Reynolds Number - Numberphile

Second of three videos we're doing on Navier Stokes and related fluid stuff... featuring Tom Crawford.
More links & stuff in full description below ↓↓↓
Playlist: bit.ly/NavierPlaylist
Part 1 (Navier-Stokes): • Navier-Stokes Equation...
Part 3 (River Water): • Where Does River Water...
Tom Crawford works at the University of Oxford... more at: tomrocksmaths.com
Smarter Every Day's color unmixing machine: • Unmixing Color Machine...
Also demonstrated by the University of New Mexico: • Laminar Flow
Discuss this video on Brady's subreddit: redd.it/czjqvt
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outr...
And support from Math For America - www.mathforamerica.org/
NUMBERPHILE
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Videos by Brady Haran
Editing and animation: Pete McPartlan
Patreon: / numberphile
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Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9

[@numberphile]

Full Playlist: @t Part 1 (Navier-Stokes): @tl3M Part 2 (Reynolds Number): @ruwY Part 3 (River Water): @zC6Y

[@leif1075]

Who wrote the music in this video please? Specifically the marimba or something at 3:58. Thx

[@DonMeaker]

Ratio of inertial forces, to viscous forces. This would suggest that if you drive your car very very slowly (V

[@NekoAlosama]

The links don't work i think.

[@kaiserruhsam]

these are still busted but the description links work for now

[@Triantalex]

??

[@Scum42]

> "We can literally time travel with low Reynolds Number" "Pff what the hell are you talking about" > Unmixes dye in syrup Convulsing on the floor, foaming at the mouth

[@carnsoaks1]

I thunk he meant, figuritively. l.u.y.b.q.

[@SoumilSahu]

I get that you're joking, but how tf is unmixing going back in time???

[@Charlie-ts6hq]

@@SoumilSahu Entropy

[@biblebot3947]

Second Law of thermodynamics: *are you sure about that*

[@Charlie-ts6hq]

@SCP 055 yes.

[@joshuakahky6891]

As a chemical engineer, this is giving me Vietnam-style flashbacks of junior year

[@lucianoosinaga2980]

bruh what's the Prandtl number of this times the Nusselt number of that times the Grashof number times the Sherwood number ? Schmidt? Rayleigh? 😓

[@MrDarkrai100]

As a student of Chemical Engineering mostly done with fluid dynamics (currently at the first year of the Master's degree), it is quite interesting (and kinda traumatizing) seeing how easily can the Reynolds number be explained. Also the value for turbulent flow is any Re>2100, not Re>1000. My OCD made me write this part. ;)

[@_catzee]

@@lucianoosinaga2980 2

[@Jedza13]

@@lucianoosinaga2980 years of therapy gone beacuse of the single youtube comment

[@jeremyarnold4798]

@@MrDarkrai100 But to be out of the transitional regime and have a fully turbulent flow you need something more like Re>4000

[@alinpopa8664]

16:30 "But unfortunately we live in a turbulent world, and we don't understand turbulence" damn, that was deep

[@freshsi165]

Haha, that comment was before 2020 as well.. its only gotten worse!

[@teemuaho4807]

@@freshsi165 And your comment was made before 2022...

[@drenz1523]

huh.

[@Triantalex]

false.

[@PsychoticusRex]

In 15 min he described the relationship and terms in the Reynolds equations and general fluid dynamics better than my professor did in an entire series of semesters at university.

[@_catzee]

What the... I've never seen a hearted comment on this channel before! Color me impressed :)

[@LegionVsNinja]

In 2 videos, he's become one of my favorite contributors to Brady's channels.

[@n00dle_king]

A video like this would be great to show at the beginning and end of the those semesters. At the beginning, it provides a grounded framework for all the heavy mathematical theory that is required to do actual work with fluid dynamics. At the end, it does the same thing but brings people who have gotten lost in the weeds of the theory back down to earth and reminds them of what their work has been about and how much understanding they've gained along the way.

[@1996Pinocchio]

My thought

[@pianojay5146]

I hope these kinds of videos more made

[@ShaneClough]

Love Toms energy and enthusiasm he has for his area of study. Definitely a welcome addition to the channel!

[@abstractlycalculated]

100% agreed !

[@NueThunderKing]

Yeah they should expand the channel to have physics added and explained. With this kind of energy and emotion this would prove very educative.

[@shambosaha9727]

You are a 3b1b fan

[@Dionisi0]

But this is not a numberphile subject anymore, it should be posted in the 2nd channel

[@abijo5052]

@@Dionisi0 Ofc it is. Numberphile covers all sorts of maths, not just pure maths

[@elementalsheep2672]

This guy seems like the James Grime of engineering mechanics.

