Latest / Mechanical Engineering Made Simple / (#64) Fluid Mechanics Viscosity and Reynolds Number

Transcript

(#64) Fluid Mechanics Viscosity and Reynolds Number · Mechanical Engineering Made Simple

• 0:00
  Welcome back to Mechanical Engineering Made Simple.
• 0:02
  Quick update before we dive in. We've officially launched paid
• 0:05
  subscriptions. That means if you want deeper
• 0:08
  cuts, special episodes, and real answers to the questions
• 0:11
  engineers actually care about, you can now support the show
• 0:14
  directly. Think of it as buying the
• 0:16
  creator a cup of coffee. $0.99 a month gets you access to
• 0:19
  exclusive content, listener requested breakdowns and
• 0:23
  episodes focused on turning engineering skills into real
• 0:25
  world leverage, opportunity, and income.
• 0:29
  OK, let's get into it. Today we're doing a deep dive on
• 0:32
  a topic that is. I mean, it's completely
• 0:35
  fundamental, but so often invisible fluid mechanics.
• 0:38
  It really is. It governs everything from, you
• 0:40
  know, the blood flowing in your veins to how a jumbo jet stays
• 0:43
  in the air. Absolutely.
• 0:44
  So I think our mission today should be to kind of cut through
• 0:47
  that complexity. I agree.
• 0:48
  Let's unpack the core ideas what a fluid actually is, how we try
• 0:52
  to model its motion even when it's chaotic, and you know, the
• 0:55
  practical tools engineers use every day to make sense of it
• 0:58
  all. Perfect.
• 0:59
  So let's start right at the beginning.
• 1:01
  When we say fluid, what are we really talking about?
• 1:04
  What's the key difference between, say, water in the air
• 1:07
  around us? What really boils down to two
• 1:10
  key characteristics, compressibility and viscosity,
• 1:14
  We usually split them into liquids and gases.
• 1:17
  A liquid like water, we generally consider it to be
• 1:19
  incompressible. It holds its volume and it will
• 1:22
  form a free surface. A gas on the other hand is easy
• 1:25
  to compress and it just expands to fill whatever container you
• 1:28
  put it in. So for most calculations with
• 1:30
  water, you can just assume it doesn't shrink under pressure to
• 1:33
  make the math easier. That's right for the most part,
• 1:36
  but if you get into really high pressure systems like heavy
• 1:39
  industrial hydraulics, that tiny bit of compression starts to
• 1:42
  matter. And for gases?
• 1:44
  With the asses, it's a bit more nuanced.
• 1:45
  They are definitely compressible, but if the
• 1:48
  pressure changes are small and the speeds are low, engineers
• 1:51
  will often treat the flow as if it were incompressible.
• 1:54
  It's a very useful simplification.
• 1:57
  And the other half of that coin is viscosity.
• 1:59
  I always think of it as you know the difference between wading
• 2:02
  through a pool and trying to run through a VAT of honey.
• 2:04
  That's a perfect visual. It's that internal friction, the
• 2:07
  fluids resistance to flowing, and that one property viscosity
• 2:12
  connects the entire history of the field.
• 2:14
  Right, because we tend to think of fluid mechanics as this
• 2:16
  modern calculus heavy field. But the practical side of it,
• 2:20
  hydraulics, is ancient. It's completely ancient.
• 2:23
  It was born out of pure necessity.
• 2:26
  Civilizations needed to move water.
• 2:28
  We have irrigation canals in Egypt and Mesopotamia that are
• 2:31
  what, over 6000 years old? And think about the Roman
• 2:34
  aqueducts. They weren't just amazing
• 2:36
  structures, they were incredible feats of engineering.
• 2:38
  They had to calculate the right conduit size, the right slope,
• 2:42
  all to overcome friction over miles and miles.
• 2:44
  But the. First person to really start
• 2:46
  looking at it with a sort of a modern scientific eye was
• 2:50
  Leonardo da Vinci. He was a true pioneer.
• 2:52
  He didn't just build things, he observed everything.
• 2:55
  He was the first person to really try to visualize flow.
• 2:58
  His notebooks are filled with these incredible sketches of
• 3:01
  streamlines and vortices or eddies.
