Talk:Reynolds transport theorem

message: I have performed this because:
1) the theorem was given incorrectly (see the following section)
2) after many years of minor edits, the article did not flow and had unnecessary material
I removed the material on "mass formulation" etcetera, because it does not appear in standard texts and it was unnecessary for the article.
Garethvaughan (talk) 03:34, 25 August 2011 (UTC)
thread_title: An Extensive Re-Write

message: It is the higher dimensional extension of Differentiation under the integral sign and should reduce to that expression in some cases.  Suppose f is independent of y-z, and that \Omega(t) is a unit square in the y-z plane and has x limits a(t) and b(t).  Then Reynolds transport theorem reduces to 
:
  \cfrac{\mathrm{d}}{\mathrm{d}t}\int_{a(t)}^{b(t)} f~\text{dx} = 
     \int_{a(t)}^{b(t)} \frac{\partial f}{\partial t}~\text{dx} + 
\frac{\partial b(t)}{\partial t} f(b(t),t)
-\frac{\partial a(t)}{\partial t} f(a(t),t) ~,
which is the expression given on Differentiation under the integral sign, except that there the variables x and t have been swapped.
Garethvaughan (talk) 10:55, 16 July 2011 (UTC)
thread_title: Interpretation and reduction to one dimension

message: 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).
: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)
replies: text: 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)
replies: text:  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)
replies: text:  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)

text: Use Vr = Vf - Vb. If the boundaries do not move (Vb = 0), then the flux terms reduce to just Vf. I apologize, I can't seem to come up with a good physical analogy for why this works. My suggestion is to try it on some examples to see how the math works out. Try a uniform 1D flow and play with different values of Vb at the inlet and outlet with the continuity equation. You'll see that it always balances out. - EndingPop (talk) 21:31, 16 February 2009 (UTC)
replies: text:  I've read the discussion of this and I think at the very least we need a definition for what is meant by Vr (it took me a while to work it out).  I've added this in, on a new line so readers in other sections will find it easy to spot.219.89.247.21 (talk) 05:39, 7 July 2011 (UTC)
thread_title: Correctness?

message: Shouldn't the case where  \eta   = 1 be included? This will reduce to the mass flow conservation equations. I believe that they are important enough to warrant its own heading along with the momentum and energy conservation. 203.59.183.57 07:43, 18 April 2007 (UTC)
replies: text: Somehow I missed a deletion of that section several edits back. I am currently working on integrating past constructive edits into the last version that had the mass formulation in it. Thanks for the head's up! - EndingPop 14:22, 18 April 2007 (UTC)
replies: text:  There, I've updated the page with the mass formulation back in there. The initial removal was my fault, I reverted some vandalism and missed the edit before by the same user that removed the mass formulation section. All subsequent constructive edits should have been included, but I'd appreciate someone checking my work. - EndingPop 14:34, 18 April 2007 (UTC)

text: Mass of a system is always constant and therefore cannot change in time, meaning \frac{DM_{sys}}{Dt}=0  is always true. - Hacktivist 15:58, 4 November 2007 (UTC)

text: In this formulation, "system" is defined as an identifiable and fixed quantity of matter. We aren't accounting for nuclear reactions, so the time-rate of change of mass in the system is necessarily zero. Don't confuse the system with the control volume (Lagrangian vs. Eulerian viewpoints) - EndingPop 15:42, 5 November 2007 (UTC)
thread_title: Mass Flow

message: I believe there is still a problem though.  In going from the general form to the specialized form for mass, you are taking the time derivative outside the integral over the c.v. - this is only true for a non-deformable c.v.  For a deformable cv, from Liebnitz theorem,
del/delt(integral_over_cv(rho*eta*dV))=integral_over_cv(del/delt(rho*eta*dV))+integral_over_cs(rho*eta*v_b.normal*dS)
so, only the relative velocity integral should show up - this issue is covered in Potter and Foss' book that is cited as a reference  —Preceding unsigned comment added by 128.138.64.39 (talk) 21:38, 23 May 2008 (UTC)
replies: text: I'm not following you. Could you point out the alleged discrepancy/error? What, specifically, is wrong, and why? Also, a page number from Potter would be good too, since you said it was dealt with in there. - EndingPop (talk) 20:31, 27 May 2008 (UTC)
replies: text:  In the conversation below I noticed and understood what you were saying. The continuity equation has been updated. - EndingPop (talk) 00:21, 9 September 2008 (UTC)
thread_title:  Formulation Error? 