[@Cliff86]

He's as excited about fluid mechanics as Cliff Stoll is about Klein bottles

[@oldcowbb]

@@Cliff86 i don't think anyone can top cliff stoll

[@ANunes06]

He basically taught an entire semester of fluid dynamics in two 15 minute videos. Obviously, you'd have to have some background in dif eq and multivariable calculus, maybe some physics, a bunch of practice with examples and definitely some guidance in how to work those examples, but damn... :slow clap:

[@subhasish-m]

He also has a series called Equations Stripped if you're interested...

[@alephnull5662]

He seems the guy you'd meet in some illigal rave party or something lol, surely not someone you'd think is so skilled and interested in math at first glance.

[@Jodabomb24]

For the record, since this wasn't explained well in the video: the bit that makes NS nonlinear is not the fact that it is time-dependent. Many linear equations include time-dependence, like the wave equation, Schrödinger's equation, the heat equation… The reason NS is nonlinear is because the time derivative is a special time derivative called a material derivative, and it includes an extra term which is not written for compactness. That is why the derivative is written as Du/Dt instead of the standard du/dt; it's actually shorthand for Du/Dt = du/dt + v•∇v.

[@schizophrenicenthusiast]

That's true. It's even worse if you consider variable density across space and/or time. Also, the second equation in the video is written only for 'u' (flow velocity along the x direction). The same equation is written twice more, for 'v' and 'w', the other two components of the flow's velocity. So overall the Navier-Stokes equations are 4 coupled non-linear differential equations with second-order mixed differentials.

[@ThePharphis]

Ya it was only clear to me because he said "acceleration". I didn't know the short-hands being used, but think of acceleration as a second-derivative

[@ChefSalad]

@@schizophrenicenthusiast I believe he was using the convention that u is the vector .

[@WojciechowskaAnna]

Sadly most science-like people are very negligent about notation, relying on context and "common usage", thanks for claryfying!

[@jannegrey593]

Navier-Stokes For The Win! And Mr. Crawford's enthusiasm is infectious.

[@micahphilson]

That Smarter Every Day experiment was incredible before, but now it blew my mind seeing it in this context!

[@aidanlevy2841]

that was my first taught when he brought it up :)

[@BartKuipersdotcom]

When he talked about forwards and backwards in time, my immediate thought was of that exact experiment, it suddenly made so much more sense than it already did

[@nicolaivalenti4045]

@@BartKuipersdotcom exactly. I love the fact he used this Destin video.

[@akash_4769]

@@BartKuipersdotcom exactly, blows my mind

[@akshayhere]

I'm just so happy a channel like this has subscribers in the millions.

[@simondziadon295]

But views are not in milions

[@druban]

Simon Dziadoń if you go to their channel and list the videos by most popular you will see all the videos that have views in the millions in fact there are many! Logically the more videos a channel has, and the longer the mean length of the videos, the fewer total views for all videos in the channel can be expected. You can’t dance to them so it’s not going to be party material

[@simondziadon295]

@@druban i know, i just gave you a fact

[@druban]

whooosh

[@Triantalex]

??

[@arielvinda6624]

I love how mathematicians (at least the ones shown in this channel) have this everlasting awe and happiness about the subject

[@arielvinda6624]

@@MathswithMuneer sweet channel brother! subscribed :D

[@brightbyte]

"Big whirls have little whirls, That feed on their velocity; And little whirls have lesser whirls, And so on to viscosity."

[@jamesdong8179]

I always imagined Brady more like a passive observer, but now I realise that he actually asks relevant and important questions and contributes to a successful explanation

[@enverko]

Yes! Exactly my thoughts, he always tries to ask interesting questions which stimulate thinking about the topic.

[@gamemeister27]

He represents us very well

[@adamgray9212]

Low Reynolds numbers: Exist 2nd law of thermodynamics: *"Now this is an Avengers level threat"*

[@6alecapristrudel]

Holy Mother Entropy demands a sacrifice!!

[@ankitaaarya]

Hhsahhaahhaa

[@Triantalex]

false.

[@antivanti]

"I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic." - Horace Lamb

[@5thearth]

He was right too. Feynman, et al figured out QED but turbulence is still a mystery.

[@diarya5573]

This is so much more fun to watch as an engineering student

[@howardbaxter2514]

Agreed. As someone currently taking Fluid Dynamics, this video is intriguing.

