A Dynamic Computational Framework For Gradually Varied Flow In Asymmetrical Trapezoidal Channels

Creative Commons License

Çiftçi E.

14th Azerbaijan Congress On Life, Engineering,Mathematical, And Applied Sciences, Baku, Azerbaycan, 26 - 27 Mart 2026, ss.352-361, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Doi Numarası: 10.30546/19023.978-9952-
  • Basıldığı Şehir: Baku
  • Basıldığı Ülke: Azerbaycan
  • Sayfa Sayıları: ss.352-361
  • Maltepe Üniversitesi Adresli: Evet

Özet

Gradually varied flow (GVF) analysis constitutes a fundamental component of open channel hydraulics and plays a critical role in the design and assessment of rivers, irrigation canals, and hydraulic structures. This study presents a comprehensive theoretical and computational framework for analyzing GVF in asymmetrical trapezoidal channels. The governing relationships, including geometric characterization of the cross section, Manning’s resistance formulation, specific energy concept, critical flow condition, slope classification, and the gradually varied flow equation, are systematically established. To operationalize the theoretical model, an interactive application was developed using GeoGebra. The computational framework employs fixed-point iteration for implicit depth calculations and sequence-based discretization for stepwise profile generation. GeoGebra Script functions such as Iteration, Sequence, Join, Segment, Polyline, and Polygon were utilized to implement numerical procedures, generate tabulated outputs, and construct dynamic graphical representations of both cross-sectional geometry and longitudinal water surface profiles. The application automatically classifies channel slope types (mild, steep, critical, horizontal, or adverse) and corresponding flow profile categories based on hydraulic conditions. By integrating rigorous hydraulic theory with an interactive computational environment, the proposed framework provides both a practical analysis tool and an instructional platform. The dynamic coupling of parameter input, numerical integration, and visualization enhances understanding of the relationship between channel geometry, resistance characteristics, and water surface behavior. The study demonstrates that dynamic mathematical software can effectively bridge classical hydraulic theory and modern computational pedagogy in open channel flow analysis.