Talk:Reynolds transport theorem

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Reynold's Transport Theorem

I have no previous knowledge of the Reynold's Transport Theorem, but as a Physcist I make a big plea to whoever knows more on this topic to convert the intergral theorems into differential theorems. Integral theorems are much harder to apply and use than differential forms of the same equations. You can also "see" the physics more easily in differential form, than in integral form. At least, differential forms are taught these days, instead of integral forms.

The differential forms of these equations are known as the Navier-Stokes equations which you may have heard of. I have to disagree with your statements that the differential forms are more useful or more often used, though that may be true in your field. I am a mechanical engineer, and the integral forms of these are both very powerful, and a lot clearer to me about what they describe. Regardless, they have already been converted for you by some smart people a long time ago. An important note: I added this page and it was written from the perspective of a mechanical engineer. If there is something that could be done to make it more useful to other specialties, I welcome the additions. -EndingPop 17:27, 16 January 2006 (UTC)
On 2/8/2006 someone added "also magnetic" to the end of one of the sentences. That sentence ended in the words "electromagnetic fields". Even though magnetic fields were already covered, if you think something is missing but don't want to add it in final form yourself make sure to put it on here on the Talk page. -EndingPop 02:03, 9 February 2006 (UTC)

If someone has the time, please consider simplifying the equations with \overrightarrow{V} = \overrightarrow{V_b} + \overrightarrow{V_r}. hoo0 05:06, 20 February 2006 (UTC)

First, thanks for the additions to the page. I really like the introduction; it gives it a lot more depth. Now, on the point of combining the equations. I added them this way because it makes more sense from a teaching point of view. The difference between Vb and Vr needs to be further explained, but I think that for a person looking for the equations would find this more useful than a condensed version. The expanded versions simply showcases more about the physical phenomena. If you still disagree, I won't revert it if you decide to make the change. - EndingPop 04:26, 21 February 2006 (UTC)

Does anyone know of a way to have a formula with a strike through it to symbolize the volume? You can see on this page it is just put there in normal text mode, and it looks terrible. - EndingPop 15:08, 21 August 2006 (UTC)

As far as I can tell you can't do strikethroughs in TeX without an extension package, which I don't know how to use on Wikipedia (if you even can). I'd suggest changing this to some other standard symbol for differential volume--dV, dΩ, d3x or some such. Starryharlequin 03:27, 5 October 2006 (UTC)
V is already used as velocity, and the strike through is what I have seen in academia as the standard. Is there another symbol that is used in thermofluids? -EndingPop 11:50, 5 October 2006 (UTC)
In my thermofluids class, as well as our book, script v is used for velocity and capital V for volume. This seems a pretty good compromise to me. Something alone the lines of:

\frac{DN_{sys}}{Dt} = \int_{c.v.}^{} \frac{\partial}{\partial t} (\rho \eta) dV + \int_{c.s.}^{} \rho \eta \vec{v_b}\cdot \widehat{n} dA+\int_{c.s.}^{} \rho \eta \vec{v_r}\cdot \widehat{n} dA

I used \vec with lowercase v, because I don't really know tex enough to figure out a script vector. !jim 18:45, 6 October 2006 (UTC)
I have always seen the script v as specific volume in thermofluids, but since that isn't used here I'll try to make that change. - EndingPop 12:57, 9 October 2006 (UTC)

[edit] Correctness?

Is the equation shown correct? Shouldn't it be:

\frac{DN_{sys}}{Dt} = \int_{c.v.}^{} \frac{\partial}{\partial t} (\rho \eta) dV -\int_{c.s.}^{} \rho \eta \vec{v_r}\cdot \widehat{n} dA

Can anyone check the reference? —The preceding unsigned comment was added by 193.1.100.105 (talk • contribs) 09:14, January 3, 2007 UTC.

I'm the original author of the article, so maybe my assurance doesn't count, but I assure you the formula is correct. The term with "vb" in it deals with the more general case of deformable control volumes. - EndingPop 14:54, 3 January 2007 (UTC)
You might encounter your version of this equation in a basic thermo class. That equation (yours) assumes that the control volume is fixed in whatever reference frame you're using, so the vb is zero, and the third term goes away. The minus sign is just related to a different sign convention, I believe. For what it's worth, my Thermo I professor also did away with the third term in the more general equation. !jim 04:21, 4 March 2007 (UTC)
Why are the \int_{c.s.}^{} \rho \eta \vec{v_r}\cdot \widehat{n} dA and the \int_{c.s.}^{} \rho \eta \vec{v_b}\cdot \widehat{n} dA two integral instead of just one \int_{c.s.}^{} \rho \eta \vec{v}\cdot \widehat{n} dA where \vec{v} = \vec{v_r} + \vec{v_b} i.e. the fluid flow at the surface? —The preceding unsigned comment was added by 129.94.6.28 (talk) 03:03, 22 March 2007 (UTC).
This was actually discussed above. It was felt that leaving the two velocities seperate was more clear or provided more information to someone not necessarily familiar with this concept. See hoo0's comment above. !jim 06:03, 22 March 2007 (UTC)
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