🌊 Gradually Varied Flow (GVF) Profile Calculator
Compute water surface profiles using the GVF differential equation with Heun integration. Classifies M1–M2–M3, S1–S2–S3 profiles and computes critical/normal depths.
🏞️ 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.