Discussions and Closures Discussion of “Experimental Study of Central Baffle Flume” by F. Lotfi Kolavani, M. Bijankhan, C. Di Stefano, V. Ferro, and A. Mahdavi Mazdeh Y. Aminpour, Ph.D. Researcher, Dept. of Hydraulic and Hydro-Environmental Engineering, Water Research Institute, Ministry of Energy, Tehran, Iran. Email: younes_aminpour@ut.ac.ir H. Khalili Shayan, Ph.D. Formerly, Ph.D. Student, Dept. of Irrigation and Reclamation Engineering, Univ. of Tehran, P.O. Box 31587-4111, 31587-77871 Karaj, Iran. Email: h_kh_shayan@ut.ac.ir J. Farhoudi Professor, Dept. of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, Univ. of Tehran, P.O. Box 4111, 31587-77871 Karaj, Iran (corresponding author). Email: jfarhoudi@ ut.ac.ir https://doi.org/10.1061/(ASCE)IR.1943-4774.0001370 The discussers appreciate the authors’ efforts and their contribution to the realm of science. They also would like to draw the attention of the authors to the following points. Deducing Stage-Discharge Relationship by Energy Conservation Approach In the original paper, the authors developed Eqs. (7), (11), and (12) to determine the discharge of the central baffle flume (CBF) by means of dimensional analysis and self-similarity. Also, Eq. (17) was developed based on the energy conservation approach. In Eq. (17), E 1 is a function of Q. Thus, the discharge should be de- termined through the trial-and-error method. The original paper highlights the explicit discharge calculation from dimensional analysis as an advantage when compared with the energy conser- vation approach. But a new relationship could be deduced by re- writing the energy conservation equation for the explicit discharge calculation, which is more accurate than the dimensional analysis and self-similarity methods. When the design discharge passes the CBF (Q ¼ Q design ), the critical depth is formed at its throat (h 2 ¼ h c ) without any chok- ings. In this case, by neglecting the energy loss and using the en- ergy balance between upstream and the contracted section, the following equations would be obtained: E 1 ¼ E c ð1Þ E 1 ¼ h þ Q 2 2gB 2 h 2 ð2Þ E c ¼ 3 2 h c ð3Þ h c ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q 2 gðB − bÞ 2 3 s ; Q 2 ¼ gðB − bÞ 2 h 3 c ð4Þ Incorporating the nondimensional parameters (λ ¼ h c =h and η ¼ b=B) in the previous equations, the following third-order equa- tion would be obtained to determine the relative critical depth: λ 3 − pλ þ r ¼ 0 ð5Þ where p ¼ 3=ð1 − ηÞ 2 and r ¼ 2=ð1 − ηÞ 2 . Solving Eq. (5) for λ, the three following roots are obtained: λ 1 ¼ 2 ffiffiffi p 3 r cos ϕ 3 ð6Þ λ 2 ¼ −2 ffiffiffi p 3 r cos  π þ ϕ 3  ð7Þ λ 3 ¼ −2 ffiffiffi p 3 r cos  π − ϕ 3  ð8Þ where ϕ ¼ cos −1 f−r=2 ffiffiffiffiffiffiffiffiffiffiffiffi ffi ð3=pÞ 3 p g. Given that −r=2 × ffiffiffiffiffiffiffiffiffiffiffiffi ffi ð3=pÞ 3 p ¼ ðη − 1Þ and 0 < η < 1, it can be concluded that π=2 < ϕ < π. It can be shown that −2=ð1 − ηÞ < λ 3 < 0. Consequently, λ 3 [Eq. (8)] is always negative. Also, 1=ð1 − ηÞ < λ 1 < ffiffi 3 p =ð1 − ηÞ and λ 1 > 1. Accordingly, from Eq. (6), the critical depth is greater than the upstream depth, which is not acceptable. On the other hand, 0 < λ 2 < 1=ð1 − ηÞ and λ 2 < 1. Consequently, from Eq. (7), h c < h. Accordingly, λ 2 from Eq. (7) is the only correct root to determine the critical depth. Based on this analysis, the design discharge of CBF can be obtained from the following equation: Q design ¼ðB − bÞ × ffiffi g p ×  2B b − B × cos  π 3 þ cos −1 ½ b−B B  3  3=2 × h 3=2 ð9Þ The preceding analysis is based on the formation of critical depth in the contracted section. To assess the flow regime in the contracted section, numerical modeling with different combina- tions of relative flume length (L=B), contraction ratio (r ¼ B c =B), relative upstream depth (h=B c ), and flow rate have been conducted by means of available experimental data sets using FLOW-3D V. 11.1 software, as detailed in in Appendix I of the original paper. Turbulent flow conditions and the re-normalization group (RNG) turbulent model have been used. The water head from the exper- imental data has been set as the upstream boundary condition and outflow has been set as the downstream boundary condition. Fig. 1 is an example of Froude number and water surface profile changing along with the structure from upstream to the contracted section as the output of the numerical model. It can be seen that the critical depth is formed along the contracted section for all se- lected cases. © ASCE 07020006-1 J. Irrig. Drain. Eng. J. Irrig. Drain Eng., 2020, 146(7): 07020006 Downloaded from ascelibrary.org by 54.161.69.107 on 07/24/20. Copyright ASCE. For personal use only; all rights reserved.