[@nousefulness]

As a meteorology major it's always great when they discuss thermodynamics or fluid mechanics on the channel

[@DomenBremecXCVI]

"If you have 5 bananas and you give me 2, how many bananas do you have left?" - "Are we talking bananas or potassium?"

[@andymcl92]

K

[@longboren]

That's easy, because the units remain the same...

[@Lena-ri2vb]

I was so frustrated about fluid dynamics, so I came to Numberphile. Not only did I gained insight, but I am now sincerely interested in fluid dynamics. Your energy and love for this topic just took me. Thanks so much you made my day.

[@nicklewry3854]

As someone currently in a Fluid Dynamics course... this was incredible. You gave me an entirely new, and very valuable perspective. Thank you.

[@TomRocksMaths]

Thanks Nick, that's great to hear.

[@justcarcrazy]

Yes! I've been using the Reynolds number for years now in aerodynamics, but this is the best insight I've ever gotten to why the Reynolds number allows for scaling of experimental results. Excellent video.

[@VideosNoOne]

As a chemical engineer student, finally theres some videos that I actually know nearly 100% of everything said in them :D

[@Jesse__H]

haha I'm jealous

[@llllllllllllllllllllllllIIIIl1]

Thermo flashbacks

[@DodyPaluify]

andrew lai Nobody is never ready for the first energy balance with reaction

[@henrypentz6491]

Wierd flex but okay

[@VideosNoOne]

@@henrypentz6491 makes you feel smart cause these are some smart people :D

[@thomasaragorn]

Hoping Buckingham-Pi theorem is next. When I learned about it in Fluid Mechanics, I was blown away by how versatile and powerful it is, seems fitting to discuss it to provide not only a roadmap to Reynolds number, but any non-dimensional number.

[@guibelmon]

Man I LOVED this guy, and fluids mechanic is the coolest part of all engineering, please keep up this series!!!

[@peter692950]

Amazing video! Can you please make this a new series and further talk about adimensionalized numbers such as Mach or Froude?

[@TimothyReeves]

And Prandtl, and Nusselt numbers. I remember them from my ChE classes, but haven’t really used them for work....

[@uualrus]

Froude with a video of waves going up steam against the flow. I always try to explain this topic to people and they never understand

[@larssjodahl7660]

Remember never understanding Re when I studied fluid mechanics. This is the best explanation for intuitive understanding I've ever seen/heard. THANK you!

[@pucek365]

Thank you for bringing fluid mechanics. The whole series would be nice, Mr. Crawford is great at explaining the subject.

[@TheRealGuywithoutaMustache]

I thought you were going to reveal Ryan Reynold's number. Ladies would've been happy with that.

[@SuviTuuliAllan]

Yeah, "the ladies" 😉

[@itisALWAYSR.A.]

Same

[@ryanfauquier7099]

This is my favorite numberphile video so far. More of this guy and engineering math!

[@sahin8780]

I am so happy, seeing the relationships between what I watch. I watched the smarter every day video and it turns out it relates to this video

[@rockswe]

I love this dude. He is so enthusiastic and easy to follow.

[@blackbird95913]

these are the first few videos that are dealing with classes im taking as an aero! so grateful its during the same time im taking them

[@bmac3933]

This guy is a really good speaker. I love his passion for this subject

[@BlaqueT]

Great video. His passion was extremely infectious. Helps me to keep pushing through with this maths degree

[@jongsuk6113]

Every time I watch your video, you really enjoy your job. Thank you for your explanation!

[@lestroarmonico]

The statement "Re > 1000 is turbulent" is not actually always true, it depends and there is always a transition region. For external flows Re above 10^5 is considered turbulent while Re > 2100 is considered turbulent for internal flows .

[@sadface7457]

The Reynolds number could be said to change the scale on which turbulence occurs.

[@PokemonStarrr]

Yes, true. For example in the flows around submerged objects like spheres, cilinders, etc.

[@SO-dl2pv]

10^5 for flat plates only

[@Elios0000]

lamer flow and super critical flow also muck about with this too

[@chiranjitray760]

it also depends on the platform or conduit it is flowing in...and then these numbers are also derived empirically

[@priyansh1210]

This guy is in love with the fact that small Reynold's number makes time vanish from Navier Stokes equations. Literally mentions it a million times.

[@numberphile]

Literally a million?

[@Longuncattr]

When Tom started talking about working in reverse in a low-Re situation, a light went off in my head and I was reminded of Destin's syrup video; then about fifteen seconds later, that very video was used as an example. Cool stuff!

[@mRcOOL5YO]

When i was studying this i could never understand why the equation sometimes was long, and sometimes small, but in this video it dawned on me. Its so very very small that it doesnt matter. Well done. I needed this video 5 years ago.

