Engineering Notes - Fluid mechanics (1 Viewer)

[blyatman]

For anyone interested, I've attached my notes on the subject of fluid mechanics. Even if there's no engineers here who are/plan to be in this field, I thought it'd be useful for even high school students to see the type of math that engineers use. Most notably, it applies a lot of the vector knowledge that you learn in the syllabus.

Context: As this is my career specialty, my goal is to understand fluid mechanics at a fundamental level. To achieve this, I've been doing research and typing up a set of notes to consolidate and supplement my knowledge on this subject. It's been a slow progress, as I add bits and pieces to it in my spare time. The attached copy took about a year to do, and probably represents less than 5% of the eventual content I plan to write up.

Feel free to point out any typos, errors, or flat out blasphemous math or physics. Probably need a basic knowledge of vector calculus (second year uni), as well as how Einstein Summation Notation works. Questions and suggestions welcome.

 

[B1andB2]

For anyone interested, I've attached my notes on the subject of fluid mechanics. Even if there's no engineers here who are/plan to be in this field, I thought it'd be useful for even high school students to see the type of math that engineers use.

Context: As this is my career specialty, my goal is to understand fluid mechanics at a fundamental level. To achieve this, I've been doing research and typing up a set of notes to consolidate and supplement my knowledge on this subject. It's been a slow progress, as I add bits and pieces to it in my spare time. The attached copy took about a year to do, and probably represents less than 5% of the eventual content I plan to write up.

Feel free to point out any typos, errors, or flat out incorrect math or physics. Probably need a basic knowledge of vector calculus (second year uni), as well as how Einstein Summation Notation works. Questions and suggestions welcome.

damn, imagine knowing all of that!!

 

[Drdusk]

For anyone interested, I've attached my notes on the subject of fluid mechanics. Even if there's no engineers here who are/plan to be in this field, I thought it'd be useful for even high school students to see the type of math that engineers use. Most notably, it applies a lot of the vector knowledge that you learn in the syllabus.

Context: As this is my career specialty, my goal is to understand fluid mechanics at a fundamental level. To achieve this, I've been doing research and typing up a set of notes to consolidate and supplement my knowledge on this subject. It's been a slow progress, as I add bits and pieces to it in my spare time. The attached copy took about a year to do, and probably represents less than 5% of the eventual content I plan to write up.

Feel free to point out any typos, errors, or flat out blasphemous math or physics. Probably need a basic knowledge of vector calculus (second year uni), as well as how Einstein Summation Notation works. Questions and suggestions welcome.

As soon as I saw Thermodynamics I knew I was out haha

Anyway I’ve looked into fluids just a bit myself and it seems mind boggling to me that we still don’t know accurately how liquids flow or something like that even though we’ve got such advanced theories in other fields of Physics.

iirc the problem to solve fluid flow has a 1 million dollar prize and is called the Navier-stokes problem, one of the millennial problems. I reckon you should solve it

 

[blyatman]

As soon as I saw Thermodynamics I knew I was out haha

Anyway I’ve looked into fluids just a bit myself and it seems mind boggling to me that we still don’t know accurately how liquids flow or something like that even though we’ve got such advanced theories in other fields of Physics.

iirc the problem to solve fluid flow has a 1 million dollar prize and is called the Navier-stokes problem, one of the millennial problems. I reckon you should solve it

Haha there's only a small bit of thermo, mostly included for background knowledge.

We generally know how fluids behave, but the problem is turbulence. Even after a century, we still haven't made any progress on solving it, so it's become one of the biggest unsolved areas in physics and engineering.

In regards to the Navier-Stokes millennial prize problem, the problem isn't even to solve the Navier-Stokes equation, but to show that there always exists a smooth and unique solution. I.e. we can't even prove that a solution always exists, much less find the solution itself. Since we don't know how to analytically solve the NS equations, we use computers to get numerical solutions, which is the field of computational fluid dynamics (which is what I do).

Fluids is an interesting field to get into since it's such a critical aspect of physics/engineering with enormous potential for technological development, yet there's still so much we don't know.

 

[Drdusk]

Haha there's only a small bit of thermo, mostly included for background knowledge.

We generally know how fluids behave, but the problem is turbulence. Even after a century, we still haven't made any progress on solving it, so it's become one of the biggest unsolved areas in physics and engineering.

In regards to the Navier-Stokes millennial prize problem, the problem isn't even to solve the Navier-Stokes equation, but to show that there always exists a smooth and unique solution. I.e. we can't even prove that a solution always exists, much less find the solution itself. Since we don't know how to analytically solve the NS equations, we use computers to get numerical solutions, which is the field of computational fluid dynamics (which is what I do).

Fluids is an interesting field to get into since it's such a critical aspect of physics/engineering with enormous potential for technological development, yet there's still so much we don't know.

Ah yeah turbulence. I think it's absolutely crazy how we've got such high tech airplanes and everything but we still don't know how turbulence will act or where it will go. It seems like the simplest thing compared to other things but clearly it's not.

Last I saw the Navier Stokes equation is a non linear differential equation which is where the whole problem arises. If we can't solve something analytically then how could a solution technically exist. What other way of solving a Non linear differential equation could possibly exist..

 

[blyatman]

Ah yeah turbulence. I think it's absolutely crazy how we've got such high tech airplanes and everything but we still don't know how turbulence will act or where it will go. It seems like the simplest thing compared to other things but clearly it's not.

Last I saw the Navier Stokes equation is a non linear differential equation which is where the whole problem arises. If we can't solve something analytically then how could a solution technically exist. What other way of solving a Non linear differential equation could possibly exist..

Yeh the fact that its non-linear is the cause of many headaches. We can solve it for very simple cases, and one of the more popular solvable cases is known as Couette flow. However, a solution can still exist even if we can't solve it analytically, we just need to solve it numerically (which is often the case with most ODE's). E.g. there's no analytical solution to y' = exp(-x^2), but it's very easy to solve that numerically if you were given the initial value.