule of our ideal universe, which is
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  the conservation of energy in fluid dynamics.
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  This concept was codified into what is arguably the most famous
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  equation in the entire discipline.
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  Bernoulli's equation. Bernoulli's equation.
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  Right Daniel Bernoulli, an 18th century Swiss mathematician.
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  He was actually the one who coined the term hydrodynamics in
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  the 1730s. He was brilliant.
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  He realized that for our perfect frictionless fluid, the total
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  energy of a fluid particle traveling along a streamline
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  remains perfectly constant. And the genius of Bernoulli was
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  identified that this total energy is distributed across
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  three distinct bank accounts, so to speak.
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  Bank accounts, I like that. What are they?
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  Well, a fluid particle has kinetic energy, which is the
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  energy of its physical speed. OK, kinetic is speed.
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  It has potential energy, which is the energy of its physical
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  height or elevation relative to gravity.
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  Potential is height. Got it.
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  And crucially, it has pressure energy.
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  Pressure energy. OK, to make the relationship
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  between potential and kinetic energy for you guys listening,
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  let's picture a roller coaster. Oh, that's a great way to
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  visualize it. Right when you are sitting in
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  that little cart, slowly clanking your way up to the very
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  top of the highest peak, you are depositing energy into your
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  potential energy bank account. You are building up height,
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  storing gravity's potential to do work.
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  Exactly at the very top, just before the drop, your potential
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  energy is maxed out, but your kinetic energy, your speed, is
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  basically zero, and then you tip over the edge.
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  Right as you plummet down the steel track, your height rapidly
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  decreases, meaning your potential energy bank account is
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  draining. With the universe demands that
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  energy be conserved, that energy doesn't vanish.
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  It is seamlessly transferred into your kinetic energy bank
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  account. Your speed skyrockets at the
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  very bottom of the hill. Your potential energy is
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  basically 0, but your kinetic energy is at its absolute
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  maximum. And assuming a frictionless
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  track, the total sum of those two bank accounts is exactly the
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  same at every single inch of the ride.
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  So fluids do the exact same thing.
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  If water flows down a mountain stream, it trades the potential
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  energy of the mountain's height for the kinetic energy of the
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  rushing Rapids. They do, yeah.
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  But here is the piece of the puzzle that makes fluids
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  completely different from a roller coaster cart.
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  Right, the third bank account. Fluids have that third bank
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  account pressure. Bernoulli proved mathematically
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  that the sum of kinetic energy, pressure energy and potential
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  energy remains constant. OK, so how do we isolate that
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  pressure variable? Let's remove gravity from the
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  equation entirely. Imagine a perfectly horizontal
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  pipe. OK, a flat pipe.
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  The potential energy never changes because the height never
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  changes. Right now, the fluid is only
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  trading energy back and forth between two accounts, its speed
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  and its internal pressure. OK, let's connect this back to
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  our garden hose, or just a pipe that gets narrower in the
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  middle. We know from the continuity
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  equation that when the horizontal pipe gets narrower,
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  the water has to speed up, its kinetic energy goes up.
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  But Bernoulli's law says the total energy cannot change.
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  So if the Kinetic Energy bank account suddenly gets a huge
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  deposit, the money has to be withdrawn from somewhere else.
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  It has to steal that energy from the pressure account.
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  Wait, so it steals from pressure?
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  Which leads to the most profound and frankly the most
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  counterintuitive realization in basic fluid dynamics.
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  What's fascinating here is that where the flow is fastest, the
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  internal pressure is lowest. That is wild.
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  If you force water through a narrow constriction, it speeds
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  up and it's internal static pressure plummets.
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  That breaks my brain every time I think about it.
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  It's hard to grasp at first. Because if I am in a wide
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  hallway and the hallway suddenly narrows into a tight corridor
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  and a crowd of people is forcing their way through, the pressure
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  goes up. People are squeezed together.
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  You feel crushed. Why does water do the exact
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  opposite? Well, the confusion comes from
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  our human bias towards solids. We intuitively think of pressure
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  as things being physically crammed together.
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  Yeah, exactly. But in a fluid pressure is
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  created by the random microscopic bouncing of
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  molecules against the walls of the pipe.
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  Mounting molecules. Imagine a swarm of angry bees
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  inside a box. OK, angry bees.
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  They are bouncing off the walls furiously.
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  That creates high pressure on the walls.
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  Makes sense? But now open one end of the box
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  and blow a massive fan behind them.
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  The bees are all swept forward at high speed.
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  Oh, I see where this is going. Because they are now spending
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  all their kinetic energy moving rapidly in one straight
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  direction, they don't have the time or the lateral energy to
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  bounce sideways against the walls anymore.
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  The straight line speed increases, but the sideways
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  pressure against the boundary dramatically decreases.
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  That is a brilliant way to visualize it.
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  Directional speed steals from lateral bouncing.
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  Fast moving fluid equals lower pressure.
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  And this realization wasn't just some abstract chalkboard math
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  that stayed in the university. It completely revolutionized
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  engineering and measurement. It really did.
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  There's this amazing historical anecdote from 1732 from our
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  sources, right around the time Bernoulli was doing his work.
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  It involves a French engineer named Henry Depito.
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  Ah. The invention of the pitot tube.
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  It's one of those rare moments in history where a complex
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  theoretical physics problem is solved with startling
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  simplicity. So Pitot is standing on the
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  banks of the river Seine in Paris.
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  He was wrestling with a very practical problem.
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  How do you accurately measure the velocity of flowing water in
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  a massive river? It's a tough problem.
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  You can throw a piece of wood in and time it, but that's wildly
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  inaccurate. Patel's thinking about this deep
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  relationship between pressure and velocity.
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  Suddenly he has an epiphany. He grabs a simple piece of glass
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  tubing, bends it into an L shape at a perfect 90° angle, and
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  plunges it straight down into the river.
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  He points the open submerged end directly upstream into the
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  oncoming current. Think about the physics of what
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  happens next. The rushing river water enters
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  the open end of the glass tube, but the tube is a dead end.
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  The water has nowhere to go inside the glass, so the tiny
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  parcel of water just inside the mouth of the tube is forced to
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  come to a complete and total stop.
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  In fluid dynamics, we call this a stagnation point.
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  The velocity drops to absolute 0.
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  And this is where Bernoulli's energy trading comes into play.
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  If the kinetic energy drops from the speed of the river down to
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  absolute 0, all of that forward energy must be instantly
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  converted back into pressure energy.
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  Exactly right. This creates A localized
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  microscopic zone of extreme high pressure at the mouth of the
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  tube. We call this the stagnation
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  pressure. Stagnation pressure.
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  And this localized high pressure physically forces the column of
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  water up the vertical part of the glass tube.
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  It pushes the water up until the column inside the glass rises
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  noticeably above the surface level of the river itself.
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  So the faster the river was flowing, the more kinetic energy
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  it had to convert, and the higher the water column rose in
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  the tube. Precisely.
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  By simply measuring how many inches the water rose above the
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  river's surface, Pitto could calculate the exact mathematical
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  velocity the current. He turns speed into a visible,
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  measurable pillar of pressure. It remains A stunningly elegant
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  instrument. A pedo tube simply compares 2
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  things. It compares the stagnation
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  pressure, the total pressure where the flow stops dead inside
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  the tube against the static pressure of the normal
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  undisturbed river flowing around it.
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  The difference between those two pressures is entirely due to the
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  dynamic pressure, which is just the kinetic energy of the flow.
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  By taking the square root of that pressure difference, you
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  have isolated the exact velocity.
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  And the most mind blowing part of this story?
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  What's that we? Still use this exact 18th
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  century technology today on our most advanced flying machines.
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  Oh yes. If you walk onto the tarmac and
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  look at the nose or the wings of a modern commercial airliner,
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  you will see these little sharp metal probes sticking out,
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  pointing straight forward. Those are pedo tubes.
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  They are using the exact same energy training principle Henry
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  Depito used in the River Seine to tell the pilots how fast the
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  plane is tearing through the atmosphere.
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  It's a perfect testament to the universal, unbreakable truth of
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  these conservation laws. Air behaves as a fluid, just
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  like water does, right? And pita tubes are often used in
• 16:24
  modern industry alongside another historical invention
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  based on Bernoulli called the Venturi tube.
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  The Venturi tube. Invented by Giovanni Batista
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  Venturi, this device measures flow rate not by stopping the
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  fluid, but by deliberately choking it.
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  Choking it like the garden hose. Exactly.
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  It's a pipe with a smoothly narrowed throat in the middle.
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  As we discussed, forcing the fluid through the narrow throat
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  makes it speed up, which makes the static pressure drop.
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  Right, higher velocity, lower pressure.
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  So by installing one pressure sensor in the wide part of the
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  pipe and a second sensor in the narrow throat, you can
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  constantly monitor the pressure drop.
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  From that precise drop in pressure, the system's computer
• 17:05
  can instantly calculate the exact volumetric flow rate
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  passing through a pipeline. OK, I have to step in here and
• 17:10
  play the role of the stubborn skeptic for a second.
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  All right, hit me. I hear what you're saying about
• 17:14
  energy trading Florida State back and forth, but if
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  Bernoulli's equation says total energy is perfectly conserved,
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  then it just infinitely trades between pressure, velocity, and
• 17:25
  height without ever losing a single drop of energy, then why
• 17:29
  the heck do we need water pumps, right?
• 17:31
  If I push water into a massive, perfectly horizontal pipeline in
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  Texas, shouldn't it just flow all the way to New York forever?
