Talk:Bernoulli's equation

Come help with WikiProject Fluid dynamics moink 23:12, 27 Dec 2003 (UTC)

Mathification
I put all of the derivation into LaTeX. (Thank God for Lyx). There may be small problems with the transition. --Colonel panic 05:56, May 31, 2005 (UTC)

Formula Conversion
Formulas would look more like in textbooks if we would remove multiplication dots (e.g. change $$a \cdot b$$ to $$a b$$). This can be very simply done by replacing all occurrences of \cdot with empty string by using text editor replace function.

I am not feeling comfortable to do this for myself.

Aleksas 21:43, 19 August 2005 (UTC)


 * The dot actually means dot product, which is wrong here. Must be changed.


 * I tried but i'm getting parse errors and stuff. Wikipedia needs a equation editor or somesort, the equations editing with weird symbols drives me mad! Sorry.--Jetru 11:46, August 23, 2005 (UTC)


 * Dot is also used to denote multiplication of numbers. So these dots are not errors. At worst they show poor style.


 * Interesting to note that we can treat scalars like one dimensional vectors. So we can think about multiplication of numbers as scalar product of one dimensional vectors.


 * PS. I will remove those dots. --Aleksas 14:52, 23 August 2005 (UTC)

3D version of scheme used in this article
I have made POV-Ray version of scheme used in this article. You can see three versions of it:
 * first one (uses oblique projection)
 * second one (uses orthogonal projection)
 * third one (uses perspective projection)

In my opinion current scheme used in article is quite good and doesn't really need any replacement. Despite this, maybe my scheme could be good replacement for current scheme? What do you think? Or should I better hide it somewhere, so no-one could see it. :) --Aleksas 14:19:42, 2005-08-28 (UTC)

compressibility
I added discussion and derivation of the compressible form of Bernoulli's equation. Style may be a bit awkward and could probably use some help from somebody who knows better than I do how to make nice Wiki entries. --petwil

Proof
This proof is for kids. A more rigorous proof is required. Will do that soon. deeptrivia (talk) 20:43, 14 December 2005 (UTC)
 * Er, which proof, and how is it for kids? Just wondering, since I wrote the one for compressible fluids. Petwil 02:02, 17 December 2005 (UTC)


 * A more general form of Bernoulli's thoerem is:

$$ {\it grad} \left( {\frac {\partial }{\partial t}}\phi \left( x,t \right) +{\frac {v.v}{2}}+{\frac {p}{\rho}}+\beta \right) = 0$$

where,

$$ v \left( x,t \right) ={\it grad} \left( \phi \left( x,t \right) \right) $$

and

$$ \rho\,b=-\rho\,{\it grad} \left( \beta \right) $$

where b is the body force.

This reduces to


 * $$ {v^2 \over 2}+gh+{p \over \rho}=\mathrm{constant} $$

when the flow is both steady and irrotational, and weight is the only body force. This proof is okay for a general audience though. deeptrivia (talk) 03:39, 17 December 2005 (UTC)


 * Deeptrivia, a few points:


 * (1) It seems to me your proof would be less general, not more. In particular your proof would apply only to potential flows.


 * (2) I am not an expert on points of style regarding Wikipedia, but it seems to me the point of Wikipedia is to provide a source of information to non-experts. Persumably experts will have the available background and reference materials available. One does not learn mechanics by beginning with the Hamiltonian. IMO, for an introduction to a topic, usually the best way to start is to keep it as simple as possible (but not simpler!) and gradually ramp up the mathematical sophistication as needed. Besides, this is the way physical discoveries are made anyway - the formalism usually comes later.


 * (3) On pure physical grounds, the most approachable proofs of Bernoulli's equation are grounded in integral formulation of fluid equations, not differential formulation.


 * (4) On the other hand, I am sure your proof would be a welcome addition if you want to append it to the page. I for one would be interested in seeing it added.


 * (5) I would agree with you that the math for the incompressible proof could be cleaned up. The notation is a bit clumsy and obfuscates the basic thrust of the argument.


 * Petwil 19:50, 10 January 2006 (UTC)