Fluid Mechanics - Why? How? Why?

[thepikminman]

Hi,

I've been studying fluid mechanics for my mech. engineering degree for the past few months. Unlike my other subjects (mechanical analysis, thermodynamics, automated systems, mechanical vibrations), I can't seem to grasp the problem-solving technique.

The annoying thing is, I find the subject extremely interesting and can see how useful it is to know, and would love to be able to solve fluids problems.

I have missed quite a few lectures due to illness which could be part of the reason, but I've missed them in the other subjects too and was able to teach myself for them, but not for fluid mechanics.

I just can't seem to see the structure to solving these problems, all solutions I see seem so different and are very intimidating. I'm sure once you get over the fact that so many variables are used it probably is a lot easier than it seems, but I can't seem to do that.

Any tips on how to approach problems in fluid mechanics? I know there's a huge range of problems, but if anyone can share a general approach, or NB equations to know, or where to start with a problem.

I have an exam on Monday and really think I'm going to fail after studying hours per day for the past few months, getting literally nowhere. Any tips that will help me at least pass the exam, ways to get SOME marks at least.

Here's a sample exam paper so you know the types of questions I'm talking about.

Cheers!

 

[boneh3ad]

Two things stand out to me in your post. The first is that you are trying to learn solution techniques, and the second is that you are pointing out that the solution techniques for different problems are very different. These two statements stand out to be because they imply that you are trying to learn the topic by just learning recipes to solve the problems and how to tweak that recipe for different problems. This is a terrible way to learn scientific topics and will not serve you well for precisely the reason you seem to have discovered: it makes it very difficult to apply any of the material to new problems.

This is especially problematic in fluid mechanics because fairly small (by appearance) changes in the problem can change the solution method pretty substantially. You need to be learning the underlying principles so that they may be applied to many problems. In fluid mechanics especially, you need to know the fundamentals because each problem essentially boils down to making a series of assumptions to simplify the otherwise extremely complicated governing equations. If you don't understand the basics and how different assumptions affect them, then you've already lost the battle.

So in short, learn the fundamental principles and learn how the various assumptions common to fluids problem affect those principles. That should help you select an appropriate set of simplified equations to use to solve the problem.

 

[thepikminman]

Two things stand out to me in your post. The first is that you are trying to learn solution techniques, and the second is that you are pointing out that the solution techniques for different problems are very different. These two statements stand out to be because they imply that you are trying to learn the topic by just learning recipes to solve the problems and how to tweak that recipe for different problems. This is a terrible way to learn scientific topics and will not serve you well for precisely the reason you seem to have discovered: it makes it very difficult to apply any of the material to new problems.

This is especially problematic in fluid mechanics because fairly small (by appearance) changes in the problem can change the solution method pretty substantially. You need to be learning the underlying principles so that they may be applied to many problems. In fluid mechanics especially, you need to know the fundamentals because each problem essentially boils down to making a series of assumptions to simplify the otherwise extremely complicated governing equations. If you don't understand the basics and how different assumptions affect them, then you've already lost the battle.

So in short, learn the fundamental principles and learn how the various assumptions common to fluids problem affect those principles. That should help you select an appropriate set of simplified equations to use to solve the problem.

That's exactly it! I'm starting to realize this, and realize I may not be able to pass the exam at this point without proper understanding of the fundamentals.

But yes, at this point I am just learning recipes to solve the problems and how to tweak that recipe for different problems, and I know that doesn't get you anywhere understanding-wise, but desperate times call for desperate measures.

You said "learn the fundamental principles and learn how the various assumptions common to fluids problem affect those principles", could you tell me what these principles are? Or what the most common ones are? Just somewhere I can start? Thanks for your input!

 

[boneh3ad]

Well, at it's most fundamental, fluid mechanics typically boils down to some simplified form of the Navier-Stokes equations or a control volume analysis (or both!).

For control volumes, I see people get tripped up most often when they get signs wrong all over the place. Ultimately, those errors are typically because they are skipping too many steps without understanding what should have happened in those steps. I would suggest starting with the full integral conservation equations every time you do a practice problem just so you get the hang of the various terms and signs. They typically boil down to relatively simple vector calculus problems. Anything more complicated is a bit much for this sort of course.

For other problems, it can be a real pain to start from the Navier-Stokes equations when something like Bernoulli's equation applies just fine, but the key is understanding when and why Bernoulli's equation applies. For that, you ought to know how it is derived from either the Navier-Stokes or control volume equations so that you understand its inherent assumptions and limitations. Then applying it directly should be no problem come test time.

 

[thepikminman]

Well, at it's most fundamental, fluid mechanics typically boils down to some simplified form of the Navier-Stokes equations or a control volume analysis (or both!).

For control volumes, I see people get tripped up most often when they get signs wrong all over the place. Ultimately, those errors are typically because they are skipping too many steps without understanding what should have happened in those steps. I would suggest starting with the full integral conservation equations every time you do a practice problem just so you get the hang of the various terms and signs. They typically boil down to relatively simple vector calculus problems. Anything more complicated is a bit much for this sort of course.

For other problems, it can be a real pain to start from the Navier-Stokes equations when something like Bernoulli's equation applies just fine, but the key is understanding when and why Bernoulli's equation applies. For that, you ought to know how it is derived from either the Navier-Stokes or control volume equations so that you understand its inherent assumptions and limitations. Then applying it directly should be no problem come test time.

Thanks very much!

Based on your experience, would you say it would be even possible to learn what you said and pass the exam, with say, 10 hours of study? Assuming I have no knowledge in the subject (even though I do, but if I didn't). I only ask because I have more exams following and am wondering if I should just ditch this one for now and focus on the others, or use those 10 hours for this, maybe with the possibility of passing.

(FYI I take my course very seriously and am not a quick-fix student, like it seems from my posts. I have just been ill this semester and have missed a lot of lectures)

 

[boneh3ad]

10 hours seems like a tall order from scratch, but everybody is different.

 

[thepikminman]

Anyone else have any tips? Ways to get some marks?

 

[thepikminman]

Something like "Always start with..." or "Definitely know...(eqn)" ...annnnyone??

 

[Vanadium 50]

Anyone else have any tips? Ways to get some marks?

Yes. Stop messing around on the internet and hit the books. You have only a few hours.

 

[thepikminman]

Yes. Stop messing around on the internet and hit the books. You have only a few hours.

Haha trust me, I'm hitting the books constantly all day and night, my only break is to ask on here, because I'm getting nowhere.

Seriously, any tips or last minute advice?

 

[Vanadium 50]

Seriously, any tips or last minute advice?

I was serious.

 

[thepikminman]

I was serious.

I wasn't asking you, I was asking the other people viewing.

And if you read my reply, you'd see that I was already doing what your "advice" specified.

 

[gmax137]

Based on your experience, would you say it would be even possible to learn what you said and pass the exam, with say, 10 hours of study?

No, I don't think it is possible, if the exam will be similar to the one attached to your OP.

Something like "Always start with..." or "Definitely know...(eqn)" ...annnnyone??

There are no such magic words.

 

[thepikminman]

No, I don't think it is possible, if the exam will be similar to the one attached to your OP.

I think you're right, did it a few hours ago...felt ashamed to even hand it up...haha thanks anyway to you and all who helped!