๐ Gradually Varied Open Channel Flow (Standard Step)
Model gradually varied open channel flow profiles (M1, M2, M3, S1, S2, S3 backwater curves): critical depth (yc), normal depth (yn), Froude number, and reach distance by Standard Step Method.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Fluid Mechanics
๐ Solver Telemetry
โ ACTIVE
๐๏ธ Views
24
โก Solves
21
๐พ Downloads
226
๐ฆ Fortran Code
4.5 KB
๐
Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ก
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๐ Open Channel Longitudinal Profile & Water Surface Curve
Real-time visual simulation: Bed slope $S_0$, normal depth $y_n$, critical depth $y_c$, and backwater surface $y(x)$๐ Configuration & Presets
Gradually Varied Flow Dynamic Equation:
โข Governing ODE: dy / dx = (Sโ โ Sf) / (1 โ Frยฒ)
โข Friction Slope: Sf = nยฒ ยท Vยฒ / Rh4/3
โข Specific Energy: E = y + Vยฒ / (2 g) [meters]
โข Standard Step Reach Distance: ฮx = (Eโ โ Eโ) / (Sโ โ Sฬf).
โข Governing ODE: dy / dx = (Sโ โ Sf) / (1 โ Frยฒ)
โข Friction Slope: Sf = nยฒ ยท Vยฒ / Rh4/3
โข Specific Energy: E = y + Vยฒ / (2 g) [meters]
โข Standard Step Reach Distance: ฮx = (Eโ โ Eโ) / (Sโ โ Sฬf).
๐ Hydraulics Results
Configure inputs and click Compute to view results.
๐ Calculation Methodology & Open Channel Hydraulics
Backwater Curve Classification
Profiles are categorized by slope (Mild $M$, Steep $S$, Critical $C$) and zone ($1: y > y_n > y_c$, $2: y_n > y > y_c$, $3: y_c > y$).
Standard Step Integration Method
Solves specific energy balance across reach increments $\Delta x$, accounting for boundary friction dissipation and non-uniform velocity distribution.
Key Engineering Assumptions
- Manning equation for reach-averaged friction slope $\bar{S}_f$.
- Prismatic channel geometry with steady one-dimensional flow.
- Applicable to river dam impoundments, canal drops, spillway chutes, and drainage systems.