• 17:39
  Why do oil and water pipelines have massive billion dollar
• 17:42
  pumping stations build every few miles?
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  Doesn't the fluid eventually just stop?
• 17:47
  That is the exact question that completely shatters the illusion
• 17:50
  of the ideal world we've been operating in for the last 20.
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  Minutes. So it's a lie.
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  Well, here are absolutely correct.
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  If the universe were perfectly ideal, water would flow through
• 17:58
  a horizontal pipe forever without any pumps.
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  But in reality, the universe demands a tax on movement.
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  The tax. We call this tax head loss, and
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  it is primarily driven by the inescapable reality of friction.
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  And that transition brings us into our second major phase of
• 18:15
  understanding today, Module 2, the reality of friction,
• 18:19
  viscosity and turbulence. This is where things get real.
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  Because Ideal Fluids are great for doing clean math on
• 18:25
  university chalkboards, but in the real world, fluids stick.
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  They really do. They stick to the solid walls of
• 18:32
  the pipes and they stick to themselves.
• 18:34
  To move from Bernoulli's perfect sandbox to the real world, we
• 18:38
  have to introduce a completely new character to the story
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  viscosity. Viscosity is, in its simplest
• 18:44
  definition, fluid friction. Fluid friction, OK.
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  It's a measure of a fluid's internal resistance to flow and
• 18:50
  deformation. We all know this intuitively.
• 18:52
  Honey has incredibly high viscosity.
• 18:54
  It flows like sludge because it's internal molecules
• 18:57
  desperately cling to each other, right?
• 18:59
  Water has a relatively low viscosity, so it flows easily,
• 19:02
  but it's viscosity is not zero. And because of this microscopic
• 19:06
  stickiness, a fascinating phenomenon occurs at the
• 19:09
  boundaries of any container. Happens at the boundary.
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  When water flows through a pipe, the outermost layer of water
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  molecules that are physically touching the steel wall of the
• 19:19
  pipe get stuck. Stuck like glued.
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  Basically, they latch onto the microscopic roughness of the
• 19:24
  metal. That outermost layer of fluid
• 19:26
  does not move at all. Its velocity is 0.
• 19:29
  We call this the no slip condition.
• 19:31
  This was another mind Bender for me when reading the source
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  material. The water physically touching
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  the pipe isn't moving. Not at.
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  All but it gets weirder. Because the water has internal
• 19:40
  viscosity, the layer of water molecules just inside that
• 19:44
  stationary layer drags against it.
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  It's trying to move forward, but the stationary layer is pulling
• 19:50
  it back. So it moves, but very slowly.
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  Then the next layer inwards drags against that slow layer,
• 19:58
  moving slightly faster. Exactly.
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  The viscosity transmits the braking force of the wall deep
• 20:03
  into the fluid. OK, so instead of a solid
• 20:06
  unified plug of water moving all at the exact same speed like a
• 20:09
  train car, you have a velocity gradient.
• 20:11
  A gradient. The water in the dead center of
• 20:13
  the pipe is moving the fastest because it is the furthest away
• 20:16
  from the sticky walls. As you move radially outward
• 20:19
  from the center toward the edge, the fluid gets slower and slower
• 20:24
  and slower until it comes to a dead stop at the wall.
• 20:27
  Imagine sliding A freshly shuffled deck of cards across
• 20:30
  the table. That's good.
• 20:31
  The bottom card sticks to the table, the card above it slides
• 20:34
  a little bit, the card in the middle slides further, and the
• 20:37
  top card slides the furthest. You end up with this angled
• 20:41
  smear deck. That's a perfect physical
• 20:44
  representation. To describe this complex,
• 20:46
  layered sliding mathematically, physicists have said move beyond
• 20:50
  the simple ideal equations and develop what are known as the
• 20:53
  Navier Stokes equations. Developed independently by
• 20:57
  Claude Louis Navier in France and George Gabriel Stokes in
• 21:00
  Ireland during the 19th century, these equations are the absolute
• 21:04
  bedrock of modern fluid dynamics.
• 21:06
  So bedrock. Essentially, they take Newton's
• 21:08
  second law of motion, force equals mass times acceleration,
• 21:12
  and apply it to a microscopic 3 dimensional cube of fluid.
• 21:16
  OK, zooming way in. They tally up every single
• 21:18
  conceivable force acting on that tiny fluid cube.
• 21:22
  The pressure force is pushing on its faces, the body force is
• 21:25
  like gravity pulling it down. And crucially, the viscous shear
• 21:29
  force is tearing at its sides. And just uttering the phrase
• 21:32
  naverstos is enough to send a shiver down the spine of any
• 21:35
  engineering student. Oh, absolute terrifying.
• 21:37
  These are famously considered some of the most difficult
• 21:40
  unsolvable equations in all of human mathematics.
• 21:43
  Right There is literally $1,000,000 prize out there from
• 21:47
  the Clay Mathematics Institute for anyone who can prove certain
• 21:50
  properties of these equations. They are notoriously
• 21:53
  impenetrable, yes, and the reason they are so difficult
• 21:57
  comes down to a mathematical nightmare known as convective
• 22:00
  acceleration. Convective acceleration, OK,
• 22:03
  break that down for me. In a standard physics problem,
• 22:06
  an object's velocity changes over time.
• 22:09
  But in a fluid, the velocity of the fluid isn't just changing
• 22:12
  over time, it's changing as the fluid moves through
• 22:15
  three-dimensional space. Wait, what?
• 22:17
  The fluid's own velocity determines how fast its velocity
• 22:21
  changes. To visualize that, imagine a
• 22:23
  massive traffic jam. The speed of the cars determines
• 22:27
  the flow of traffic, but the flow of traffic dictates the
• 22:30
  speed limit of the cars. It's a snake eating its own
• 22:33
  tail. That feedback loop creates non
• 22:35
  linear terms in the differential equation.
• 22:37
  Non linear meaning. Non linear means the variables
• 22:40
  multiply against themselves. The math doesn't scale up in
• 22:43
  straight predictable proportional lines.
• 22:46
  A tiny change in one variable can cause an exponentially
• 22:49
  massive chaotic change in another.
• 22:52
  The butterfly effect kind of thing.
• 22:53
  Exactly because of this non linear, there are no general
• 22:57
  analytical solutions to the Navier Stokes equations.
• 23:00
  We can't just draw a random shape of a pipe on a piece of
• 23:03
  paper, plug it into the equation, and get a perfect
• 23:06
  mathematical answer for how the fluid will behave.
• 23:09
  We can only solve them exactly if we aggressively cheat and
• 23:12
  constrain the physical world. Pretty much.
• 23:15
  For example, if we imagine a steady slow flow moving between
• 23:19
  two infinite perfectly parallel flat plates, in that highly
• 23:23
  specific, highly unrealistic case, all those nasty complex,
• 23:27
  chaotic non linear terms zero out.
• 23:30
  And when you simplify it that much, you can prove
• 23:32
  mathematically that the velocity profile of the fluid forms a
• 23:35
  perfect smooth mathematical parabola.
• 23:38
  The fastest fluid is exactly in the center, and it curves
• 23:40
  symmetrically down to 0 at the walls.
• 23:42
  We call that beautifully smooth, orderly flow, laminar flow.
• 23:45
  Laminar flow. The fluid moves in parallel
• 23:48
  microscopic layers or laminate, sliding past each other without
• 23:52
  any mixing across the layers. In the mid 1800s, a German
• 23:57
  engineer named Gothelf Hagen and a French physician named Jean
• 24:00
  Poiseau independently derived the formulas for this type of
• 24:03
  flow in cylindrical pipes. They proved that in laminar
• 24:07
  flow, the pressure drop required to push the fluid is directly
• 24:11
  linearly proportional to the velocity.
• 24:13
  Nice and simple. Right.
• 24:15
  If you want the water to move twice as fast, you just need
• 24:17
  twice as much pressure. It's a linear predictable
• 24:19
  relationship. But there is a massive catch.
• 24:22
  Always a catch. Laminar flow is incredibly
• 24:24
  fragile. It only exists at very low
• 24:26
  speeds, or in very narrow capillary tubes, or with highly
• 24:30
  viscous fluids like oil. If you take a normal pipe with
• 24:33
  water and you start turning up the flow rate, the fluid becomes
• 24:36
  unstable. To determine exactly when that
• 24:38
  stability shatters, engineers use a critical metric called the
• 24:41
  Reynolds Number, named after the British physicist Osborne
• 24:45
  Reynolds. The Reynolds number.
• 24:46
  The Reynolds number is essentially A mathematical tug
• 24:49
  of war. It is a ratio that pits the
• 24:51
  inertial forces against the viscous forces.
• 24:54
  Think of the inertial forces as the raw momentum of the fluid.
• 24:58
  It's the mass of the water violently trying to plunge
• 25:01
  straight ahead as fast as possible.
• 25:03
  OK, forward plunging. The viscous forces, on the other
• 25:05
  hand, are the stickiness of the fluid, desperately trying to
• 25:09
  keep all the microscopic layers sliding smoothly and parallel to
• 25:12
  each other. When the fluid is moving slowly,
• 25:15
  the viscous stickiness is strong enough to hold everything
• 25:18
  together. The Reynolds number is low and
• 25:21
  the flow remains smooth and laminar.
• 25:23
  But as you crank open the valve, the velocity increases.
• 25:27
  The brute force forward momentum of the inertial forces starts to
• 25:30
  overwhelm the delicate sticky bonds of viscosity.
