[Sagar karan]

I will put my doubts related to this question if you like to answer......

[agd]

Is there a reason why you don't just google "reynolds transport theorem"? It is a well-documented theorem that essentially expresses the time rate of change of a quantity contained within a fixed mass to a set of integrals that represent the time rate of change of the quantity within and passing through a control volume. The control volume may be fixed or moving.

[Sagar karan]

Thanks to show interest in the question!. Yes, there is a reason because I have stopped at certain line while reading it on Googlehttps://sbainvent.com/fluid-mechanic...sport-theorem/
I am reading from the given above link and I have stopped in the given image that I sent

Can you please explain the doubt red line circle around the given equation in the image?

[agd]

I'm not sure what reference you are using but it looks to me that the line you have marked as unclear contains an error. Since I can't see more than what you have posted I can only speculate based on the fact that the equation you have circled is not dimensionally consistent, among other things. I would look for another reference to use.

[Sagar karan]

Originally Posted by agd

I'm not sure what reference you are using but it looks to me that the line you have marked as unclear contains an error. Since I can't see more than what you have posted I can only speculate based on the fact that the equation you have circled is not dimensionally consistent, among other things. I would look for another reference to use.

https://sbainvent.com/fluid-mechanic...sport-theorem/

The image I have sent here is given in the above link. Can you explain the 2nd equation of the image? I want explanation only on that equation...

[FMDenaro]

Originally Posted by Sagar karan

https://sbainvent.com/fluid-mechanic...sport-theorem/

The image I have sent here is given in the above link. Can you explain the 2nd equation of the image? I want explanation only on that equation...

The product Bcv*B1 makes no sense in my opinion

[Sagar karan]

Originally Posted by FMDenaro

The product Bcv*B1 makes no sense in my opinion

Yeah, I was also thinking that. I think it should be Bcv - B1. Do you think?

[agd]

I would agree with that. However, there are other problems with that writeup as well. The math is sloppy in making the step after that even with the minus sign. If you are really interested in studying the RTT, there are better resources out there. This link (hopefully it works for you) is one that makes use of Leibniz's theorem, but there are others out there that do a better job from a standpoint similar to what you have.


https://www.me.psu.edu/cimbala/me521...em_and_RTT.pdf

[Sagar karan]

Originally Posted by agd

I would agree with that. However, there are other problems with that writeup as well. The math is sloppy in making the step after that even with the minus sign. If you are really interested in studying the RTT, there are better resources out there. This link (hopefully it works for you) is one that makes use of Leibniz's theorem, but there are others out there that do a better job from a standpoint similar to what you have.


https://www.me.psu.edu/cimbala/me521...em_and_RTT.pdf

Thanks! I am reading your link and will discuss soon after getting some idea about it.

[Sagar karan]

Originally Posted by agd

I would agree with that. However, there are other problems with that writeup as well. The math is sloppy in making the step after that even with the minus sign. If you are really interested in studying the RTT, there are better resources out there. This link (hopefully it works for you) is one that makes use of Leibniz's theorem, but there are others out there that do a better job from a standpoint similar to what you have.


https://www.me.psu.edu/cimbala/me521...em_and_RTT.pdf

From your link , I have sent my understanding in image under the heading " Reynolds transport theorem"→ Now consider the special case where V(t) is a material volume – a volume that moves with the fluid. As the fluid moves and
distorts in the flowfield, the material volume moves and distorts with it.

Have I understood the given statement right?

[FMDenaro]

A rigorous demonstration of the RTT is given here
https://link.springer.com/book/10.10...-1-4684-0364-0

[Sagar karan]

Originally Posted by FMDenaro

A rigorous demonstration of the RTT is given here
https://link.springer.com/book/10.10...-1-4684-0364-0

But it is asking for money to open e-book. I don't know whether I can satisfactory understand RTT or not from this book. May you have other link for RTT...