{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:00:55Z","timestamp":1760234455857,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T00:00:00Z","timestamp":1621296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In irrigation and drainage channels, vertical drops are generally used to transfer water from a higher elevation to a lower level. Downstream of these structures, measures are taken to prevent the destruction of the channel bed by the flow and reduce its destructive kinetic energy. In this study, the effect of use steps and grid dissipators on hydraulic characteristics regarding flow pattern, relative downstream depth, relative pool depth, and energy dissipation of a vertical drop was investigated by numerical simulation following the symmetry law. Two relative step heights and two grid dissipator cell sizes were used. The hydraulic model describes fully coupled three-dimensional flow with axial symmetry. For the simulation, critical depths ranging from 0.24 to 0.5 were considered. Values of low relative depth obtained from the numerical results are in satisfactory agreement with the laboratory data. The simultaneous use of step and grid dissipators increases the relative energy dissipation compared to a simple vertical drop and a vertical drop equipped with steps. By using the grid dissipators and the steps downstream of the vertical drop, the relative pool depth increases. Changing the pore size of the grid dissipators does not affect the relative depth of the pool. The simultaneous use of steps and grid dissipators reduces the downstream Froude number of the vertical drop from 3.83\u20135.20 to 1.46\u20132.00.<\/jats:p>","DOI":"10.3390\/sym13050895","type":"journal-article","created":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T12:17:16Z","timestamp":1621340236000},"page":"895","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Three-Dimensional Investigation of Hydraulic Properties of Vertical Drop in the Presence of Step and Grid Dissipators"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1012-8342","authenticated-orcid":false,"given":"Rasoul","family":"Daneshfaraz","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 8311155181, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8901-2232","authenticated-orcid":false,"given":"Ehsan","family":"Aminvash","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 8311155181, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8661-6302","authenticated-orcid":false,"given":"Amir","family":"Ghaderi","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan 537138791, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7464-8377","authenticated-orcid":false,"given":"Alban","family":"Kuriqi","sequence":"additional","affiliation":[{"name":"CERIS, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3818-8681","authenticated-orcid":false,"given":"John","family":"Abraham","sequence":"additional","affiliation":[{"name":"School of Engineering, University of St. Thomas, St. Paul, MN 55105, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Daneshfaraz, R., Majedi Asl, M., Bazyar, A., Abraham, J., and Norouzi, R. 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