• 25:33
  The Reynolds number climbs. And once it passes a certain
• 25:36
  critical threshold, which in a standard round pipe is a
• 25:39
  Reynolds number of roughly 2320, the orderly layers breakdown
• 25:43
  completely and permanently. The flow descends into total
• 25:46
  chaos. We call this turbulent flow.
• 25:49
  Osborne Reynolds actually visualized this beautifully in
• 25:52
  1883. How?
• 25:53
  Did he do that? He set up a clear glass pipe
• 25:55
  with water flowing through it, and he injected a tiny needle
• 25:59
  thin stream of dark dye into the very center of the flow.
• 26:03
  OK, injecting dye. When the water was moving
• 26:06
  slowly, the dye formed a perfectly straight, beautiful,
• 26:11
  unbroken thread running the entire length of the pipe.
• 26:14
  It was a perfect visual of laminar flow.
• 26:17
  The layers weren't mixing right, but the moment he increased the
• 26:20
  velocity past that critical Reynolds number, the straight
• 26:24
  thread of dye instantly shattered.
• 26:26
  It floated into a chaotic swirling cloud, instantly mixing
• 26:31
  across the entire width of the pipe.
• 26:33
  Chaos is absolutely the right word.
• 26:35
  Reynolds discovered that in turbulent flow, the fluid
• 26:37
  particles aren't just moving cleanly forward anymore.
• 26:40
  No, they're not. On top of their average forward
• 26:42
  speed, they are constantly violently fluctuating in every
• 26:44
  conceivable direction. They are vibrating, swirling and
• 26:48
  darting sideways. Mathematically, physicists
• 26:50
  started representing the velocity and turbulent flow not
• 26:53
  as a single number, but as an equation.
• 26:56
  OK, an equation. Instantaneous velocity, which we
• 26:59
  call U is equal to the steady average velocity U bar plus a
• 27:04
  chaotic constantly changing fluctuating velocity U prime.
• 27:08
  So U = U bar plus U prime. And it's those fluctuating
• 27:12
  velocities, specifically the ones darting laterally sideways
• 27:16
  across the pipe, that ruin everything.
• 27:18
  They really do. Because of those sideways
• 27:20
  fluctuations, macroscopic chunks of fluid literally slam into
• 27:24
  each other. You have incredibly fast moving
• 27:27
  groups of molecules from the center of the pipe getting
• 27:30
  violently thrown outward into the slower moving layers near
• 27:33
  the edge. At the same time, slow moving
• 27:36
  chunks from the edge are getting sucked into the fast center.
• 27:39
  This violent lateral mixing transfers a massive amount of
• 27:43
  momentum across the pipe. It's like imagine 2 trains
• 27:46
  running on parallel tracks at different speeds and passengers
• 27:48
  are constantly throwing heavy bowling balls back and forth
• 27:51
  between the trains. That's a great analogy.
• 27:53
  The fast train will be slowed down and the slow train will be
• 27:55
  dragged forward in a fluid. This violent momentum exchange
• 27:59
  creates a massive new type of internal friction.
• 28:02
  We call these Reynolds stresses. And Reynolds stresses create an
• 28:07
  unbelievable amount of extra drag.
• 28:09
  This is why pumping water through a turbulent municipal
• 28:12
  pipeline requires exponentially more electrical energy than if
• 28:16
  the flow were laminar. Oh, because of the extra
• 28:18
  friction. Right.
• 28:19
  The pump isn't just fighting the friction of the pipe wall
• 28:22
  anymore, it has to provide the energy for the fluid to
• 28:25
  violently fight itself in building of microscopic swirling
• 28:28
  eddies. And trying to calculate the
• 28:30
  mathematical value of these Reynolds stresses was a massive,
• 28:34
  seemingly insurmountable roadblock in physics for
• 28:38
  decades. A.
• 28:38
  Huge roadblock. The Navier Stokes equations were
• 28:41
  too complex to solve for this level of chaos.
• 28:44
  You couldn't predict EU prime fluctuations.
• 28:46
  It seemed like a dead end. That is, until a man named
• 28:49
  Ludwig Prantle came along. This is genuinely one of my
• 28:52
  favorite stories in the history of science because it shows how
• 28:54
  raw observation can crack impenetrable math.
• 28:57
  It's a great story. The big Prantle is widely
• 29:00
  considered the founding father of modern fluid dynamics.
• 29:03
  He was a professor at Gutney University in Germany in the
• 29:06
  early 1920s, and the story goes that he was incredibly
• 29:10
  frustrated. Understandably so.
• 29:11
  He had been staring at chalkboards, trying to figure
• 29:14
  out how to mathematically model these chaotic, turbulent
• 29:18
  fluctuations to calculate the Reynolds stresses, but the math
• 29:22
  was too abstract. He couldn't find a way to anchor
• 29:24
  it to reality. He needed a physical model, a
• 29:27
  tangible, measurable variable that could describe the size and
• 29:30
  behavior of these swirling eddies.
• 29:33
  Completely burnt out, Pranville decides to take a walk outdoors
• 29:36
  to clear his head. He's standing on a balcony or a
• 29:39
  hill, looking out at the horizon, and he sees an
• 29:42
  industrial factory in the distance with a tall smokestack.
• 29:45
  OK, a smokestack. There is a strong breeze blowing
• 29:48
  and a massive plume of smoke is trailing horizontally out of the
• 29:50
  chimney, and he just stops and stares at the swirling, chaotic
• 29:54
  vortices of smoke tumbling through the sky.
• 29:57
  And in that chaotic plume, his genius mind recognized a
• 30:00
  pattern. Yes, he realizes that the
• 30:03
  vortices of smoke, the swirly eddies, are not entirely random
• 30:06
  inside, right? The eddies swirling down near
• 30:08
  the solid ground are relatively small and tight, but as he looks
• 30:13
  higher up into the open sky, further away from the solid
• 30:16
  boundary of the earth, the swirling eddies of smoke are
• 30:19
  massive, expansive and broad. He mathematically estimates in
• 30:23
  his head that the diameter of a swirling vortex is directly
• 30:28
  linearly proportional to its physical distance from the solid
• 30:31
  ground. Specifically, he theorizes that
• 30:33
  the vortex size is roughly 0.4 times its distance from the
• 30:37
  boundary. It was a monumental epiphany
• 30:39
  that changed engineering forever.
• 30:41
  It really did. Pratt Channel rushed back to his
• 30:44
  chalkboard and applied this visual observation directly to
• 30:47
  his turbulent pipe flow problem. He theorized that these
• 30:50
  microscopic turbulent eddies inside a pipe act like distinct
• 30:54
  parcels of fluid. Parcels of fluid.
• 30:56
  They travel a certain average lateral distance before they
• 30:59
  crash into another parcel mix and transfer their momentum.
• 31:02
  He called this specific travel distance the mixing length.
• 31:05
  And the the absolute stroke of genius was realizing that this
• 31:09
  mixing length isn't a random variable.
• 31:12
  Just like the factory smoke, the size of the turbulent eddies
• 31:15
  inside a steel pipe depends entirely on how far away they
• 31:18
  are from the solid wall. Exactly.
• 31:20
  Right next to the steel wall, there's no room to swirl, so the
• 31:22
  eddies are tiny. In the dead center of the pipe,
• 31:25
  far away from the walls, the eddies are massive.
• 31:28
  By substituting this mixing length theory, specifically his
• 31:32
  observation that the mixing length equals 0.4 times the
• 31:36
  distance from the wall into the complex Reynolds stress
• 31:38
  equations, Prant bolted the impossible.
• 31:41
  He produced a computable algebraic formula for turbulent
• 31:44
  friction. He managed to tame the
• 31:46
  mathematical chaos. Which is.
• 31:48
  Incredible. So if we step back and look at a
• 31:50
  pipe with turbulent flow, what does the velocity profile
• 31:53
  actually look like? When you graph Prandtl's math,
• 31:56
  it must look completely different from the smooth,
• 31:58
  pointy parabola of laminar flow. It looks fundamentally different
• 32:03
  because that violent, turbulent mixing is so incredibly
• 32:06
  efficient at transferring high momentum from the fast center
• 32:09
  out to the slow edges. The velocity profile across the
• 32:13
  vast majority of the pipe is much flatter.
• 32:15
  Flatter. It's much more uniform.
• 32:17
  The water across most of the pipe is moving at roughly the
• 32:19
  same bulk speed. But right against the wall,
• 32:22
  something deeply strange happens.
• 32:24
  Viscous sub layer. This is the ultimate paradox of
• 32:28
  turbulence. Precisely because of the
• 32:30
  physical presence of the impenetrable solid wall, those
• 32:33
  transverse turbulent fluctuations, EU prime sideways
• 32:37
  darting motions are physically suppressed.
• 32:40
  You cannot have a chaotic Eddie swirl straight through a solid
• 32:43
  steel boundary. Exactly.
• 32:45
  So as you get closer and closer to the wall, the mixing length
• 32:48
  approaches 0 in an unimaginably thin microscopic layer directly
• 32:53
  touching the wall, sometimes only fractions of a millimeter
• 32:56
  thick. Turbulence is completely
• 32:57
  extinguished. That is wild.
• 33:00
  Tiny zone called the viscous sublayer.
• 33:02
  Viscous friction rules supreme, and the flow actually behaves as
• 33:05
  if it were perfectly smooth laminar flow.
