Bignose

and 'without a calculator' is actually a fairly broad condition. Because would that allow me to use a slide rule? How about a wheel with the trig funtions on it (like http://thumbs1.ebaystatic.com/d/l225/m/mY0p2yLqWcm_BM6fIlsKGXQ.jpg)? Or what more people did before speedy calculation was available... look it up in a table (like http://upload.wikimedia.org/wikipedia/commons/2/2e/Abramowitz%26Stegun.page97.agr.jpg). Also, might want to have a read through this recent thread on a very similar topic: http://www.scienceforums.net/topic/78655-how-do-you-get-the-sine-of-an-angle-without-calculator/

k, fine, whatever. Another handwaving dismissal of my criticism by just -- for no reason other than it fixes this immediate issue -- the units of the drag coefficient are now changed. No real justification. No answer of how it now changes all the other previous equations to having wrong dimensions. Just suddenly, D has units of 1/length. I'm done. This hand waving slapdash of each issue is not real science and very uninteresting.

I can criticize an idea that has the wrong units without knowing all the details of how it ended up with the wrong units. Your dimensionless drag coefficient has dimension of length. End of story. Something is wrong. Having the correct units doesn't mean the formula is correct, but it is a good first check. This is like changing F = ma to F = mal. You just can't do it. The units on the left hand side and the right hand side have to match. There is no formula in physics anywhere where this isn't true. Also, I want to say, I don't think it is fair for you to criticize me for 'not understanding' when I've pointed out where the misunderstandings are, I ask pointed questions about them, and you do nothing but hand wave them away. A significant source of the misunderstanding is the poor communication and presentation of your idea. So, yes, I don't understand because you haven't made it understandable.

So, if I measured in inches and you measured in mm, then you wouldn't divide? I've never heard of a theory dependent upon two people using the same ruler. And you'd still have your drag coefficient having a unit of length if everybody did use the same ruler. That still isn't fixed. The point being, that your equation for a dimensionless number shouldn't have dimensions on one side of the equation. You need an equation that all the dimensions cancel out on both sides.

No, that's nonsense again. What are you going to divide by? Inches? mm? or light years? All are perfectly valid units of length, why is any one of them more special than the others? The laws of physics are actually independent of units and coordinate systems. There is no good reason that drag should be the one exception to this.

There is a length in the Reynolds number, already. Though you have to be very careful about what Re you are defining. On a cube, there is only 1 length, so it is obvious what length the Re would use. Same thing with a sphere. For something with multiple lengths, you need to explicitly state what length you are using

I read the post, but it is nonsense. How do you include a length, but not use units? That's jibberish. If I went to the lumber yard, to buy a piece of wood, and the clerk said "sure, no problem, how long do you need" and I just said "10". What would the clerk do? Units are paramount. And if you don't include the units, then your formula is just hookum. Do you include the length in inches? mm? m? furlongs? chains? light years? hands? or any of the thousands of other units of length that mankind has invented over the years? When you have a length, you have a unit that comes with it. That always happens. You can't just dismiss this.

So you're saying that the drag coefficient has a unit of length? That that's wrong, too. The drag coefficient is dimensionless. Look, seriously. These are major errors in your idea. Correct dimensions are paramount to actually predicting something useful. If you're going to just have wave this away too, then I'm done. You've done this over and over, and I need to just accept that you aren't open to my criticisms. I've been trying to point you toward the knowledge we do have on drag, but you seem ultimately reluctant to actually go and learn any of it. I would consider this borderline trolling behavior. I just don't care to even try to help anymore if you aren't going to actually look at it.

So between this and this something more is dead wrong. D = 33.941*l/Re has to be completely wrong, because Re is dimensionless. So you are effectively saying here that the units of drag are length. That just isn't right. Drag is a force, not a length. We're not even making elementary fluid mechanics mistakes here, this is 1st day physics mistakes. If you want to continue, you need to get these errors corrected. It is pointless to talk about the predictions made by an equation that isn't even dimensionally sound. You need to take some time, regroup, and correct these errors.

Then your assumption for Re<<1 is wrong. If you actually would do the calculation at Re<<1, you'd find there is no wake -- and this led to the famous D'Alembert's paradox. There is zero form drag at that slow of a flow. Sure. If you can show me the calculation for drag for a sphere at Re << 1 then maybe I will believe that you have some knowledge. Let's see it. And why are you yet again refusing to answer direct questions? What is 'l' in your formula? Why can't you answer this?!?! Answer this before trying to solve the N-S eqns, please.