[@rabidfurify]

Fluid dynamics is one of those topics where you really want a physicist and a mathematician to introduce you to the topic at the same time because the parts that one discipline tends to gloss over is looked at more rigourously in the other. I distinctly remember having two fluids based courses in the same year at uni and at times it felt like they were totally different topics instead of heavily related ones due to the difference in background of the lecturers.

[@baoboumusic]

Yes! Glad to see this back, love his enthusiasm!!

[@seonaxus]

Normally I watch for fun facts, but this has actually really helped me rethink and get a better grasp on some of the mhd I'm doing at the moment.

[@JaviRP97]

Having a fluid mechanics test soon, this gave me powah! Thanks for the knowledge and enthusiasm!

[@Tytoalba777]

So what you’re saying is that syrup is the key to time travel?

[@SoumilSahu]

So what you're saying is lobsters are better than humans?

[@goji_crafter]

@@SoumilSahu yes. Yes I am

[@000Krim]

it's obvious at this point.

[@donmoore7785]

Awesome explanation and supporting experiment, and lots of enthusiasm.

[@PMo-lk4jb]

I suddently understood when he said "time vanishes from our equations" and this reminded me a SmarterEveryDay video... I paused to watch it and when i came back i realized it was also in this video xD Perfect connection between those two, I say good job!

This has to be the best Numberphile video!

[@mathewperring]

Okay I am a chemist and that has to be the coolest experiment I have ever seen, weirdly I have just begun a new job where measuring viscosity is important. This was really helpful to get a understanding of this new field to me.

[@amauta5]

I hope that he teaches. Having teachers with this enthusiasm and love for what they do is so important to get students engaged.

[@GarryDumblowski]

Thinking about this helped me understand the famous molasses flood of 1919, which was a lot of fluid crashing very quickly and very suddenly from acceleration due to gravity. A lot of people today thought that the molasses flood would have been "slow" because molasses typically is, but there was so much gravitational potential energy it was able to achieve a very high Reynolds number and ignore viscosity. Then, as the fluid settled, viscosity became more important from the Reynolds number lowering to near zero (zero velocity = zero Re) which is why people became trapped.

[@itsraahul]

I can't thank enough both of you guys 🙌 making science and maths easy to understand

[@Paldasan]

Did Destin push for this topic?

[@DisabledCreation]

L A M I N A R

[@M1stersupersonic8]

@@DisabledCreation F L O W

[@veralife95905]

It'd be really fun to see more videos on dimensionless numbers in the future!

[@modernkennnern]

Very good idea Brady. I never thought I'd find fluid dynamics this interesting

[@mrinalvashisth]

I love it that how passionate he seems talking about the subject :))

[@wanderingrandomer]

7:49 made me really happy for some reason. That was like magic!

[@evilotis01]

same!

[@andronikosnik4855]

I love this guy's enthusiasm

[@Cruuzie]

That was so cool when you finally understand the syrup colour thing because how the equation works!

[@kevinmartin7760]

An extra μ seems to have crept into the second term on the first equation shown on-screen at 5:33. It doesn't match the one he just wrote on the paper. Also, it isn't clear how the small-Re equation at 9:24 relates to the large-Re equation on the paper at 5:29. It isn't just a case of multiplying all the terms by Re because the "pressure" terms doesn't change.

[@kongolandwalker]

Kevin Martin i also can't understand how they did nondimensionalisation

[@engineer_leo]

He forgot to multiply the pressure by the Reynolds number. Apart from that, he made many conceptual mistakes regarding low Reynolds number flow.

[@hamed2800]

in viscous flow (low Re) the pressure is considered with (mu*U/L) from layer tension in the fluid : tension (pressure) = (mu) * dU/ dL in dynamic flows (high Re) the pressure is nondimensionalized with (ro * U^2) from dynamic pressure and bernoulli equation : pressure + (0.5 ro * U^2) + (ro * g) = constant so the pressure gradiant will be present in both

[@groundhogsday6731]

It's not quite the same pressure gradient. The above comment mentions that math. Essentially, low Re flow pulls at component of the object (car, marble, etc.) parallel to the flow while high Re flow pushes on the normal components.

[@peglor]

It looks like bad algebra to me - you can't just choose which terms in an equation are affected by the value you're multiplying or dividing the equation by and that's exactly what I'm seeing here. I've been to fluid mechanics lectures where exactly the same thing has been paraded out in my undergrad days and it made just as little sense then. Either this is one of those 'simplifications' academics like to use to make an explanation shorter while also making it wrong (And therefore not a satisfactory explanation at all) to anyone paying attention or he's skipped some critical detail he assumes we all know. Usually Brady's questions pull people up on things like that, but in this case it wasn't even commented on unfortunately.