• 3:04
  He was basically searching for the most efficient shape, the
• 3:07
  path of least resistance. Exactly.
• 3:09
  He was trying to find the least resistive streamline shape.
• 3:13
  He was laying the groundwork for concepts.
• 3:15
  We now need supercomputers to model with CFD.
• 3:18
  And that brings us to the mathematical elephant in the
• 3:21
  room, the Naver Stokes equations.
• 3:23
  Right. The fundamental equations of
• 3:25
  fluid motion. They were worked out in the 19th
• 3:27
  century, and they're basically Newton's second law, F equals
• 3:31
  MA, but applied to a tiny moving piece of fluid.
• 3:36
  So if they describe everything, why are they so notoriously
• 3:38
  difficult to solve? Why do they haunt engineering
• 3:41
  students? Because they're nonlinear, and
• 3:43
  that nonlinearity comes from what we call the convection
• 3:46
  terms. These are the bits of the
• 3:47
  equation that describe how the velocity changes from one point
• 3:50
  to another. So the.
• 3:50
  Fluid is essentially interacting with itself.
• 3:53
  That's a great way to put it. The motion of one part of the
• 3:55
  fluid instantly and chaotically effects all the other parts.
• 3:59
  That's where turbulence comes from.
• 4:01
  It's why tiny changes in the starting conditions can lead to
• 4:04
  wildly different outcomes. Which is why an exact solution
• 4:07
  is almost impossible to find in most cases.
• 4:10
  So how do engineers get around this?
• 4:12
  How do we simplify? We use a very powerful shortcut,
• 4:17
  the Reynolds number. OK, tell us about that.
• 4:18
  The Reynolds number or REE is just a ratio.
• 4:22
  It's a ratio of the inertia forces, the forces trying to
• 4:25
  keep the fluid moving to the viscous forces, which are the
• 4:28
  frictional forces trying to slow it down.
• 4:30
  So by calculating that one number by.
• 4:32
  Calculating that one number, you know which forces are dominant
• 4:36
  and if one is much bigger than the other, you can just drop the
• 4:39
  smaller term from the Navier Stokes equations.
• 4:41
  It cleans up the mass beautifully.
• 4:43
  OK, so let's take the extremes. What if the Reynolds number is
• 4:45
  very very small? Viscosity is dominant.
• 4:49
  That's a situation we call creeping flow.
• 4:51
  Think of lava, or maybe the oil film in a sliding bearing.
• 4:55
  Inertia is so small it's basically negligible, so we just
• 4:58
  omit the entire inertia part of the equation.
• 5:00
  And that simplified version is solvable.
• 5:03
  Often, yes, Analytically. Now what about the other end of
• 5:06
  the spectrum, a huge Reynolds number?
• 5:09
  Like the air flowing over a jet wing at high speed.
• 5:12
  Perfect example there. Inertia is completely
• 5:15
  overwhelming viscosity, so we do the opposite.
• 5:18
  We neglect the viscosity term and treat the fluid as if it
• 5:21
  were in viscid or frictionless. What about that messy middle
• 5:25
  ground where inertia and viscosity are both important?
• 5:28
  Right. And that's most real world
• 5:30
  engineering problems. You can't simplify and that is
• 5:32
  the domain of computational fluid dynamics or CFD.
• 5:35
  Using computers to do the heavy lifting.
• 5:37
  Exactly. We use numerical methods to
• 5:40
  break the problem into millions of tiny pieces and solve the
• 5:43
  full equations for each one, step by step.
• 5:45
  It's the only way to follow that kaleidoscopic change of flow
• 5:49
  that defines reality. That intermediate range of
• 5:51
  Reynolds number also brings us to another key concept that
• 5:54
  people always want to understand, the difference
• 5:57
  between laminar and turbulent flow.
• 5:59
  Yes, this is absolutely fundamental.
• 6:01
  Laminar flow is smooth, it's orderly.
• 6:04
  You can picture it as these neat layers of fluid just sliding
• 6:07
  over each other. It's very efficient.
• 6:09
  Low energy loss. Very low.
• 6:11
  Turbulent flow, on the other hand, is chaos.