• 33:08
  It is wild to visualize. You have a pipe full of
• 33:11
  violently churning, chaotic, turbulent water, but clinging to
• 33:15
  the inner wall is a microscopic, incredibly slow, sticky skin of
• 33:20
  perfectly smooth water. And then as you move inward from
• 33:23
  that skin, the turbulence violently ramps up, creating
• 33:27
  what Prantle mathematically drived as a logarithmic velocity
• 33:30
  curve. The laws of physics completely
• 33:33
  change depending on whether you're 1mm or 10mm from the
• 33:37
  steel. It's amazing to think about all
• 33:39
  of this complex, invisible architecture happening inside
• 33:43
  the plumbing hidden behind our drywall every time we turn on a
• 33:45
  faucet. It is a beautifully complex
• 33:48
  system, but everything we have discussed so far, from
• 33:51
  Bernoulli's energy trading to Prantle's mixing length, has
• 33:54
  assumed one critical thing, which is we are dealing with
• 33:57
  closed pressurized systems, Pikes completely full of water.
• 34:00
  But what happens to the physics when we remove the pressure
• 34:03
  constraint? Which brings us to the third
• 34:05
  phase of our journey module. Three Rivers, sewers and
• 34:08
  aqueducts. The mechanics of oven channel
• 34:11
  flow. Ripping the roof off.
• 34:12
  Exactly. We've looked inside enclosed
• 34:15
  pipes where water is shoved forward by the pressure of a
• 34:17
  pump. But what happens when you RIP
• 34:19
  the roof off the pipe, expose the top surface of the water to
• 34:22
  the open atmospheric air, and let gravity take the wheel?
• 34:26
  Well, the moment you have a free surface exposed to the open air,
• 34:30
  the atmospheric pressure pushing down on the water is constant
• 34:33
  everywhere. Therefore, the internal pressure
• 34:36
  gradient that was driving the fluid in a pipe drops to 0.
• 34:39
  So it can't be pushed by pressure anymore.
• 34:41
  Right. A river cannot be pushed by
• 34:43
  pressure. Instead, open channel flow is
• 34:45
  driven entirely by gravity. The water flows because it is
• 34:48
  falling down a slope. But as we just spent 20 minutes
• 34:52
  discussing, the fluid was also experiencing viscous friction
• 34:55
  against the solid bottom and sides of the riverbed or the
• 34:58
  concrete channel, so it becomes an eternal tug of war.
• 35:02
  Gravity is constantly pulling the mass of the water down the
• 35:05
  incline, trying to accelerate it faster and faster, but the
• 35:09
  viscous friction and the turbulent eddies dragging along
• 35:12
  the rough riverbed are pulling backwards, trying to slow it
• 35:15
  down. And when a steady state is
• 35:17
  finally reached in a river or a canal, those two opposing forces
• 35:22
  achieve perfect equilibrium. Perfect balance.
• 35:24
  The specific component of gravity pulling the water down
• 35:27
  the geometric slope exactly equals the frictional shearing
• 35:31
  force of the channels boundary. When this mathematical balance
• 35:35
  is achieved, the water flows at a constant steady depth and a
• 35:39
  constant steady velocity. It stops accelerating.
• 35:42
  To predict this velocity, civil engineers use empirical
• 35:45
  equations, the most famous being the Manning equation or Chezzy's
• 35:49
  formula. And these formulas rely on a
• 35:51
  really clever, incredibly important geometric concept
• 35:54
  called the hydraulic mean depth or hydraulic radius.
• 35:58
  The hydraulic mean depth is a ratio.
• 36:00
  OK, how does that work? You calculate it by taking the
• 36:02
  total cross-sectional area of the flowing water and dividing
• 36:06
  it by what we call the wetted perimeter.
• 36:07
  The wetted perimeter, the. Wetted perimeter is simply the
• 36:10
  total linear length of the solid channel that is physically
• 36:13
  touching the water. If you look at a cross section
• 36:16
  of a river, it's the length of the riverbed from the Left Bank,
• 36:19
  down across the bottom and up to the right bank.
• 36:22
  It represents the total zone of friction.
• 36:25
  Let me make sure I understand the implications of this.
• 36:28
  Yeah, if I want water to flow as fast and efficiently as possible
• 36:31
  down a hill, I want the largest possible area of water pushing
• 36:35
  forward, but I want the smallest possible wetted perimeter
• 36:39
  dragging it back. I want to maximize the flow area
• 36:42
  while minimizing the friction surface.
• 36:44
  That is the exact optimization problem every civil engineer
• 36:47
  faces when designing A drainage canal or a sewer system.
• 36:51
  Let's do a mental exercise. Imagine you need to design A
• 36:55
  rectangular concrete channel with exactly 10 square feet of
• 36:59
  cross-sectional area. You could design it to be 10
• 37:01
  feet wide, but only one foot deep.
• 37:03
  OK, 10 wide, 1 deep. In that scenario, the wedded
• 37:07
  perimeter is 10 feet along the bottom, plus one foot on the
• 37:11
  left wall, plus one foot on the right wall.
• 37:13
  That's 12 total feet of friction surface.
• 37:17
  OK, but what if I redesign it to be 5 feet wide and two feet
• 37:21
  deep? The Gary is still exactly 10
• 37:23
  square feet, but now the wetted perimeter is 5 feet across the
• 37:27
  bottom, +2 feet on the left, +2 feet on the right Right.
• 37:30
  That's only 9 total feet of friction surface.
• 37:34
  By just changing the geometry, I've eliminated 25% of the
• 37:37
  frictional drag, even though it's carrying the exact same
• 37:40
  volume of water. The narrower, deeper channel
• 37:43
  will flow much faster. Exactly and mathematically, if
• 37:47
  you take this geometric optimization to its absolute
• 37:49
  limit, calculus dictates that for any given cross-sectional
• 37:53
  area, a full circle has the absolute smallest possible
• 37:56
  perimeter. Which brings me to one of my
• 37:58
  favorite historical mind blowers of all time from our sources,
• 38:01
  the Roman aqueducts. Oh, the Romans were geniuses.
• 38:04
  Starting around 300 BC with the Aqua appia, the Romans built
• 38:08
  these towering stone structures that carried millions of gallons
• 38:11
  of fresh water over dozens of miles to supply the baths and
• 38:15
  fountains of Rome. And if you climb to the top of
• 38:17
  an intact aqueduct today and look at the cross section of the
• 38:21
  actual water channel carved into the stone, what shape is it?
• 38:26
  It's a perfect semicircle. It is a breathtaking feat of
• 38:29
  engineering intuition. By carving A semicircular
• 38:32
  channel, the Roman engineers were unknowingly perfectly
• 38:35
  optimizing the hydraulic mean depth.
• 38:38
  Unknowingly. A semicircle flowing right to
• 38:41
  the brim has the mathematical minimum possible wedded
• 38:44
  perimeter for an open channel exposed to the air.
• 38:47
  They minimize the frictional drag of the rough stone walls to
• 38:50
  the absolute theoretical limit, which allowed the maximum
• 38:53
  possible volume of water to flow.
• 38:55
  They built these massive spanning stone structures
• 38:58
  stretching to the horizon, maintaining an imperceptible
• 39:01
  tiny downward slope, sometimes dropping only a few inches over
• 39:04
  an entire mile, all perfectly optimized for advanced fluid
• 39:08
  dynamics to millennia before the Naver Stokes equations were ever
• 39:11
  written down. It is just staggering to think.
• 39:13
  About it really is. It is a testament to the power
• 39:15
  of trial, error and observation. But open channel flow isn't just
• 39:19
  about steady rivers and ancient, gently sloping plumbing.
• 39:23
  What else is there? Because the top surface of the
• 39:25
  water is unconstrained and free to move up and down, open
• 39:29
  channels can exhibit some incredibly dynamic, violent and
• 39:33
  unstable behaviors. To understand these extreme
• 39:36
  behaviors, we have to look at the energy of the flow
• 39:39
  differently. We use a concept called specific
• 39:41
  energy. OK, let's unpack specific
• 39:43
  energy. How is this different from the
• 39:45
  total energy we talked about with Daniel Bernoulli and the
• 39:48
  roller coaster? It's a subtle but vital shift in
• 39:51
  perspective. In a closed pipe, we track total
• 39:55
  energy relative to some arbitrary fixed datum point,
• 39:58
  like sea level. But in an open channel, the
• 40:01
  bottom of the channel itself is constantly sloping downward.
• 40:04
  So specific energy measures the total energy of the fluid
• 40:07
  relative to the bottom of the channel it is currently flowing
• 40:10
  over. Relative to the bottom, got it.
• 40:12
  It's the sum of the water's physical depth, which represents
• 40:15
  its pressure and potential energy, plus its velocity head,
• 40:18
  which is its kinetic energy. So if a river is carrying a
• 40:21
  constant flow rate of 1000 gallons per second, it can
• 40:24
  physically carry that volume in two very different ways.
• 40:28
  It could be a very deep, slow moving lazy river.
• 40:32
  That flow has massive depth energy but very little kinetic
• 40:36
  energy. Or that exact same 1000 gallons
• 40:39
  per second could be flowing through a shallow incredibly
• 40:43
  fast moving mountain Rapids. That flow has very low depth
• 40:47
  energy but massive kinetic energy.
• 40:49
  Precisely. And if you graph the specific
• 40:52
  energy required to sustain both of those states, you find that
• 40:55
  the curve is shaped exactly like a sideways C.
• 40:57
  Sideways C. And right at the vertex, the
• 41:00
  absolute leftmost tip of that C curve, there's a minimum point.
