Water Surface Profile (Advanced GVF)

Computes gradually varied flow (GVF) water surface profiles along a prismatic channel (rectangular or trapezoidal), with the option for two discharges and an internal structure/transition (second reach slope / roughness and optional bed drop).

Inputs

Units

Current units: Q in m³/s, B & elevations in m.

Design discharge Q₁ m³/s

Check discharge Q₂ m³/s (optional)

Channel geometry

Bottom width B m

Side slope z H:1 (both sides)

Manning n₁

Bed slope S₀₁ m/m, positive in flow direction

Reach length L m

Step size Δx m

Bed level at control Z₀ m (optional)

Boundary condition type

Depth at control y₀ (Profile 1) m

Depth at control y₀₂ (Profile 2) m (optional)

Control location / regime

Internal structure / second reach (optional)

Structure/transition station x_struct m from control (0–L)

Bed drop at structure ΔZ m, positive downward (optional)

Second reach slope S₀₂ m/m (optional, default = S₀₁)

Second reach Manning n₂ (optional, default = n₁)

Summary

Enter discharge(s), geometry, roughness, bed slope(s) and a boundary depth or water level, then click Compute profiles to see water surface elevation for Profile 1 (Q₁) and optional Profile 2 (Q₂), including the effect of an internal structure / second reach if specified.

Station x is measured from the control section in the direction of integration (upstream or downstream depending on choice). Bed level is built from Z₀, S₀₁ and optional S₀₂ and ΔZ at the internal structure.

Water surface profiles & table

Water surface and bed elevation vs station

Bed elevation is based on Z₀ and slopes S₀₁/S₀₂ (with optional drop ΔZ at x_struct). Water surfaces are shown for Profile 1 (Q₁) and Profile 2 (Q₂, if defined). Dashed lines indicate WSE at normal and critical depths for Profile 1.

Profile	Station x	Bed Z	Depth y	WSE	Velocity V	Fr	Regime
No profiles yet. Enter data and click “Compute profiles”.

Theory (brief)

Geometry: Rectangular: A = B · y, P = B + 2y, T = B. Trapezoidal (symmetric): A = y (B + 2 z y), P = B + 2 y √(1 + z²), T = B + 2 z y.
Hydraulic radius: R = A / P.
Manning’s equation (uniform flow): Q = (1/n) · A · R^(2/3) · √S₀.
Friction slope (for GVF): S_f = n² Q² / (A² R^(4/3)).
Froude number: Fr = V / √(g · y), where V = Q / A and y is depth (approximate hydraulic depth for prismatic channels).
GVF equation: dy/dx = (S₀ − S_f) / (1 − Fr²), integrated numerically along the channel.
Normal depth yₙ: Depth for which Manning’s equation with slope S₀₁ and discharge Q₁ gives uniform flow (found numerically).
Critical depth y_c: For a given Q, the depth at which Fr = 1. For general prismatic channels this is found numerically (Q² T − g A³ = 0).
Profile classification: Comparing y with yₙ and y_c and slope type (mild or steep) yields M1/M2/M3 or S1/S2/S3, etc., for conceptual description.
Warning: This tool assumes steady, 1D, gradually varied flow in prismatic channels. Use numerical river models and detailed design codes for final design.