I need some self-contained introductory books on Fluid Mechanics

[Adesh]

By Fluid Mechanics I mean the mechanics of fluids, both at rest and in motion. I'm unable to find introductory books on Fluid Mechanics which contains everything in itself, for example I downloaded Fundamentals of Fluid Mechanics by Munson, Young, Okiishi, Huebsch and I don't know why but I struggled with it so much. The definition of fluid is stated as "a fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude", and I want to tell you all that although I knew the meaning of shearing stress (stress parallel to plain) then also it took me few days to understand what author really meant by deform, the author explains nowhere that the deform he meant was not the expansion, contraction, change in volume, or a typical example of shearing strain. I asked it on internet and there I got the answer that deform means flow of layers (I can accept that here it may that my ignorance would have caused this some problem). When the book comes to Surface Tension it says something like this " If the spherical drop is cut in half, the force developed around the edge due to surface tension is $2 \pi R \sigma$. This force must must be balanced by the pressure difference, $\Delta p$, between the internal pressure , $p_i$, and the external pressure , $p_e$, acting over the circular area, $\pi R^2$ " , I couldn't understand from "this force must be balanced by..."

So, because of this I thought I should read some introductory books, therefore, I moved to University Physics by Young and Freedman (some people prefer to call it Zemansky's and Sear's) but in that the only topics covered are : Density, Pressure in a Fluid, Buoyancy, Fluid Flow, Bernoulli's Equation, Viscosity and Turbulence.

By now you all must have got the idea what I meant by self-contained. I have no problem with Calculus (single variable) , I know basics of multivariable Calculus, I have done Newtonian Mechanics and Thermodynamics (elementary Statistical Mechanics and first and second laws).

I request you all to please guide me and suggest me some books on introductory Fluid Mechanics.

 

[vanhees71]

For fluid dynamics you need tensor calculus (to start Cartesian components are fully sufficient). To get this, I recommend vol. II of Sommerfeld's Lectures on Theoretical physics, which is about fluid mechanics. For fluid mechanics itself, I think Landau + Lifshitz vol. 6 is the most lucid book ever written on the subject.

 

[Adesh]

For fluid dynamics you need tensor calculus (to start Cartesian components are fully sufficient). To get this, I recommend vol. II of Sommerfeld's Lectures on Theoretical physics, which is about fluid mechanics. For fluid mechanics itself, I think Landau + Lifshitz vol. 6 is the most lucid book ever written on the subject.

Do I need to know Tensor analysis for studying Fluids? I downloaded Sommerfield's Mechanics on Deformable Bodies and he using Tensors for explaining almost everything. Is there any other way?

 

[jasonRF]

Adesh,You say you know single variable calculus and the basics of multivariable calculus. Have you learned vector calculus (curl, div, grad, etc)? It is essential if you want to learn fluids. I don't think you need to know full-blown tensor analysis to learn fluids, but you should know basic linear algebra which will allow you to easily learn elementary aspects of Cartesian tensors.

One online "book" that I think is pretty well written is
https://farside.ph.utexas.edu/teaching/336L/336l.html
The "html" link has the entire book but the rendering of the math can be bad at times, and includes appendices on tensors. The "book" link brings you to the IOP site, and you are allowed to read the pdf version of the first chapter for free. If you have enough math and physics to read that first chapter then you should be ready to learn fluids. Jason

 

[Adesh]

Adesh,You say you know single variable calculus and the basics of multivariable calculus. Have you learned vector calculus (curl, div, grad, etc)? It is essential if you want to learn fluids. I don't think you need to know full-blown tensor analysis to learn fluids, but you should know basic linear algebra which will allow you to easily learn elementary aspects of Cartesian tensors.

One online "book" that I think is pretty well written is
https://farside.ph.utexas.edu/teaching/336L/336l.html
The "html" link has the entire book but the rendering of the math can be bad at times, and includes appendices on tensors. The "book" link brings you to the IOP site, and you are allowed to read the pdf version of the first chapter for free. If you have enough math and physics to read that first chapter then you should be ready to learn fluids. Jason

Yes, I know divergence, curl and gradient. Those books are confusing because they don’t use Tensor, is it like that?

 

[jasonRF]

Yes, I know divergence, curl and gradient. Those books are confusing because they don’t use Tensor, is it like that?

Did you download and read the pdf file for chapter 1? It develops the basic fluid model, and does indeed use basic tensor notation in the presentation.

 

[Adesh]

Did you download and read the pdf file for chapter 1? It develops the basic fluid model, and does indeed use basic tensor notation in the presentation.

I downloaded the first chapter and began reading it. First two pages were very well and I really liked it, but when I came to surface forces I couldn't understand the meaning of net flux density of x -directed fluid momentum and after that I couldn't follow.

Please give me some advice.

 

[Lord Jestocost]

By Fluid Mechanics I mean the mechanics of fluids, both at rest and in motion. I'm unable to find introductory books on Fluid Mechanics which contains everything in itself...

