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Very Short Introductions #708
Fluid Mechanics: A Very Short Introduction
Fluid mechanics is an important branch of physics concerned with the way in which fluids, such as liquids and gases, behave when in motion and at rest. Starting from the fundamental underlying physical principles, Eric Lauga highlights the role of fluid motion in both the natural and industrial world, and considers future applications.
- GenresPhysicsScienceNonfiction
144 pages, Paperback
Published April 28, 2022
17 people are currently reading
138 people want to read
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Displaying 1 - 6 of 6 reviews
January 12, 2023
Why does the plane fly
As a PhD student I liked the fact that the book not only skims the most important concepts in the field (familiar to the engineers and researchers alike) but also broadens your horizons: it brings together all the branches of this the most versatile of sciences and connects the dots that one might have left disconnected.
As a person who studied the pipe flow a lot I've found it shocking how close I'd been all this time to a proper answer to the familiar childish questions: "Why does the plane fly? How come there is a tornado? How does Helmholtz's theorem about inviscid flows translates to our better understanding mixing processes in a non-newtonian fluids?".
Anyway, there is something for everybody. The book is as simple as it gets and requires only basic understanding of everyday physics. It doesn't go too deep, although the chapters about instabilities and dimensionless analysis might come across straight up boring. The work doesn't go too deep though, so if you're a master in the field it's rather useless.
All in all, the book is highly recommended to anyone who is interested in the topic.
As a PhD student I liked the fact that the book not only skims the most important concepts in the field (familiar to the engineers and researchers alike) but also broadens your horizons: it brings together all the branches of this the most versatile of sciences and connects the dots that one might have left disconnected.
As a person who studied the pipe flow a lot I've found it shocking how close I'd been all this time to a proper answer to the familiar childish questions: "Why does the plane fly? How come there is a tornado? How does Helmholtz's theorem about inviscid flows translates to our better understanding mixing processes in a non-newtonian fluids?".
Anyway, there is something for everybody. The book is as simple as it gets and requires only basic understanding of everyday physics. It doesn't go too deep, although the chapters about instabilities and dimensionless analysis might come across straight up boring. The work doesn't go too deep though, so if you're a master in the field it's rather useless.
All in all, the book is highly recommended to anyone who is interested in the topic.
September 23, 2022
I would like to read an ebook version because the topic doesn't lend itself well to audio format.
May 18, 2025
While listening to this book (not highly recommended, it has lots of figures and equations), I found myself sticking a knife in jam at breakfast and thinking about the dizzying complexity of modelling the motion: vector calculus, Lagrangian field theory…Seeing the world in a grain of sand and all that.
So two starting questions about fluid mechanics: what is "fluid" and what is "mechanics"? Defining a "fluid" is tricky. A solid is something which retains its shape (it resists "shearing force"). A fluid does not. However, it isn't a binary, toothpaste being an example of something in the middle.
"Mechanics" includes various types of motion (dynamics and statics), and there is also "kinematics" which describes the mathematical side. "Statics" is a bit misleading: from far, sand or water look continuous and still. However, if you zoom in you can see them as a bunch of discrete, writhing particles. (We generally ignore this when studying fluids, treating them as they appear at the macroscopic level - this is known as the continuum assumption.)
Pascal discovered that fluids have pressure (and gave his name to the SI unit for it). If you press on them, they press back. Gases are different from liquids in that they are compressible, whereas liquids are mostly not. Pressure is isotropic (the same in every direction). Gravity affects pressure (this is greatly noticeable in water, where going a little deeper can be much less pleasant: humans are very sensitive to pressure). Since pressure depends only on height and area, the hydraulic press (a tall and narrow tube) can create high pressure pretty cheaply. (Recent relevant xkcd.) Buoyancy is also a result of pressure pushing an object out.
Surface tension is the bond around the outside of a fluid, maintaining its shape. This is why liquids are round in space, since the sphere is the smallest surface area. On earth gravity is stronger and drags them down.
Things get a bit gnarlier when we get to movement. We can model it with a set of partial differential equations which have a simpler (the Eulerian) or more complicated form (the Lagrangian), the former assuming motion relative to a stable reference point. However these make a few unrealistic assumptions, such as ignoring viscosity (how "treacly" a fluid is, as I think of it). The equations required to model realistic fluids are much more complicated, the famous Navier-Stokes equations (one of the subjects of the $1M Millennium Prize). Lauga says that they are very beautiful, and I must take him at his word.