• 41:03
  There is one specific mathematically derived critical
• 41:06
  depth where the specific energy required to push that exact flow
• 41:10
  rate is at its absolute minimum. This critical depth isn't just a
• 41:14
  math trivia fact, it acts as a massive physical boundary line
• 41:18
  in nature. It does.
• 41:19
  If the water is flowing deeper than this critical depth, it is
• 41:21
  moving relatively slowly and peacefully.
• 41:24
  We call this a tranquil or subcritical flow.
• 41:26
  But if the water is shallower than the critical depth, it is
• 41:29
  moving violently fast. We call this a rapid or
• 41:33
  supercritical flow. The laws of fluid behavior
• 41:35
  completely invert depending on which side of this boundary you
• 41:39
  are on. And we have a neat mathematical
• 41:41
  tool to determine which side of the boundary we are on, right?
• 41:44
  The Froude number. Yes, named after William Froude,
• 41:47
  a 19th century naval architect. The Froude number is a
• 41:51
  dimensionless ratio. What does it compare?
• 41:54
  It compares the actual forward flow velocity of the river to
• 41:57
  the speed at which a shallow surface wave naturally travels
• 42:01
  through that same depth of water.
• 42:03
  Like a ripple. Right.
• 42:05
  If you drop a heavy Pebble into a still pond, ripples spread
• 42:08
  outward in perfect circles. Those ripples have a strict
• 42:11
  mathematical speed limit dictated by gravity and the
• 42:14
  depth of the water. Let me see if I can visualize
• 42:16
  the implications of this. In a tranquil subcritical flow,
• 42:19
  like a deep lazy river, the bulk velocity of the water is slower
• 42:24
  than the natural speed of a ripple.
• 42:26
  The fraud number is less than one.
• 42:28
  This means if I throw a rock into that tranquil river, the
• 42:31
  ripples can actually travel upstream, fighting against the
• 42:35
  current because the wave is moving faster than the river
• 42:37
  itself. Exactly.
• 42:39
  The river can feel obstacles ahead of it because the pressure
• 42:42
  waves travel upstream to warn the water.
• 42:45
  That is a perfect visualization. But now consider a rapid
• 42:49
  supercritical flow, a shallow, violently fast mountain stream
• 42:54
  rushing over rocks. OK, supercritical.
• 42:57
  In this state, the bulk water is moving much faster than the
• 43:00
  natural wave speed. The fraud number is greater than
• 43:03
  one. Wow.
• 43:04
  If you throw a rock into a supercritical Rapids, the
• 43:07
  ripples cannot travel upstream. They try, but the sheer speed of
• 43:11
  the river sweeps them downstream faster than they can propagate.
• 43:14
  That's fascinating. The water is moving entirely
• 43:17
  blind. It cannot send pressure waves
• 43:19
  upstream to warn the incoming fluid.
• 43:21
  What about an obstacle? Wait a minute.
• 43:23
  Moving faster than your own ways, Unable to send pressure
• 43:26
  signals ahead of you? That is exactly how a supersonic
• 43:29
  fighter jet works. The jet is flying faster than
• 43:32
  the speed of its own sound waves in a super critical rapid flow.
• 43:36
  The water is literally supersonic relative to its own
• 43:40
  wave speed. The analogy is mathematically
• 43:43
  and physically flawless. Tranquil flow is subsonic.
• 43:46
  Rapid flow is supersonic. It's just get good.
• 43:48
  And just as a fighter jet decelerating from supersonic to
• 43:52
  subsonic speeds creates a violent explosive shockwave, a
• 43:56
  Sonic boom, water transitioning from rapid to tranquil flow does
• 44:00
  something equally dramatic, violent, and visible.
• 44:02
  What does it do? It creates a hydraulic.
• 44:04
  Jump. A hydraulic jump.
• 44:06
  This is where the jock board math suddenly explodes into
• 44:09
  massive real world destruction. Rapid flow is inherently
• 44:13
  unstable. I mean it's stable.
• 44:14
  If you have a super fast shallow layer of water racing down a
• 44:17
  steep concrete incline, and then the incline suddenly flattens
• 44:21
  out, the water cannot sustain that rapid supersonic state,
• 44:24
  right? It violently rear ends the
• 44:26
  slower, deeper, tranquil water ahead of it, and it explosively
• 44:29
  shifts states. It literally jumps.
• 44:31
  The surface of the water abruptly near vertically rises,
• 44:35
  churning into a massive frothing stationary wave of extreme
• 44:38
  turbulence. A tremendous amount of kinetic
• 44:41
  energy is violently dissipated as heat and deafening noise as
• 44:45
  the fast water violently crashes into the slow water.
• 44:48
  And civil engineers use this explosive phenomenon
• 44:51
  intentionally. They.
• 44:52
  Do. Think about the spillway of a
• 44:54
  massive structure like the Hoover Dam.
• 44:56
  When the reservoir gets too high, they release water down
• 44:59
  that massive, steeply angled concrete slide.
• 45:03
  It drops hundreds of feet, building up terrifying speed.
• 45:06
  It is a highly supercritical, extremely rapid flow moving at
• 45:10
  highway speeds. If that water were allowed to
• 45:12
  just blast into the natural dirt riverbed at the bottom at 100
• 45:16
  mph, the sheer kinetic energy would scour the earth.
• 45:19
  Oh, it would. It would erode the foundational
• 45:21
  bedrock of the dam itself, potentially causing the entire
• 45:24
  multibillion dollar structure to collapse within hours.
• 45:27
  It would be catastrophic. So to prevent this, at the very
• 45:30
  bottom of the spillway, engineers design a massive
• 45:33
  concrete basin called a stilling basin, often with a slight
• 45:36
  upward ramp. And what does that do?
• 45:37
  They deliberately, mathematically trigger a
• 45:40
  hydraulic jump. They force that rapid,
• 45:43
  supersonic water to crash into a deep wall of tranquil water,
• 45:47
  creating a massive, churning, boiling standing wave the size
• 45:51
  of a building. They use the hydraulic jump to
• 45:54
  act as a giant liquid brake. Yes, it dissipates all of that
• 45:58
  destructive kinetic energy safely within the heavily
• 46:01
  armored concrete basin, tumbling over itself.
• 46:04
  So by the time the water exits the basin and continues down the
• 46:07
  Colorado River, it has returned to a slow, safe, tranquil flow.
• 46:11
  It is the aquatic equivalent of harnessing an acoustic shockwave
• 46:15
  to protect our infrastructure. It's a perfect manipulation of
• 46:18
  energy states. That is just incredible.
• 46:20
  Which provides the ideal pivot point for our final transition.
• 46:24
  So far we've looked at fluids moving around solid boundaries,
• 46:27
  inside pipes and down concrete channels, but for our final
• 46:31
  phase we need to completely invert our perspective.
• 46:34
  Phase 4, Module 4 Flying, driving and slicing.
• 46:37
  Instead of a fluid flowing through a stationary pipe, what
• 46:40
  happens when a solid object violently forces its way through
• 46:43
  a stationary fluid? Yeah, this is the realm of
• 46:45
  external aerodynamics. We are talking about the
• 46:48
  aerodynamic drag on your car when you hit 70 on the highway,
• 46:51
  the lift generated by a Boeing 737 wing and the immense forces
• 46:56
  crushing a submarine. When an object forces its way
• 46:59
  through a fluid, it experiences a mechanical force resisting its
• 47:03
  motion. We broadly call this drag.
• 47:06
  But just as we learned that fluid friction is complex inside
• 47:10
  a pipe, drag on an external body is not a single simple
• 47:13
  phenomenon. It is fundamentally split into
• 47:15
  two wildly different types, friction drag and form drag.
• 47:19
  OK, friction drag makes intuitive sense based on what
• 47:22
  we've talked about with viscosity in the no slip
• 47:24
  condition. This is simply the fluid
• 47:26
  physically rubbing against the skin of the object.
• 47:29
  It's the viscous sheer stress trying to grab the surface.
• 47:33
  If you have a long thin flat plate slicing edge 1st through
• 47:36
  the air, perfectly parallel to the wind, almost 100% of the
• 47:40
  drag it experiences is friction drag.
• 47:43
  The air is just grabbing at the microscopic roughness of the
• 47:46
  metal sides. Exactly.
• 47:47
  But form drag, which is also commonly known as pressure drag,
• 47:51
  is entirely different, and it is the dominant force on blunt
• 47:54
  objects like a cylinder, a sphere, a golf ball, or the flat
• 47:58
  grille of a semi truck. Blunt objects.
• 48:00
  And to truly understand why form drag exists, we have to revisit
• 48:04
  our ideal world one last time to look at a hilarious historical
• 48:08
  math fail known as Dell and Bear's Paradox.
• 48:10
  I love the history of scientists just getting utterly baffled by
• 48:13
  their. It's pretty funny.
• 48:15
  So in the 1750s, a brilliant French mathematician named Jean
• 48:19
  Leron de Lambert applies Euler's ideal perfectly frictionless
• 48:23
  fluid equations to calculate the drag on a simple cylinder placed
• 48:26
  in a flowing stream of water. The math says that the fluid
• 48:29
  hits the dead center front of the cylinder, creating a high
• 48:32
  pressure stagnation point. Then the fluid smoothly divides,
• 48:36
  flowing perfectly around the curved sides, speeding up and
• 48:40
  dropping in pressure. Because of Bernoulli, right?
