Review Reports

Round 1

Reviewer 1 Report

The reply has properly addressed the comments from Majid Niazkar. And provided updated approximations to the Colebrook equation for flow friction. The newly introduced approximations have increased accuracy of the estimated flow friction factor.
The reply can be considered for publication in its current form.

Author Response

Thank you very much for your valuable comments. We will resubmit revised version.

Reviewer 2 Report

The reply by the authors brings an added value, as it shows how the optimization procedure improved the precision of flow friction estimators. The relative error was reduced significantly: up to 50%, even though the complexity remains unchanged.  For this reason, the Reply is suitable for publishing and would be of significant interest to the research community in this field of work. As I have also reviewed the discussion of the original paper, my assessment is that this is an appropriate reply.   Some suggestions and necessary corrections are given below:   1. The authors refer to 15 publications, which is practically the border value for a paper in a renowned journal, despite the fact that the type of paper is Reply. I suggest the authors extend the reference list somewhat, as there are several places in the text that call for this. It is left to the authors to decide which references and where in the text.    2. Eq. (4) is missing, or rather one of the existing equations (between Eq. (3) and Eq. (5)) is missing numbering. Similarly, two Sections are numbered as 2. Obviously, Conclusion should be Section 3.

Author Response

Thank you very much for your valuable comments. We have accepted all of them:

1. We extended reference list and we cited more throughly through the manuscript.
2. We corrected typos: order of equations and sections is updated.