Next the book discusses fluids moving through pipes: sucking a drink through a straw, plant leaves drawing moisture from the soil or nitrogen from the air, blood moving through veins, pumping water and petroleum through pipes, and so on. This leads to the concept of turbulence: flow can be either laminar (smooth and constant) or turbulent (uneven and random). As you might guess, basically all real-life flows are turbulent, which makes them much harder to model. Turbulence is measured by the Reynolds number, which is dimensionless (it has no unit). (The idea that all variables in a formula should have similar units, or be dimensionless, is credited to Fourier.) d'Allembert's paradox is that an object moving through a fluid that is not viscous should experience zero drag, which seems to be contradicted by reality.
Then there is a chapter about foams, and one about vortexes, or vorticity. Not exactly sure what this is, I was a bit lost by this point. I once read that traffic jams can also be modeled by fluid dynamics, but this fact is unfortunately not discussed in the book. Anyway, I still got quite a bit out of it, and hopefully will get further still upon my next foray into fluid mechanics.
So two starting questions about fluid mechanics: what is "fluid" and what is "mechanics"? Defining a "fluid" is tricky. A solid is something which retains its shape (it resists "shearing force"). A fluid does not. However, it isn't a binary, toothpaste being an example of something in the middle.
"Mechanics" includes various types of motion (dynamics and statics), and there is also "kinematics" which describes the mathematical side. "Statics" is a bit misleading: from far, sand or water look continuous and still. However, if you zoom in you can see them as a bunch of discrete, writhing particles. (We generally ignore this when studying fluids, treating them as they appear at the macroscopic level - this is known as the continuum assumption.)
Pascal discovered that fluids have pressure (and gave his name to the SI unit for it). If you press on them, they press back. Gases are different from liquids in that they are compressible, whereas liquids are mostly not. Pressure is isotropic (the same in every direction). Gravity affects pressure (this is greatly noticeable in water, where going a little deeper can be much less pleasant: humans are very sensitive to pressure). Since pressure depends only on height and area, the hydraulic press (a tall and narrow tube) can create high pressure pretty cheaply. (Recent relevant xkcd.) Buoyancy is also a result of pressure pushing an object out.
Surface tension is the bond around the outside of a fluid, maintaining its shape. This is why liquids are round in space, since the sphere is the smallest surface area. On earth gravity is stronger and drags them down.
Things get a bit gnarlier when we get to movement. We can model it with a set of partial differential equations which have a simpler (the Eulerian) or more complicated form (the Lagrangian), the former assuming motion relative to a stable reference point. However these make a few unrealistic assumptions, such as ignoring viscosity (how "treacly" a fluid is, as I think of it). The equations required to model realistic fluids are much more complicated, the famous Navier-Stokes equations (one of the subjects of the $1M Millennium Prize). Lauga says that they are very beautiful, and I must take him at his word.
Next the book discusses fluids moving through pipes: sucking a drink through a straw, plant leaves drawing moisture from the soil or nitrogen from the air, blood moving through veins, pumping water and petroleum through pipes, and so on. This leads to the concept of turbulence: flow can be either laminar (smooth and constant) or turbulent (uneven and random). As you might guess, basically all real-life flows are turbulent, which makes them much harder to model. Turbulence is measured by the Reynolds number, which is dimensionless (it has no unit). (The idea that all variables in a formula should have similar units, or be dimensionless, is credited to Fourier.) d'Allembert's paradox is that an object moving through a fluid that is not viscous should experience zero drag, which seems to be contradicted by reality.
Then there is a chapter about foams, and one about vortexes, or vorticity. Not exactly sure what this is, I was a bit lost by this point. I once read that traffic jams can also be modeled by fluid dynamics, but this fact is unfortunately not discussed in the book. Anyway, I still got quite a bit out of it, and hopefully will get further still upon my next foray into fluid mechanics.
October 11, 2022
Fascinating throughout, at the heart of this gem is the rational understanding of phase transition in fluid dynamics through the appreciation of dimensionless numbers such as the Reynolds Number. Real world applications are illustrated. Only elementary mathematics is required as the author eschews the use of calculus even though the Navier-Stokes equations are quoted for their beauty. Certain bits are admittedly not simple or easy. Overall a very good read. Four stars.
August 7, 2023
3.5 Stars
April 10, 2023
I read it for teaching and learned a lot about fluids outside of the kind I do research in. It is a great introductory book. It talks about the beauty of fluid mechanics without too much of the math. Great for getting someone to become interested in fluids. Useful as a companion book for a fluids class when the students are frustrated with the math.
Displaying 1 - 6 of 6 reviews