• 48:42
  Exactly. And finally, because the fluid
• 48:45
  is perfectly ideal, it flows perfectly back together at the
• 48:48
  exact rear of the cylinder, slowing down and seamlessly
• 48:52
  regaining all of its original high pressure.
• 48:54
  And because the flow is perfectly symmetrical front to
• 48:56
  back in an ideal fluid, the high pressure pushing backward on the
• 49:00
  front of the cylinder is exactly mathematically cancelled out by
• 49:03
  the equally high pressure pushing forward on the back of
• 49:06
  the cylinder. Resulting in Dallin Baer
• 49:08
  publishing a paper concluding that a solid cylinder
• 49:11
  experiences absolutely 0. Drag.
• 49:14
  You could theoretically throw a baseball in this ideal fluid and
• 49:17
  it would glide forward forever without ever slowing down.
• 49:20
  Which of course, is completely absurd and contrary to literally
• 49:23
  all human experience of walking against the wind or throwing a
• 49:26
  rock into a pond. He was so confused.
• 49:29
  Dolenbeer himself was totally baffled.
• 49:31
  He reportedly said that the theory of fluids was an
• 49:34
  illusion. The paradox remained A
• 49:36
  humiliating stain on fluid dynamics for over a century,
• 49:40
  until our old friend Ludwig Prantle finally solved it with
• 49:43
  his boundary layer theory. Frank Riedel again.
• 49:45
  Yes, the fatal flaw was ignoring viscosity.
• 49:50
  In the real world, a thin, viscous, slow moving boundary
• 49:54
  layer forms on the surface of the cylinder due to the no slip
• 49:57
  condition. Here's where the physics gets
• 49:59
  intense. As the fluid travels past the
• 50:02
  widest, thickest part of the cylinder and tries to negotiate
• 50:04
  the curved rear half to close the gap, it has a massive
• 50:08
  problem. A huge problem.
• 50:09
  According to Bernoulli, the pressure at the wide sides is
• 50:13
  very low, but the pressure at the rear stagnation point it's
• 50:15
  supposed to be very high. So the fluid flowing around the
• 50:18
  back half has to flow from a low pressure zone into a high
• 50:21
  pressure zone. It has to flow against what we
• 50:23
  call an adverse pressure gradient.
• 50:25
  They're trying to flow uphill. In terms of pressure, it's like
• 50:27
  trying to push a car up a steep hill.
• 50:29
  Exactly. Now the fast moving fluid far
• 50:32
  away from the cylinder has plenty of kinetic momentum to
• 50:35
  push through this high pressure hill and close the gap right?
• 50:38
  But the fluid trapped deep inside the microscopic boundary
• 50:42
  layer has already lost a massive amount of its kinetic energy due
• 50:46
  to the viscous friction rubbing against the cylinder's surface.
• 50:50
  Exhaustive. It simply doesn't have enough
• 50:52
  momentum left to push uphill against the adverse pressure
• 50:55
  gradient all the way to the back.
• 50:56
  So the boundary layer fluid literally stalls out.
• 50:59
  It stops moving, the high pressure behind it actually
• 51:02
  pushes it in reverse, and the flow completely rips away from
• 51:05
  the surface of the cylinder. We call this catastrophic
• 51:08
  failure flow separation. Flow separation.
• 51:10
  And when the flow separates, it cannot smoothly close back in
• 51:13
  around the rear of the object. Instead, it creates a massive,
• 51:16
  chaotic, churning wake of swirling turbulent eddies behind
• 51:20
  the cylinder. Because the fluid never smoothly
• 51:23
  regains its pressure, the pressure inside this chaotic
• 51:26
  wave remains very, very low. Now look at the balance of
• 51:29
  forces on the object. You have high stagnation
• 51:32
  pressure violently slamming into the front grille of the
• 51:35
  cylinder, but you have a low pressure vacuum of chaotic
• 51:38
  eddies sitting directly behind the cylinder.
• 51:41
  Depression is completely lopsided.
• 51:43
  That massive difference in pressure literally sucks the
• 51:46
  object backward. That suction is form drag.
• 51:49
  And this explains the entire basis of aerodynamic design.
• 51:52
  It's why modern sports cars, airplane wings and submarine
• 51:56
  holes are shaped like teardrops. Teardrops, right?
• 51:58
  A long, gently tapering, streamlined rear end gently
• 52:02
  guides the high speed air back together, dramatically reducing
• 52:05
  the steepness of the adverse pressure gradient.
• 52:07
  So the boundary layer can make. It exactly.
• 52:09
  This allows the exhausted boundary layer to make it all
• 52:12
  the way to the end, delaying or entirely preventing flow
• 52:15
  separation. No flow separation means no low
• 52:18
  pressure wake, which means practically zero form drag.
• 52:20
  Streamlining is simply the art of tricking the air into gently
• 52:24
  closing the gap behind you. But completely blunt objects
• 52:27
  like a telephone pole or a round power line can't trick the air.
• 52:32
  They're going to suffer massive flow separation.
• 52:34
  They absolutely will. And the low pressure wake they
• 52:36
  leave behind is not just a random fuzzy jumble of air.
• 52:40
  As the wind speed the Reynolds number increases.
• 52:42
  Past a certain point, the swirling eddies in the wake
• 52:45
  begin to organize themselves into an incredibly beautiful,
• 52:48
  mathematically precise alternating pattern.
• 52:51
  Yes, the Carmen Vortex St., named after Theodore von Karman,
• 52:56
  another legendary 20th century fluid dynamicist.
• 52:59
  The Carmen Vortex St. Instead of a continuous messy
• 53:03
  blur of turbulence, the cylinder starts shedding distinct massive
• 53:07
  individual vortices. 1 vortex spins off the top edge, creating
• 53:11
  a low pressure zone, pulling the wire up.
• 53:14
  Then, a moment later, a vortex spins off the bottom edge,
• 53:16
  pulling the wire down, then the top, then the bottom, over and
• 53:19
  over, trailing behind the object downwind like a staggering,
• 53:22
  perfectly spaced line of alternating whirlpools.
• 53:25
  This vortex shedding is incredibly regular and rhythmic.
• 53:28
  Engineers can even predict the exact frequency how many times
• 53:31
  per second these vortices will shed using a dimension metric
• 53:35
  called the strohol number. The strohol.
• 53:37
  Number. And this alternating rhythmic
• 53:39
  shedding exerts a violent, cyclical, oscillating physical
• 53:44
  force on the object itself. It Yanks the object up, then
• 53:47
  down, then up, then down, like a rapidly plugged guitar string.
• 53:50
  And that leads to one of the most poetic phenomena in
• 53:53
  physics. Yes, here's where it gets really
• 53:55
  interesting. This exact phenomenon of
• 53:58
  alternating vortex shedding is what causes telephone and power
• 54:02
  lines to sing or hum on cold, windy, wintry days.
• 54:06
  It's such a haunting sound. The wind blows across the
• 54:09
  perfectly cylindrical wire, and as the Carmen vortices shed
• 54:12
  alternately from the top and bottom at hundreds of times per
• 54:15
  second, they violently vibrate the heavy wire.
• 54:18
  The eerie singing tone you hear isn't the wind itself, it is the
• 54:22
  audible acoustic frequency of the strohole number of vibrating
• 54:25
  the metal wire. It is literally fluid mechanics
• 54:28
  making music. It's the same principle behind
• 54:31
  the ancient Eolian harp, an instrument played entirely by
• 54:34
  the whim. It is beautiful, but vortex
• 54:35
  shedding isn't always so benign. Really.
• 54:37
  When is it bad? If the frequency of the shedding
• 54:39
  the stroller member happens to perfectly match the natural
• 54:42
  structural resonant frequency of the object that's hitting, it
• 54:46
  can cause catastrophic oscillations.
• 54:48
  Oh, residents like shattering a glass.
• 54:50
  Precisely. The alternating low pressure
• 54:53
  zones will literally tear a tall steel chimney or suspension
• 54:56
  bridge apart, violently shaking it until the metal yields.
• 54:59
  OK, so we've exhaustively covered drag.
• 55:02
  The Force is pushing you backward and shaking you apart.
• 55:05
  Now let's talk about the Holy Grail of aerodynamics, the force
• 55:08
  pulling you upward against gravity well.
• 55:10
  Fun stuff. How exactly does a multi ton
• 55:14
  Boeing 777 wing work? How do hundreds of tons of metal
• 55:19
  and luggage managed to float in the thin sky?
• 55:22
  To understand lift, you need a specific fluid ingredient that
• 55:25
  drag doesn't inherently require. What's that?
• 55:28
  Circulation. To generate a sustained lifting
• 55:30
  force, you must induce A Rotary spinning motion in the fluid
• 55:33
  around the object. The spin.
• 55:35
  If you take a uniform straight horizontal flow of wind and
• 55:38
  mathematically superimpose a circulated flow of air spinning
• 55:41
  in a circle around the object, something magical happens to the
• 55:44
  velocity profile. Let's visualize this on the top
• 55:47
  of the object. The circulating spinning flow is
• 55:50
  moving in the exact same direction as the uniform
• 55:53
  headwind. Exactly.
• 55:54
  The two velocities add together, making the air rushing over the
• 55:57
  top move incredibly fast. But on the bottom of the object,
• 56:01
  the circulating flow is spinning forward, fighting against the
• 56:05
  uniform headwind, right? They subtract from each other,
• 56:08
  making the air on the bottom move much slower.
• 56:10
  And because of our deep dive into module one, we know exactly
• 56:14
  what happens next. Bernoulli's equation.
