Fluid Flow Development in a Pipe as a Demonstration of a Sequential Change in Its Rheological Properties

Round 1

Reviewer 1 Report

See the attached file.

Comments for author File: Comments.pdf

Author Response

Dear Sir or Madam,

Thank you very much for your warm and helpful review.

Regarding to your suggestions.

1. The notation in the paper is often confusing, possibly leading to misinterpretation.

All incorrect letters, powers notations, logarithms are fixed 

2. In relation (4) you are introducing V∗ that you call ”dynamic velocity”. Is it the same that other people usually call friction velocity?

Yes, this is the friction velocity - the translation problem. Fixed

3. At the line 76 you speak about ”average flow rate Vav”, but the quantity in question is in fact average velocity and not a flow rate. Please clarify or fix that.

This is a mistake. Fixed

4. I suggest to review again the language quality of the whole paper and certain strange formulations.

Perhaps we do not see something important. One of the authors worked in Norway about 10 years and it is possible his language is not perfect. May we ask you to give us couple examples of such formulations? It would be very helpful to understand what is necessary to fix. 

The most of sentences were written in passive form. Perhaps  it would be more correct to write text in active forms?  

5. In addition of the above listed formal comments, suggest to include some paragraph about intended use or future extensions of the work. Personally I am a bit skeptical about the impact of this paper. Based on the models and methods used in this work, the paper could have been easily written 50-80 years ago and I don’t see any connection to any up-to date research efforts, models or methods. Are you at least considering some comparison of your model predictions with some more detailed models that can be built on direct numerical solution of the underlying systems of PDEs, for possibly more complex rheology or geometry?

The main purpose of the article was to achieve more deep understanding of behavior of flows of non-Newtonian fluids. We used the proposed approach, because it allows to obtain analytical results for simple shear flows. We believe this is a great advantage.

Subsequently, it is planned to compare the model with modern approaches such as DNS, and also perform calculations for more complex geometries.  Could you recommend an article where we can find DNS results for such flows?

 

 

 

Reviewer 2 Report

COMMENTS FOR AUTHORS

Review report for the paper entitled “Fluid Flow Development in a Pipe as a Demonstration of a Sequential Change in its Rheological Properties”.

 

     The author’s main focus in this investigation is about to present the significance of changing the velocity profile and laws of resistance during the flow of a fluid in the pipe. The authors described that with increasing of Reynolds number which causes transition from laminar to turbulent nature. The turbulent nature of the fluid is observed with increasing behavior whenever small addition of polymers are added along with Tom effects. Furthermore, with increase in the Reynolds number for polymer solutions the limiting Virk flow regime is noticed. In the sense of power law generalization, all the mentioned flow regimes as well as all types of rheology’s are described. This generalization can be further extended to the special cas of flow and the rheological relation and can be presented in form of tensor. With more particular sense, the final modeled problem can be expressed in terms of differential equations with arbitrary rheology. This work seems to be a much related work to the major contents of Applied Sciences. Therefore, I recommended this for publication after the following minor corrections.

 

• Please provide the flow configuration with no slip condition.
• How the Vav is calculated on page no. 3 after eq. 8. Please explain [6] in the revised version.
• With higher values of n, what will be the complexities arises in terms of integration evaluation defined through eq. 10?
• Please correct eq. 17.

Author Response

Dear Sir or Madam,

Thank you very much for your positive review.

Regarding to your comments.

1. Please provide the flow configuration with no slip condition.

This is a not simple problem and requires additional research. We shall do this in future research

2. How the Vav is calculated on page no. 3 after eq. 8. Please explain [6] in the revised version.

The average velocity is always calculated through the integral, and there is a mistake in the line 69: the reference to paper [6] is incorrect, the correct reference are papers [9] and [11]. Fixed.

3. With higher values of n, what will be the complexities arises in terms of integration evaluation defined through eq. 10?

For large n power values, integration of the Equation 10 gives Y(n) value equal to 0.5: if n -> ∞, then Y(n) -> 0.5. Added to the manuscript.

4. Please correct eq. 17.

Formula (17), as well as Formula (16), has a typo: on the left side there, instead of the V notation, which is used to denote dimensionless velocity according to Formula 3, u notation should be used, which denotes dimensional velocity according to Formula 1. Fixed.