Best way to learn fluid mechanics while in high school

[DylCG10]

Hi,

I am a high school student doing a project on fluid dynamics and need to understand the relevant maths so that I can understand how to apply the mathematics of fluid flow (particularly air flow around a cylinder). I have a basic calculus understanding and need to understand the navier stokes equations in depth and any other maths to be able to create a mathematical model of air flow around a cylinder. What is the best and most efficient way to have a mathematical understanding of the fundamentals of fluid dynamics maths in under a month? E.g. through online videos, textbooks (and if so, which textbooks are good that aren't too advanced)?

 

[jedishrfu]

Your problem will be bridging your calculus to classical mechanics and then to fluid mechanics and learning about partial differential equations along the way.

There are videos on youtube about the Navier-Stokes equation and how folks apply various boundary conditions to come up with a simpler equation to model.

Some history:



Intro to Navier-Stokes:





To give you an idea of the partial differential equations and how the Navier Stokes was derived:



3blue1brown has several video collections that you should check out:

 

[berkeman]

I have a basic calculus understanding and need to understand the navier stokes equations in depth and any other maths to be able to create a mathematical model of air flow around a cylinder. What is the best and most efficient way to have a mathematical understanding of the fundamentals of fluid dynamics maths in under a month?

Sounds like a pretty challenging (and fun) project. Maybe @boneh3ad has some suggestions on ways to simplify the project to make it more practical to accomplish in that short timeframe...

 

[boneh3ad]

I have a basic calculus understanding and need to understand the navier stokes equations in depth... What is the best and most efficient way to have a mathematical understanding of the fundamentals of fluid dynamics maths in under a month?

This is a fool's errand. You won't get this in under a month. Your best bet is to finish 3 years of a BS in one of several flavors of engineering if you want to approach this in an effective, methodical way.

...to be able to create a mathematical model of air flow around a cylinder.

You may be in luck due to this portion of your request. You can get a lot of good information on this topic by first exploring potential flow theory. You won't capture any physics related to viscosity that way, but it is orders of magnitude more straightforward than the Navier-Stokes equations. Whether it is sufficient depends on why exactly you want to do this.

 

[zanick]

get a job putting in sprinkler and /or plumbing systems ;)

 

[PeroK]

Or, take swimming lessons.

Studying fluid mechanics itself is very much going in at the deep end.

 

[bigfooted]

In the limit case that you are interested in making a small computer program to compute some velocities and pressures around a cylinder without the time to go into the details of partial differential equations, have look at this page:
https://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinderThe basic idea behind solving potential flow problems is that you can compute the potential flow around an object by using combinations of simple and well known solutions and add them to get the solution of your more complicated problem. This method is also called a panel method.

Here are some lecture notes that will show you how you can compute some flows around simple objects.

http://web.mit.edu/16.unified/www/FALL/fluids/Lectures/f15.pdf
Please also look into the limitations of potential flow: in models there is usually a trade-off between simplicity and accuracy.

 

[boneh3ad]

In the limit case that you are interested in making a small computer program to compute some velocities and pressures around a cylinder without the time to go into the details of partial differential equations, have look at this page:
The basic idea behind solving potential flow problems is that you can compute the potential flow around an object by using combinations of simple and well known solutions and add them to get the solution of your more complicated problem. This method is also called a panel method.

It's not the same as a panel method. A panel method is one application of potential flow, but not all potential flow problems use panel methods. Panels are one example of a class of simple solutions you can add together but they aren't the only solution.