🏞️ Gradually Varied Flow Profile
Simulate gradually varied open-channel water surface profiles (M1, M2, S1, S2 etc.) using Heun integration of the GVF equation.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
Fluid Mechanics
📊 Solver Telemetry
● ACTIVE
👁️ Views
129
⚡ Solves
104
💾 Downloads
642
📦 Fortran Code
4.5 KB
📅 Released
Jun 2026
⏱️ Latency
< 1 ms
💡
Hardware & Sizing Partner: Need to size a control valve or check ASME flange bolt torque for this line?
🏞️ Channel Profile Schematic
📝 Configuration
Key Equations:
dy/dx = (S₀ − Sf) / (1 − Fr²)
Sf = [Qn/(ARh2/3)]²
Fr² = Q²T/(gA³)
Integration: Heun (improved Euler) method.
dy/dx = (S₀ − Sf) / (1 − Fr²)
Sf = [Qn/(ARh2/3)]²
Fr² = Q²T/(gA³)
Integration: Heun (improved Euler) method.
📊 Results & Water Surface Profile
Configure inputs and click Calculate to view results.
📘 Calculation Methodology
Mathematical Model
The GVF equation dy/dx = (S₀ − Sf)/(1 − Fr²) is integrated using a Heun (improved Euler) scheme. Manning's equation provides friction slope. Critical and normal depths are found by bisection.
Profile Classification
Profiles are classified based on the relationship between starting depth, normal depth, and critical depth: M1/M2/M3 for mild slopes, S1/S2/S3 for steep slopes, and A/H/C for adverse, horizontal, and critical slopes.
Assumptions
- Prismatic channel with constant cross-section.
- Hydrostatic pressure distribution.
- Manning friction — constant n along reach.
- No lateral inflow or wind effects.
- Gradually varied: dy/dx ≪ 1.