message: I read this article. I don't have in-depth knowledge about the topic but I want the article should elobrate so that one can build there thinking from "particle based computation to control volume based computation" and then corelate the importance of Reynolds-Transport equation. Too much math can take away the beauty of wikipedia article (My personal view..No offence :)).  —Preceding unsigned comment added by 203.91.193.50 (talk) 12:10, 4 November 2008 (UTC)
thread_title:  Should be elobrated bit more 

message: ¿Is there a missing term in the energy equation? first term of the RHS should be:
\int_{c.v.}^{} \frac{\partial}{\partial t} (\rho \eta) dV 
If \eta = \frac{\upsilon^2}{2}+gz+\tilde{u}+\frac{p}{\rho} then I believe there is a \frac{p}{\rho} term missing in the first term on the RHS.  —Preceding unsigned comment added by 200.27.56.84 (talk) 13:25, 25 February 2009 (UTC)
thread_title:  Energy 

message: Typically, a discussion of Reynolds Transport Theorem will include a discussion of material volume (changing volume and location, zero property flux) vs. control volume (fixed volume and location, arbitrary flux), also sometimes referred to as closed system vs. open system.  I see that as a very important distinction (see e.g. , Schobeiri's Fluid Mechanics for Engineers: A Graduate Textbook (2010) p. 42, Yamaguchi's Engineering Fluid Mechanics (2008) p. 35, Trif's Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics (2005) p. 13, Batchelor's classic text Introduction to Fluid Mechanics (1950) p. 131, etc etc.  However, this is not mentioned in the article at all, primarily due to the fact that the article uses a single primary reference (Potter and Foss, Fluid Mechanics) and therefore does not incorporate other perspectives (this is the reason I added the "One source" template).  As all can see from the discussion on this page, the article's formulation isn't sufficiently general enough to satisfy all.  Incorporating additional references will certainly help with that - at the very least, it will provide more substantial justification when others disagree with the formulation.
I am planning on incorporating this distinction, and several of the references listed, into the article (particularly the classical text by Batchelor). --Charlesreid1 (talk) 08:48, 1 November 2010 (UTC)
thread_title:  Material vs. Control Volume 

message: In the section "General Form" we had an equation with 
\frac{DN_\text{sys}}{Dt} ,
denoting the material derivative, but I think this should be 
\frac{dN_\text{sys}}{dt} 
denoting the total derivative, since N_\text{sys}  is a function solely of time.
This is because N_\text{sys} = \int_\text{c.v.}^{} \rho \eta dV  is not a function of x.  Once we've defined the control volume we integrate over x: the variable no longer appears.
I have made a change to \frac{dN_\text{sys}}{dt} .219.89.247.21 (talk) 02:22, 7 July 2011 (UTC)
replies: text:  The theorem applies to more than just integrals over Lagrangian volumes.  The total derivative is appropriate. 
Garethvaughan (talk) 05:46, 20 January 2013 (UTC)
thread_title:  Incorrect use of the material derivative 

message: As an undergraduate studying fluid mechanics in my second year, this article is next to useless for me. It should at least include an 'unclear' template until someone improves it showing its significance in fluid mechanics in a way decipherable (and useful) to the passing engineer.
The current intro (three alternative names, a reference to the rule in maths, the person it's named after, a statement that it is useful and a use of the word 'recast' which I have never encountered before) is not useful for those who use it. --عبد المؤمن (talk) 19:15, 16 January 2013 (UTC)
thread_title:  Unclear 

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