What is this l now? What are its units? Where did this come from?!? Because I don't even see it your previous equations. You keep telling me I don't understand your idea... that's true! Because I don't think a complete and thorough posting of your idea has been made yet! You keep changing functions, changing variables, etc. And most importantly, how does this compare to the experimental values? Another critique I have is that you used the given answer already CD = 24/Re. I thought your idea here could derive it on its own. Why do you need that result in an intermediate step? I have the same critique for the previous posts, where you needed the value for a cube. The current theory can derive the drag around a sphere at Re<<1 as CD = 24/Re from first principles... that is as a direct consequence of solving the Navier Stokes equations. It doesn't need any other inputs. If your method cannot even replicate this simplest of scenarios, I have no confidence it is doing anything more complicated, like a cube. Lastly, this could not be more wrong. At Re<<1, there is nothing but skin friction. How many more of these elementary mistakes am I going to have to correct before I can convince you to actually read some basic fluid mechanics texts?

You are missing the point. You do not need the exact value of the sphere radius. You do not need the fluid viscosity. You do not need the exact value of the free stream velocity. The ratio of those combined correctly makes the dimensionless number Re. And when Re is much less than 1, all the drag can be calculated by CD = 24/Re. You don't need an reference to a cube. You don't need anything else asked for. If your idea can't replicate the very very well confirmed formula above, then it is less useful. And it doesn't match what is observed in reality. And I didn't make you do this in a half hour... Not sure why that's a problem. Take all the time you need. Isn't da/dx 0? You set a to a constant, 45 degrees. the derivative of any constant is 0. Found this in 25 seconds of looking. http://www.sciencedirect.com/science/article/pii/0032591089800087 I know there is more out there. Gotta improve your researching skills, my friend.

Sorry. That is no where near the classical exceptionally well verified result. For Re << 1, CD = 24/Re. Your calculations here are greatly at odds with rock solid knowledge. Your idea is wrong.

I'm sorry, but this tells me that your knowledge is severely lacking. Because I really gave you all that info already by saying the Reynolds number was much less than 1. The exact size of the sphere doesn't matter... The size of the sphere in relation to the free stream velocity and the fluid properties matters. That's what Re means. If you really need the exact info, make up your own values such that Re = something much less than 1. And BTW, for spheres where Re<<1, the flow is very very laminar. That's why I asked you to answer this problem since per your above post, your formula is only valid for laminar flows.

Before you dive into the extraordinarily complicated world of non-Newtonian fluids, best to get Newtonian fluids right. Even if the flow is laminar, it still isn't going to be that easy to get exactly the flow field at every point. Analytic solutions are still only available in very special cases. CFD is still the main tool here. And your geometry-based solution still won't work, in my book. The fluid flow is not only dependent on that geometry. Your calculation there still doesn't take into account the entire flow. But, prove me wrong. Explicitly using your formula (i.e. show every step, please), calculate the drag for a sphere at very low Re flow. Re<<1. This is a classical result that if your formula is right, should be replicated easily.

I don't think it is necessarily nonsense. It is just that you've made some really rather extraordinary claims. You're going to have to back it up with some really really extraordinary evidence. It will become nonsense if you can't demonstrate some extraordinary evidence to support your claim here. e.g. for one of many examples, you claim to have eliminated the need for dark matter. Then demonstrate exactly how your idea recreates those maps of dark matter: http://www.scientificamerican.com/article.cfm?id=biggest-map-yet-of-universes

If you hope to avoid differential equations in any of these topics, as per your 1st post above, you're going to be out of luck. Differential equations are very prevalent in all 3 of these topics. If you are truly looking for 'comprehensive knowledge' in these areas, you can't avoid the differential equation. If you are truly looking for comprehensive knowledge of thermodynamics see Tester and Model's Thermodynamics and Its Applications. Tough, tough book, but if you get through it you will be an expert. For Heat Transfer, I liked Engineering Heat Transfer by Rathore and Kapuno, though I personally prefer to study the abstractions wherein momentum, heat, and mass transfer are seen as very similar/analogous phenomena. Bird, Stewart, and Lightfoot's Transport Phenomena is the classic in that field. I am not as familiar with the mechanics of materials texts, so someone else will have to give you recommendations there.

So, you think free stream velocity and geometry is enough to give you the wall shear stress? That isn't right. You have zero consideration for whether the bulk flow is laminar or turbulent. You have zero consideration for whether the boundary layer is laminar or turbulent -- or where this transition happens. You have zero consideration for where the boundary layer separates from the body, or if it does or doesn't. You have zero consideration for the flow itself -- except in the simplest of geometries, usually a very difficult task. This is why computational fluid dynamics is considered very important. Again (broken mp3 player here!), this kind of stuff is covered in Schlichting's Boundary Layers text listed above. And this is why almost always, the estimation of Cf is done via a correlation, and not directly calculated. The direct calculation is a bear.... you basically have to know the entire fluid field. That leads back to the CFD.