• 56:16
  Exactly right. High velocity on the top means
• 56:19
  very low static pressure. Low velocity on the bottom means
• 56:23
  much higher static pressure. The high pressure on the bottom
• 56:25
  literally pushes the object upward trying to fill the low
• 56:29
  pressure void on on the top. That net upward pressure
• 56:32
  difference is lift. We calculate the exact magnitude
• 56:35
  of this force using the Kuda Jakowski theorem, which proves
• 56:39
  mathematically that lift is directly proportional to the
• 56:42
  density of the air, the velocity of the airplane, and the
• 56:44
  strength of that invisible circulation.
• 56:47
  And this principle isn't just for heavy airplanes.
• 56:49
  It absolutely dictates the physics of modern sports.
• 56:53
  Oh, everywhere in sports. Think about a pitcher throwing a
• 56:55
  devastating curveball in baseball.
• 56:58
  When the pitcher violently snaps their wrist upon release, they
• 57:02
  put a massive, rapid spin on the ball.
• 57:05
  The baseball is a simple sphere, but because of the viscosity of
• 57:08
  the air, and specifically the raised rough red cotton seams on
• 57:12
  the leather gripping that air, the spinning ball violently
• 57:15
  drags a microscopic layer of air around with it as it flies.
• 57:19
  It physically creates its own circulation, yes.
• 57:22
  So if a pitcher throws A fastball with extreme top spin,
• 57:25
  the top of the ball is spinning forward directly into the
• 57:28
  oncoming air. It slows the air down, creating
• 57:30
  high pressure on top. OK the bottom of the ball is
• 57:33
  spinning backward with the air speeding it U and creating low
• 57:36
  pressure on the bottom. The high pressure on top
• 57:38
  physically pushes the ball down toward the Earth faster than
• 57:42
  gravity alone. Which?
• 57:42
  Is terrifying for a batter. A 95 mile per hour fastball with
• 57:46
  extreme top spin will suddenly sharply drop an extra foot right
• 57:50
  as the batter swings over it. It's called the Magnus effect.
• 57:53
  It's the exact same aerodynamic reason a tennis player uses
• 57:57
  extreme backspin slice to make a ball float seemingly endlessly
• 58:01
  over the net. Oh, right.
• 58:03
  Or why a skilled soccer player can bend a free kick laterally
• 58:07
  around a solid wall of defenders into the corner of the goal.
• 58:11
  They are using viscosity to weaponize Bernoulli's equation.
• 58:15
  Weaponizing Bernoulli. I like that.
• 58:17
  But perhaps the most incredible, counterintuitive manipulation of
• 58:21
  fluid dynamics in all of sports has to be the golf ball.
• 58:24
  The dimples. Yeah, every kid wonders why golf
• 58:27
  balls aren't perfectly smooth. A smooth shiny sphere seems like
• 58:31
  it should be more aerodynamic. It seems like it, yeah.
• 58:33
  But if a professional golfer hits a perfectly smooth ball
• 58:36
  with a driver, yeah, it will only fly about half as far as a
• 58:39
  standard dimpled one. It will literally fall out of
• 58:42
  the sky. This brings us perfectly full
• 58:43
  circle back to form drag, adverse pressure gradients, and
• 58:46
  flow separation. That's it.
• 58:48
  Well, a golf ball is a blood spherical object.
• 58:51
  As it flies through the air at high speed, the flow naturally
• 58:55
  wants to separate very early on the curvature of the ball
• 58:58
  creating a massive turbulent low pressure wake that violently
• 59:02
  sucks the ball backward, killing its forward momentum.
• 59:05
  So how do dimples help? The hundreds of tiny dimples
• 59:08
  carved into the surface act as microscopic vortex generators.
• 59:12
  They intentionally tripped the delicate boundary layer.
• 59:15
  They force the smooth, fragile lameter boundary layer to
• 59:19
  immediately transition into a chaotic, turbulent boundary
• 59:22
  layer. Exactly, And to a layman it
• 59:25
  seems completely counterintuitive.
• 59:26
  Why on earth would you intentionally create turbulence
• 59:29
  on the surface of a projectile? Yeah, that sounds bad.
• 59:32
  Because, as we learned with Printwell, A turbulent boundary
• 59:35
  layer involves massive lateral mixing.
• 59:38
  It is constantly pulling high speed, high kinetic energy air
• 59:41
  from further out and violently mixing it down right next to the
• 59:45
  surface of the ball. Oh wow.
• 59:46
  That extra injected energy allows the boundary layer to
• 59:49
  fight against the adverse pressure gradient.
• 59:51
  Much, much longer. It has the strength to cling to
• 59:54
  the curved surface of the ball much further around the backside
• 59:58
  before it finally, inevitably stalls and separates.
• 1:00:02
  The gymbles delay the flow separation by making the high
• 1:00:05
  energy air cling longer. The physical size of the low
• 1:00:08
  pressure wake behind the ball is drastically reduced.
• 1:00:11
  The backward suction of the form drag plummets.
• 1:00:13
  It's a brilliant, highly calculated engineering trade
• 1:00:17
  off. You willingly accept a tiny bit
• 1:00:19
  more friction drag from the rough dimpled surface rubbing
• 1:00:22
  the air in exchange for a massive game changing reduction
• 1:00:25
  in form drag. The ball effortlessly slices
• 1:00:28
  through the air and flies twice as far.
• 1:00:31
  It is arguably the most elegant fluid engineering in consumer
• 1:00:34
  sports. Now obviously a massive
• 1:00:36
  commercial aircraft wing does not spin like a baseball to
• 1:00:38
  create circulation, and it isn't covered in golf ball dimples.
• 1:00:41
  No, it is not. So how does a rigid stationary
• 1:00:44
  wing generate that required circulation to fly?
• 1:00:46
  They achieve it entirely through their highly specific
• 1:00:49
  asymmetrical geometry. The aerofoil shape.
• 1:00:52
  A wing has a thick, rounded leading edge of the front, but a
• 1:00:56
  very, very sharp tapering trailing edge at the back.
• 1:00:59
  That razor sharp trailing edge is the absolute key to flight.
• 1:01:03
  Why is it so sharp? When an amplane powers up its
• 1:01:06
  engines and starts to accelerate down the runway, the air
• 1:01:09
  initially tries to flow symmetrically, wrapping all the
• 1:01:12
  way around the back of the wing from bottom to top.
• 1:01:15
  But the air simply cannot negotiate that incredibly sharp
• 1:01:19
  hairpin turn at the trailing edge at high speed.
• 1:01:23
  The flow violently separates there, and the viscosity of the
• 1:01:26
  air rips off a tight, violently spinning Eddy of air called a
• 1:01:30
  starting vortex. A starting vortex.
• 1:01:33
  This vortex is literally left behind, spinning on the runway
• 1:01:36
  tarmac as the plane accelerates away.
• 1:01:38
  But the universe and the laws of physics demand gallons.
• 1:01:42
  According to Jakowski's hypothesis regarding the
• 1:01:44
  conservation of angular momentum, if a vortex spins
• 1:01:47
  clockwise in the fluid and equal and opposite counterclockwise,
• 1:01:51
  circulation must be created somewhere else to maintain zero
• 1:01:54
  net angular momentum in the total system.
• 1:01:56
  Right. You can't just create spin out
• 1:01:58
  of nowhere precisely when the wing violently sheds that
• 1:02:02
  starting vortex off the back. An invisible theoretical bound
• 1:02:06
  vortex of equal strength is mathematically and physically
• 1:02:10
  locked around the wing itself, spinning in the exact opposite
• 1:02:13
  direction. And that spinning is what we
• 1:02:15
  need for lift. Yes.
• 1:02:17
  This bound vortex provides the massive circulation needed to
• 1:02:20
  make the air over the top of the wing move much faster and the
• 1:02:23
  air under the bottom moves slower.
• 1:02:26
  The pressure drops on top, the pressure spikes in the bottom,
• 1:02:29
  and lift is born. The plane leaves the ground.
• 1:02:33
  But wings have hard physical limits.
• 1:02:35
  If a pilot gets too aggressive, pulls back on the yoke and tilts
• 1:02:38
  the nose, the plane up too high, increasing what we call the
• 1:02:40
  angle of attack, they are forcing the air to work too hard
• 1:02:44
  to climb the steep slope of the upper wing.
• 1:02:46
  Very true. Just like the flow separating
• 1:02:48
  behind the blunt cylinder, the boundary layer on top of the
• 1:02:51
  wing runs out of kinetic energy trying to climb that massive
• 1:02:53
  adverse pressure gradient, and it violently rips away from the
• 1:02:56
  metal. The flow separates entirely.
• 1:02:59
  The smooth, high speed clinging air that was creating the
• 1:03:02
  massive low pressure suction on top of the wing instantaneously
• 1:03:06
  collapses into a chaotic, churning, useless wake of
• 1:03:10
  turbulence. And then what?
• 1:03:12
  Lift drops to near 0 in a fraction of a second and drag
• 1:03:15
  spikes massively. This catastrophic event is
• 1:03:19
  called an aerodynamic stall. A stall.
• 1:03:22
  If a heavy commercial plane stalls at a low altitude, it
• 1:03:25
  simply stops being a flying machine and becomes a falling
• 1:03:28
  rock. The physical angle of the wing
• 1:03:30
  has pushed the fluid dynamics past its absolute breaking
• 1:03:33
  point. And Speaking of pushing fluids
• 1:03:35
  past their physical breaking point, we absolutely cannot end
• 1:03:39
  this deep dive without returning to the destructive hook we
• 1:03:41
  started the show with. The ship propellers.
