Drag forces and the Reynolds number: intuitive understanding

Using a simple physical model to explain why drag force in a fluid is sometimes proportional to velocity, and sometimes proportional to the square of velocity. Along the way we'll discuss inertial and viscous forces, and introduce the Reynolds number as a way to distinguish between the two regimes.
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About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
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#physics #mathematics #fluidmechanics #fluids #fluid #dynamics #mechanics #momentum #newtonslaws #reynoldsnumber #drag #dragforce #airresistance #waterresistance #stokeslaw #viscosity #viscous #friction #stress #strain #shear #physicsproblems #maths #math #science #education

[@elibrahimi1169]

great stuff ! i was told that we use quadratic drag when velocity or the viscosity is high, but never told how high exactly, this video actually gave me a better idea about it, thanks

[@DrBenYelverton]

I'm glad it helped!

[@MissPiggyM976]

Very interesting, many thanks!

[@christiancorrao6591]

Excellent!

[@DrBenYelverton]

Thank you!

[@noelsiony6265]

More fluid mechanics please!

[@DrBenYelverton]

I'll see what I can do!

[@gauravraj3945]

Sir can you look at the problems of pathfinder physics...there are many good and quality questions

[@surry99]

Very nice! It is interesting you did not use the term "no slip condition" at the top surface but tried instead to emphasize its source which is fluid friction (viscosity).

[@DrBenYelverton]

Thanks for watching. Yes, very much an intuition-focused video!

[@r2k314]

That was very good. I never saw that kind of explanation before. By the way, does the difference between your D and dy ever become important in practice?

[@DrBenYelverton]

Thanks! The length scale over which v changes won't be exactly D, but this analysis only gives an order of magnitude estimate of F anyway. So, there would only be an issue if the actual length scale differed from D by more than an order of magnitude. I'd be surprised if that were possible, but maybe there are fluid dynamics experts out there who'd be able to correct me on this! This is the sort of effect that we're just absorbing into the parameter β, which can only be determined by a more detailed solution or by experiment.

[@shrivatsa8604]

Hello dr ben, great video! How would the equations change if the surface were to be spherical

[@DrBenYelverton]

Thanks! The shape of the object determines the constants of proportionality, α and β. For a sphere, the drag at low Reynolds number for example is 6πηrv, which is Stokes' law. It's not possible to derive that using this simplified model, though.