I'd put it here... you're explaining how you intend to calculate the wall shear stress (NOT exactly the same at the shear rate... gotta get these right, my friend) in order to calculate your Cf. That's a natural continuation of this thread.

gotta work on that communication again. It is NOT ux/x or u/x. It is [math]\frac{\partial u}{\partial x}[/math] can't just drop the partial signs willy nilly here. Must be very, very clear about getting the math right. This has been a cause of a lot of the problems to date.

So, your q is not an actual pressure, but the pressure they use for nondimensionalization, like with the Euler number. e.g. [math]q=\frac{1}{2}\rho U^2_\infty[/math] Sheesh. Clear communication would have helped here tremendously. ok. Let's address the next issue then. How are you going to get the shear stress at the boundary, then? And you should be adding a qualifier that [math]\tau_w = \mu \frac{\partial u}{\partial x}[/math] for a Newtonian fluid only. But, it is the calculation of [math]\frac{\partial u}{\partial x}[/math] that is very difficult to do. How are you proposing to do it?

Where do you see this?! I posted exactly the same formula from wikipedia! There is no pressure in the denominator! [math]C_f = \frac{\tau_w}{\frac{1}{2}\rho U^2_\infty}[/math] You even quoted this in my reply! Where is the pressure in this equation!?!?!

And I don't think that there is a single good scientist who is claiming to understand all of the universe. Every good scientist should fully admit that there is plenty that we don't know. And that anyone who claims that, it acting on faith alone. Again, I don't think that this is a problem, it just needs to be acknowledged as such, and use the words per their definitions.

You mean this page? http://en.wikipedia.org/wiki/Parasitic_drag Where it says [math]C_f = \frac{\tau_w}{\frac{1}{2}\rho U^2_\infty}[/math]? The equation that doesn't include pressure at all? The equation that is similar to the nondimensionalization I posted above? You're missing the bigger point here. Total drag = skin drag + form drag + possible others. Skin drag is due entirely to surface friction effects. That is why it contains the shear stress at the wall. Form drag is due entirely to pressure effects. That is why it contains the pressure difference. I have never seen anyone turn that above sum into some kind of product. That is, the surface terms and the pressure terms are kept separately and then added together -- not multiplied. And if you want to propose blending there two terms together, then I am going to request extraordinary evidence to support this. Note that I'm not saying that the two effects don't interact, because I have little doubt that they do. But the first order approximation has the terms separate. And given the difficulties in measuring the terms directly as above, usually the first order terms are sufficient. Teasing out any higher order effects would require significant evidence and experimental verification. And, I'd like to see some very compelling reason to change the well established and accurate 1st order terms that are already in common use. Lastly, a meta-comment. In clicking on the above wikipedia page and following some links there, I suspect very strongly that most of this work is based on those wikipedia pages. (In the future, you ought to get in the habit of citing the references you use.). This is a case where wikipedia isn't bad, but it really isn't all that good. If you really want an understanding of fluid mechanics, you are not going to learn it from wikipedia. You are going to need to put in some time with some good books. Back when I taught the class, I used to tell the students that fluid mechanics was one of the first classes where just doing the homework and memorizing the text wasn't going to guarantee them a good grade. Because, there are so many different problems in fluid mechanics, that I would write exams different enough from all the others that the only way to get a good grade was to actually understand fluid mechanics. This was a shock to some students that otherwise had very good marks to date. Because they were very good at symbol pushing and memorizing equations, but no real understanding of those equations. Fluid mechanics -- if taught well -- can expose those flaws. This is why I keep repeating myself, but I cannot recommend strongly enough that you put in some time with some good textbooks. If you don't want to buy new books, there are many good used texts out there -- and the basics of fluid mechanics haven't changed in the last 20 years, so even a good text from 1990 can be valuable. I don't know of any web resource that can supplant a good text. And wikipedia as I viewed it today certainly can't.

Because faith, by its definition is to accept or believe something based on no evidence. Rationality, on the other hand, by its definition only accepts something because of the supporting evidence. Faith and rational are almost explicitly opposites. Again, I want to make sure that you understand that I think that it is okay to have a belied based only on faith. You just need to be fair to the definitions of the words, and use them correctly per their definitions.