🌊 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.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 24

⚡ Calculs faits 21

💾 Téléchargements 125 📦 Code Fortran 4.5 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🌊 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 $y(x)$

📝 Configuration & Presets

🏞️ Dam M1 Backwater 📉 Drop M2 Drawdown 📐 Trapezoidal S1 Steep ⚡ Sluice Gate M3 Flow

📐 Channel Cross-Section Geometry

Channel Geometry Type:

Bottom Width b [m]:

Side Slope z (H:1V):

💧 Flow & Bed Slope Parameters

Discharge Flow Rate Q [m³/s]:

Bed Slope S₀ [m/m]:

Manning Roughness n:

Control Boundary Water Depth y₀ [m]: Known water level at weir, dam, gate or drop

Gradually Varied Flow Dynamic Equation:
• Governing ODE: dy / dx = (S₀ − S_f) / (1 − Fr²)
• Friction Slope: S_f = n² · V² / R_h^4/3
• Specific Energy: E = y + V² / (2 g) [meters]
• Standard Step Reach Distance: Δx = (E₂ − E₁) / (S₀ − S̄_f).

📊 Hydraulics Results

📊 Output Summary
💾 Fortran Source

Water Surface Profile Classification

M1 (BACKWATER)

Normal Depth y_n: 2.54 m | Critical Depth y_c: 1.25 m

MILD (M-Slope)

Normal Depth (y_n) 2.54 m Uniform equilibrium flow

Critical Depth (y_c) 1.25 m Fr = 1.0 threshold

Boundary Froude Number (Fr₀) 0.15 Subcritical Flow

Control Section Velocity 0.97 m/s At y = 4.5 m

📈 Water Surface Elevation y(x) (m) vs Reach Distance x (m)

📉 Specific Energy Diagram E(y) (m) vs Water Depth y (m)

=================================================================
 THERMOFLUIDCALC — GRADUALLY VARIED FLOW (GVF) REPORT
=================================================================
Case Title                 : River Dam Impoundment (M1 Backwater Curve)
Channel Dimensions         : Bottom Width b = 8.00 m, Side Slope z = 0.00, Slope S0 = 0.00080, n = 0.022
Discharge & Control Depth  : Q = 35.00 m3/s, Boundary Depth y0 = 4.50 m
-----------------------------------------------------------------
NORMAL DEPTH (yn)          : 2.538 meters (Uniform Flow Level)
CRITICAL DEPTH (yc)        : 1.250 meters (Fr = 1.0 Minimum Energy)
SLOPE CLASSIFICATION       : MILD (M-Slope)
WATER SURFACE PROFILE      : M1 (BACKWATER)
Boundary Flow Velocity     : 0.972 m/s
Boundary Froude Number     : 0.146 (Subcritical)
=================================================================

📘 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.

ThermoFluidCalc Engineering Report