• 1:03:44
  Right, we touched on how air stalls, but what happens when
• 1:03:47
  liquid water itself breaks down? This raises A profound question
• 1:03:50
  about the absolute limits of Bernoulli's equation.
• 1:03:52
  Also, we established early on that as fluid velocity
• 1:03:56
  increases, static pressure decreases.
• 1:03:59
  But water has a hard physical limit on how low its internal
• 1:04:02
  pressure can possibly go before its molecular bonds fail.
• 1:04:06
  That limit is its vapor pressure, the precise pressure
• 1:04:10
  at which liquid water physically boils and turns into a gas.
• 1:04:14
  Normally we boil water by putting a pot on a stove and
• 1:04:18
  heating it up to 100°C. We raise the internal energy of
• 1:04:21
  the water until it can overcome the heavy atmospheric pressure
• 1:04:25
  pushing down on it from the air. That's the normal way, but.
• 1:04:28
  You can also boil water at room temperature without adding a
• 1:04:30
  single degree of heat, simply by removing the pressure pushing
• 1:04:34
  down on it. And that is exactly what high
• 1:04:36
  speed underwater machinery accidentally does.
• 1:04:39
  Let's return to the massive steel propeller of a cargo ship,
• 1:04:43
  or the impeller inside a high power industrial water pump.
• 1:04:46
  OK, the propeller. The blades of a propeller are
• 1:04:49
  essentially just spinning hydrofoil wings.
• 1:04:51
  They create lift, which in a nautical context we call forward
• 1:04:56
  thrust, by moving water extremely fast over their highly
• 1:05:00
  curved metal surfaces. If the captain throttles the
• 1:05:02
  engines and the propeller spins fast enough, the velocity of the
• 1:05:06
  water rushing over the curved back of the blade becomes so
• 1:05:09
  incredibly high that following Bernoulli's law, the local
• 1:05:13
  static pressure drops drastically.
• 1:05:15
  If it spins fast enough, the pressure drops below the ambient
• 1:05:19
  vapor pressure of water. The water doesn't just flow over
• 1:05:22
  the blade anymore, the liquid water literally rips apart and
• 1:05:26
  boils that ocean temperature right on the surface of the
• 1:05:30
  spinning metal blade. It instantaneously flashes into
• 1:05:33
  millions of tiny localized vapor bubbles or cavities, hence the
• 1:05:37
  name cavitation cavitation. But these vapor bubbles are
• 1:05:40
  incredibly short lived. The propeller is spinning
• 1:05:43
  rapidly, violently sweeping these low pressure bubbles out
• 1:05:46
  of the ultra low pressure zone on the curve of the blade and
• 1:05:49
  shoving them backward into the surrounding normal high pressure
• 1:05:52
  ocean water. And when a microscopic ultra low
• 1:05:55
  pressure vapor bubble is suddenly surrounded by heavy,
• 1:05:58
  crushing high pressure water, it doesn't just gently pop like a
• 1:06:02
  soap bubble in the. Air.
• 1:06:03
  No it does not. It collapses implosively,
• 1:06:06
  violently. The surrounding high pressure
• 1:06:08
  water rushes inward from all sides simultaneously to fill the
• 1:06:11
  void left by the collapsing vapor.
• 1:06:13
  The walls of water violently crash into themselves at the
• 1:06:17
  absolute dead center of the bubble at supersonic speeds.
• 1:06:20
  Supersonic implosion. This microscopic supersonic
• 1:06:24
  implosion generates an intense acoustic shockwave along with a
• 1:06:28
  microscopic high speed jet of water that shoots out from the
• 1:06:31
  center of the collapse. A shockwave that can reach
• 1:06:34
  localized pressures of up to 200 Atmos sheres.
• 1:06:37
  That is roughly £3000 per square inch of force.
• 1:06:40
  It's like a microscoic stick of dynamite going off.
• 1:06:43
  Exactly. And if that bubble happens to
• 1:06:44
  collapse while it's physically touching, or even just hovering
• 1:06:47
  millimeters away from the solid metal blade of the propeller.
• 1:06:51
  The supersonic jet of water and the acoustic shockwave act like
• 1:06:54
  an infinitesimally sharp, incredibly powerful microscopic
• 1:06:57
  drill. It strikes the metal with such
• 1:07:00
  unfathomable force that it instantly micro fractures the
• 1:07:03
  surface of the steel. Wow.
• 1:07:05
  A single bubble does microscopic damage.
• 1:07:07
  But over hours, days and months, millions upon millions of these
• 1:07:11
  supersonic bubble collapses will literally eat away solid steel,
• 1:07:16
  bronze or titanium. Which explains the pitted,
• 1:07:18
  scarred propellers we talked about at the beginning.
• 1:07:21
  They leave deep, jagged pock marks that look exactly like
• 1:07:24
  severe acid burns, completely destroying the heavy machinery
• 1:07:28
  and eventually causing the propeller to snap.
• 1:07:30
  Mechanical Engineers have to spend thousands of hours
• 1:07:33
  designing entire complex systems, massive municipal water
• 1:07:37
  pumps, hydroelectric dam turbines, high speed submarine
• 1:07:40
  hulls, specifically to calculate and strictly avoid hitting that
• 1:07:45
  critical cavitation threshold. Because fluid dynamics at that
• 1:07:48
  extreme is no longer just moving water, it is literally a
• 1:07:51
  destructive force that annihilates solid metal.
• 1:07:54
  Is the ultimate humbling testament to the hidden, awe
• 1:07:57
  inspiring power of fluids. We started this hour by looking
• 1:08:01
  at a simple garden hose, imagining an ideal, perfectly
• 1:08:05
  behaved, frictionless stream of mathematical energy trading.
• 1:08:08
  We've come a long way. And we end by visualizing
• 1:08:11
  microscopic acoustic shock waves chewing their way through thick
• 1:08:14
  solid steel in the depths of the ocean.
• 1:08:16
  It's quite the journey. Class dismissed.
• 1:08:18
  What an unbelievable paradigm shifting journey.
• 1:08:21
  Today, we have literally unpacked the invisible
• 1:08:23
  architecture of the physical world.
• 1:08:25
  We really covered a lot of ground.
• 1:08:26
  We saw how Daniel Bernoulli's concept of energy trading gives
• 1:08:30
  us the high speed pico tubes on commercial airliners.
• 1:08:34
  We walked with Ludwig Prantel as you watch factory chimney smoke
• 1:08:38
  and mathematically tamed the impossible chaos of turbulent
• 1:08:41
  friction. Incredible minds.
• 1:08:42
  We saw how brilliant Roman engineers unknowingly optimize
• 1:08:46
  the hydraulic mean depth of their spanning aqueducts, and
• 1:08:49
  how modern dam builders harness the violent supersonic shock of
• 1:08:53
  a hydraulic jump to protect our vital infrastructure.
• 1:08:56
  Yeah. We learned why wintry power
• 1:08:59
  lines sing their stroll number, why golf balls rely on dimpled
• 1:09:03
  turbulence to fight form drag, and why spinning propellers can
• 1:09:06
  literally boil the ocean and tear themselves apart.
• 1:09:08
  The mental toolkit is complete. You now have the fundamental
• 1:09:12
  lens required to see the invisible mechanics behind the
• 1:09:14
  motion of the world. I certainly do.
• 1:09:16
  But before we sign off, I want to leave you with one final,
• 1:09:19
  deeply personal thought to Moll over.
• 1:09:22
  We've spent this entire deep dive talking about massive
• 1:09:24
  industrial pipes, rushing rivers, commercial airplanes,
• 1:09:28
  and ocean freighters. But consider the fluid dynamics
• 1:09:31
  happening inside your own body at this exact second.
• 1:09:34
  That is a wild pivot. Where are you going with?
• 1:09:36
  This. Well, your heart is a biological
• 1:09:38
  pump, right? Tirelessly cycling roughly 2000
• 1:09:41
  gallons of fluid every single day.
• 1:09:43
  But it isn't pumping ideal frictionless water.
• 1:09:47
  It is pumping blood. A highly viscous, non Newtonian
• 1:09:51
  fluid densely packed with red cells, white cells and complex
• 1:09:54
  proteins. That's true.
• 1:09:56
  And it is pumping it through a massive, sprawling, branching
• 1:09:59
  network of flexible living pipes that constantly expand and
• 1:10:04
  contract with pressure. OK, I see where you're going.
• 1:10:06
  How do the microscopic boundary layers and viscous shear
• 1:10:09
  stresses we discussed behave when the pipe itself is actively
• 1:10:12
  pulsing? How do the sheer stresses of
• 1:10:14
  viscous friction affect the delicate cellular inner lining
• 1:10:18
  of your arteries over a lifetime?
• 1:10:20
  Wow. How do Bernoulli's principles of
• 1:10:22
  narrowing vessels, pressure drops, and velocity spikes
• 1:10:25
  dictate the long term health of your vascular system every time
• 1:10:29
  your heart beats every single second of your life?
• 1:10:32
  The laws of fluid dynamics aren't just out there in the
• 1:10:34
  industrial world, they are the very mechanical laws keeping you
• 1:10:37
  alive right now. That is absolutely something to
• 1:10:40
  think about the next time you feel your pulse racing.
• 1:10:43
  If you haven't already, give us a like and follow and please
• 1:10:46
  leave us a comment if you enjoy the podcast.
• 1:10:48
  We'd love to hear from the folks who make this possible.