• 6:13
  It's full of random lateral motions and swirling eddies.
• 6:16
  It's a mess. So if laminar is so much more
• 6:19
  efficient, why don't we just design everything to stay in the
• 6:22
  laminar regime? Because to get the the
• 6:24
  performance we need, the speed, the flow rate, we often have to
• 6:28
  push the velocity up and that pushes the Reynolds number up
• 6:32
  right into the turbulent zone. And that turbulence cost you a
• 6:34
  ton in energy. How do you even quantify that
• 6:37
  cost, that chaos? We measure it with something
• 6:40
  called shearing stress. In turbulent flow.
• 6:43
  The total stress has two parts, the normal viscous stress and an
• 6:47
  extra component called the turbulent shearing stress, and
• 6:50
  this extra stress is related to something called the Reynolds
• 6:53
  stress, which is basically a measure of the momentum being
• 6:56
  violently exchanged between fluid layers by those chaotic
• 6:59
  eddies. And this is all happening most
• 7:01
  intensely right near a surface. Which brings us to another huge
• 7:05
  breakthrough, the boundary layer.
• 7:08
  Ludwig Prandtl's brilliant insight from the early 1900s.
• 7:12
  You realize that all the important effects of friction
• 7:14
  are basically confined to a very thin layer right next to a solid
• 7:17
  surface? Boundary layer.
• 7:19
  The boundary layer. Inside that layer the velocity
• 7:21
  goes from zero because the fluid sticks to the wall.
• 7:24
  The no slip condition all the way up to the full free stream
• 7:27
  velocity just a tiny distance away.
• 7:30
  And this layer isn't static, it changes as it moves along the
• 7:32
  surface, doesn't it? It does.
• 7:34
  It starts off as a nice smooth laminar boundary layer at the
• 7:38
  leaning edge, but as it flows downstream it gets thicker and
• 7:43
  more unstable, eventually transitions into a chaotic,
• 7:46
  thick, turbulent boundary layer. And that transition is bad news
• 7:49
  for drag. Very bad news.
• 7:51
  A turbulent boundary layer creates much much more skin
• 7:54
  friction drag than a laminar 1. Now, the power of these
• 7:57
  dimensionless numbers, like Reynolds extends beyond just
• 8:01
  predicting flow types. It's crucial for design and
• 8:04
  testing right through dimensional analysis.
• 8:07
  It's the engineer's secret weapon.
• 8:09
  The idea is to group variables into non dimensional quantities.
• 8:13
  This lets us summarize tons of experimental data onto a single
• 8:16
  chart, and more importantly, it lets us achieve dynamic
• 8:20
  similarity. Meaning you can test a small
• 8:22
  model and know it will behave exactly like the full scale.
• 8:25
  Version as long as the key dimensionless numbers match.
• 8:28
  If viscous forces are important, your models Reynolds number must
• 8:32
  match the prototypes Reynolds number.
• 8:34
  What if other forces are at play, like gravity for a ship
• 8:38
  moving through water? Then you need to match the
• 8:40
  Froude number, which is the ratio of inertia to gravity
• 8:43
  forces. If you match the Froude number
• 8:45
  for your model boat in a test tank, you can be confident the
• 8:48
  wave patterns will be similar to the real ship.
• 8:50
  And for something really fast where the fluid starts to
• 8:53
  compress. Then the Mach number is king.
• 8:56
  It's the ratio of the fluids velocity to the speed of sound.
• 8:59
  Subsonic is Mach less than one, supersonic is greater than one.
• 9:03
  For any high speed design, Mach number is critical.
• 9:06
  And Ernst Mach, the man it's named after, actually used these
• 9:09
  ideas to solve a really interesting military mystery.
• 9:13
  You did. Back in the 19th century,
• 9:15
  artillery men noticed that for very high speed shells, they'd
• 9:18
  hear 2 bangs down range, not just 12.
• 9:21
  Bangs. Why?
• 9:22
  Mach figured it out. The first bang was the muzzle
• 9:24
  blast. The second bang was the
• 9:26
  shockwave, the Sonic boom created by the shell itself
• 9:29
  traveling faster than sound. That's incredible.
• 9:31
  And he also solved another kind of a gruesome mystery.