Maybe, the following book might be of help:
"Basics of Fluid Mechanics" by Genick Bar-Meir
https://www.e-booksdirectory.com/details.php?ebook=299

 

[vanhees71]

Do I need to know Tensor analysis for studying Fluids? I downloaded Sommerfield's Mechanics on Deformable Bodies and he using Tensors for explaining almost everything. Is there any other way?

Physics cannot be talked about without the adequate mathematics, and the adequate minimal mathematics is vector and tensor calculus. Of course, you don't need the fully rigorous math of pure mathematicians but a good understanding about the geometrical meaning and calculational techniques (differentiation, integration etc.). Sommerfeld gives a very good introduction covering exactly this need, using fluid dynamics also as a intuitive picture for the operations on vectors and tensors like grad, div, curl, and the different kinds of integrals (line, surface, volume integrals) in Euclidean 3D space.

There's the tendency in some didactical circles to avoid mathematics at any cost, but that's cheating the students, because physics becomes very much more complicated than with the adequate math.

 

[Adesh]

Physics cannot be talked about without the adequate mathematics, and the adequate minimal mathematics is vector and tensor calculus. Of course, you don't need the fully rigorous math of pure mathematicians but a good understanding about the geometrical meaning and calculational techniques (differentiation, integration etc.). Sommerfeld gives a very good introduction covering exactly this need, using fluid dynamics also as a intuitive picture for the operations on vectors and tensors like grad, div, curl, and the different kinds of integrals (line, surface, volume integrals) in Euclidean 3D space.

There's the tendency in some didactical circles to avoid mathematics at any cost, but that's cheating the students, because physics becomes very much more complicated than with the adequate math.

Yes I do agree with that. When I started Electromagnetism I couldn’t understand nothing (because books seemed to jump over Gauss’s law and never defines the flux). It was when I read Feynman’s Second Volume things became clearer to me, he taught vector calculus first and then moved on to the actual subject.

Did Sommerfield teaches it that way? I mean the mean of things like flux (well Feynman almost never defines flux as related to field lines he just said “this integral $\int_A \mathbf{F} \cdot d\mathbf{A}$ is called the flux of $\vec{F}$ through A” and I must admit that accepting this mathematical definition of flux is more useful than that field lines definition). I didn’t read Sommerfield much yesterday, I just skim read him.

 

[vanhees71]

Sommerfeld was the most successful physics professor ever. Just look at the list of Nobel laureats having learned theoretical physics from him. Sommerfeld originally was a mathematician, who then switched to theoretical physics, which was a pretty new specialization at his time (2nd half of the 19th century) but gaining more and more importance.

Another great resource to learn vector calculus is the textbook by Abraham and Becker on classical electrodynamics, which has a nice chapter on it too.

 

[Adesh]

Sommerfeld was the most successful physics professor ever. Just look at the list of Nobel laureats having learned theoretical physics from him. Sommerfeld originally was a mathematician, who then switched to theoretical physics, which was a pretty new specialization at his time (2nd half of the 19th century) but gaining more and more importance.

Another great resource to learn vector calculus is the textbook by Abraham and Becker on classical electrodynamics, which has a nice chapter on it too.

So, I'm going with Sommerfield's. Thank you.

 

[Flaming Physicist]

My suggestion would be Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris, which has the advantage of teaching both things and also being very cheap.

 

[Adesh]

My suggestion would be Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris, which has the advantage of teaching both things and also being very cheap.

Thank you so much. It considers Tensors completely and separately, wow!. I will surely get to it as right now my mind is being captivated by Sommerfeld.

 

[Demystifier]

When I started Electromagnetism I couldn’t understand nothing (because books seemed to jump over Gauss’s law and never defines the flux). It was when I read Feynman’s Second Volume things became clearer to me

So you need something like fluid mechanics a'la Feynman. Did you read chapters 40 and 41 in the second volume of Feynman Lectures?

 

[Adesh]

So you need something like fluid mechanics a'la Feynman. Did you read chapters 40 and 41 in the second volume of Feynman Lectures?

No. I didn’t because I had no previous knowledge of that subject and Feynman assumes that the reader knows some basic concepts.

 

[Demystifier]

No. I didn’t because I had no previous knowledge of that subject and Feynman assumes that the reader knows some basic concepts.

So you need something even more elementary than Feynman? I don't know, maybe Halliday and Resnick, Fundamentals of Physics, Chap. 14 Fluids.

By the way, we have the same avatar.

 

[Adesh]

So you need something even more elementary than Feynman? I don't know, maybe Halliday and Resnick, Fundamentals of Physics, Chap. 14 Fluids.

I don’t why but whenever I went with any books I used to get stuck as we move from elasticity to fluids, so I acted according to the advice of @vanhees71 and started reading Sommerfeld. And I say it with a joy that till now I haven’t got any conceptual problem with Sommerfeld.

I could never understand from those books when they calculated the radius of water droplet by using the concept of surface tension.

 

[Adesh]

By the way, we have the same avatar.

Yeah! You have demystified it. I have seen many replies of yours in this forum and found that you must someone above the PhD level (actually for people like me who are about to go for UG, PhD is a very big thing ).

So, may you please share something about Mr.Russell which inspired you most.

 

[Demystifier]

So, may you please share something about Mr.Russell which inspired you most.

I may, but not on this thread.