[@11pupona]

this is guy is fantastic!! the passion and love he has when he speaks about the topic is amazing!! great videos!!

[@peetiegonzalez1845]

11:57 I had the sudden flash of what the implications were, and I was screaming at the screen "Destin demonstrated this!" then of course 5 seconds later you refer to his video. Great explanation of the maths, for it to make such clear sense before you even mentioned the demo!

[@yusufjamilu7014]

Doing research on Chemotaxis, your explanation is wonderful and really helpful.thanks

[@Drink6the6Blood6]

Since taking fluid mechanics in university, I've learned more about extreme ultra high vacuum (XUHV) systems. I would love to see a video about the Knudsen number and how it relates to viscous, transition, and molecular flow.

[@eduardpertinez4767]

Amazing. I knew nothing about fluids and suddenly I wanna know more!

[@Prasen1729]

Such a beautiful body of math and interesting experiment. This guy is awesome.

[@nilushanissanka8316]

So happy to learn from a guy with passion. Its next level

[@austynhughes134]

Another great video! Hopefully we will see more of Tom Crawford.

[@smokymcbongwater1088]

As a large cruise ship, I enjoy this channel.

[@viktorstade]

I would love to see more videos with this guy!

[@MrCalcium99]

Getting me so hype for my second year of mechanical engineering!!!!

[@MrJacksjb]

Takes me back to my aerodynamics classes in college. When you are building a scale model to put in a wind tunnel if the Reynold's number of the model matches the Reynold's number of the full scale then your results will scale between the two (as long as the flow of both were both either above or below Mach 1).

[@SunayH01]

Another brilliant video!

[@salahissa7010]

I really love your videos. Keep it up

[@marktredway1431]

It's nice to see people excited about what they do!

[@lara.0783]

I love this, thank you so much, it is very clear to me!

[@robertreynolds9228]

So glad my family contributed to mathematics!

[@PetervanGinneken]

I am a civil engineer so I learned this in school but pfff this teaches you how easy it is to forget stuff.

[@c1osmo]

Nice work on the maths.. I really loved Destin's video when it was released earlier this year.

[@flirkami]

Isn't it necessary to divide by density in the pressure term at about 5:30 ?

[@bharatrawat5909]

More engineering videos like this please!!!

[@morbidmanatee5550]

Fantastic demo!

[@fdggfgdfgd251]

the genius of this video is the constant asking of basic questions. brilliant

[@leonjones7120]

Nice and clear. Well done!

[@reverseila4363]

In all of numberphile videos, there is one common thing: The Guest Speaks Very Well.

[@SaddamHossain-jj8xk]

You explained it way more simpler then many bloggers

[@Jcontardo]

My little Hydraulic Engineering Heart is bursting with joy ❤️

[@garyknight8616]

Brilliant. More fluid mechanics please.

[@technoguyx]

this guy looks like the lead singer of an early 2000's pop punk band and I like it

[@ethansmith5560]

Saaaaameee

[@DaneliusUK]

"The universe has no obligation to make sense to you." - Neil deGrasse Tyson.

[@matthewnuzzaco2849]

I just watched your three part series on fluid dynamics... Making tea with milk and honey will never be the same again 😛

[@davidgillies620]

This is the difference between being able to write down the equations and knowing what the equations mean. It's the "on first looking into Chapman's Homer" feeling, and one of the reasons this stuff can be so rewarding.

[@tompw3141]

You can get low a Reynolds number through high viscosity OR through small length scales... which is why bacteria in water look like they are swimming in treacle (the movement of small lengths and low viscosity is like that of large lengths and high viscosity)

[@Alienrookie]

Really good explanation!

[@BooBaddyBig]

There's a slight error @12:40 in the video, you can't actually mix anything at low Reynolds. If you could, then it wouldn't be reversible. That experiment doesn't actually mix the dyes together, they're kept separate in different layers. It only looks like they've been mixed up.

[@boman987]

“If it needs to be invisible...”. I like the Drax reference.

[@Thomas171198]

Great video, so interesting!

[@wademarshall2364]

I love all the Numberphile videos which are on the same topic as Sixty Symbols videos, but a totally different perspective.

[@spypruduktion]

At 2:25 the thing marked as pressure should really be the pressure gradient, since pressure is a scalar and the LHS is a vector

[@MrScottev]

Put in layman's terms like that helps so much.

[@411sponge72]

Absolutely brilliant!!!