• 9:35
  Yes, during the Franco Prussian War, the French were being
• 9:38
  accused of using illegal explosive bullets because of the
• 9:41
  horrific wounds they caused. But they weren't.
• 9:43
  No Mach proved it was just physics.
• 9:46
  The highly pressurized Airways, the bow shock in front of the
• 9:49
  high speed bullet was causing the massive tissue damage before
• 9:52
  the bullet even hit pure fluid dynamics.
• 9:55
  It's amazing. OK, let's bring this back from
• 9:57
  shock waves to a more day-to-day engineering problem.
• 10:01
  Getting fluid through a pipe without losing all your
• 10:04
  pressure. A bread and butter task and for
• 10:07
  laminar flow we have a wonderfully useful formula, the
• 10:10
  Hagen Poiseau equation. It gives you the exact pressure
• 10:14
  drop in a pipe based on flow rate, fluid viscosity and the
• 10:18
  pipes dimensions. And what's the killer take away
• 10:21
  from that formula for a designer?
• 10:22
  It's the diameter. The pressure drop is inversely
• 10:25
  proportional to the diameter to the 4th power.
• 10:28
  The 4th power. So a small change makes a huge
• 10:30
  difference. A massive difference.
• 10:31
  If you double your pipe diameter, you cut your pressure
• 10:34
  loss by a factor of 16. It's a huge lever for designing
• 10:37
  efficient systems. And what about calculating the
• 10:39
  actual force the fluid exerts, like on a pipe bend OR a turbine
• 10:43
  blade? For that we use the principle of
• 10:45
  conservation of momentum. You draw a control volume around
• 10:48
  your object and calculate the net change in momentum of the
• 10:51
  fluid flowing through it. That change in momentum is equal
• 10:55
  to the force exerted on the object.
• 10:57
  Very cool. Let's wrap up the applications
• 10:59
  with efficiency. Let's talk about a diffuser, A
• 11:02
  component that's designed to slow flow down and recover
• 11:05
  pressure. Diffusers are critical in things
• 11:08
  like jet engines. And your first instinct might be
• 11:10
  that inefficiency comes from, you know, just friction, viscous
• 11:14
  losses inside. But the research actually shows
• 11:17
  something different. The biggest killer of
• 11:19
  performance is often insufficient flow diffusion, and
• 11:22
  the cause of that is the boundary layer at the inlet
• 11:25
  getting too thick. So it's not the friction inside
• 11:28
  the diffuser, it's the quality of the flow you feed into it
• 11:31
  that matters most. Precisely.
• 11:33
  If you have a thick, unhealthy boundary layer coming in, one
• 11:37
  that's close to separating from the wall, the diffuser just
• 11:39
  can't do its job of recovering pressure effectively.
• 11:42
  The initial state of the flow almost predetermines the
• 11:45
  outcome. What a journey we've gone from
• 11:47
  ancient Roman aqueducts and Da Vinci sketches all the way to
• 11:50
  the nonlinear complexity of Navier Stokes.
• 11:53
  And the power of the Reynolds number to help us simplify that
• 11:55
  chaos. Right.
• 11:56
  We've seen how it dictates whether flow is smooth and
• 11:59
  laminar or costly and turbulent, and how this tiny boundary layer
• 12:03
  right at the wall really ends up controlling the performance of
• 12:06
  the entire system. Which leaves us with a final
• 12:08
  provider ocket of thought for you to consider.
• 12:11
  If the thickening of the inlet oundry layer is the primary
• 12:14
  Causeway of poor performance in a diffuser, how fundamentally
• 12:18
  does the initial state of the fluid, its existing turbulence
• 12:22
  structure, constrained the efficiency of the entire system
• 12:24
  before the fluid even enters the component?
• 12:27
  That is a powerful question to end on.
• 12:29
  Thank you for joining us for this deep dive.
• 12:31
  And if you haven't already, get over to our YouTube channel
• 12:33
  Mechanical Engineering Made Simple by Strike Vision Studio,
• 12:36
  where we post hands on how to videos, visual breakdowns, and
• 12:39
  practical engineering walkthroughs you can actually
• 12:41
  use.