Advanced Water Surface Profile

Computes gradually varied water surface profiles for prismatic channels using a standard-step style formulation of the GVF equation. Supports up to three channel reaches, rectangular or trapezoidal sections, and up to three discharges. Results are shown as bed & water surface elevations vs station, table of hydraulic parameters, and XLSX / PDF export.

Inputs

Current units: SI – lengths in m, discharges in m³/s, elevations in m. When switching units, please re‑enter inputs.

Channel cross-section

Bottom width Bm

Side slope zH:1 V

Start bed elevation Z₀m

Downstream water surface elevationm

Discharge Q₁m³/s

Discharge Q₂(optional)

Discharge Q₃(optional)

Reaches (length, slope & roughness)

Reach 1 length L₁m

Bed slope S₀₁m/m (positive downstream)

Manning n₁

Reach 2 length L₂(optional)

Bed slope S₀₂m/m

Manning n₂

Reach 3 length L₃(optional)

Bed slope S₀₃m/m

Manning n₃

Step size Δxm along channel

Max computation pointscap to avoid runaway

Summary (for Q₁ at reach 1)

Enter channel, flow and boundary data on the left, then click Compute profiles. This panel will report slope type, normal & critical depth, and regime description for the first discharge.

For subcritical backwater, stage is specified at the downstream end and profiles integrate upstream. For supercritical drawdown, stage is specified at the upstream end and profiles integrate downstream. Channel geometry is assumed prismatic within each reach.

Water surface profiles & table

Water surface & bed elevation vs station

Bed elevation and water surface elevation (WSE) are plotted along the channel. Profiles are drawn for each discharge entered (Q₁–Q₃). Station origin is at the upstream end.

Profile table

Profile	Station x	Bed Z	Depth y	WSE	Velocity V	Fr	Regime
No profile yet.

Theory (brief)

Geometry (rectangular / trapezoidal): area \(A\), wetted perimeter \(P\), top width \(T\), hydraulic radius \(R = A/P\), hydraulic depth \(D = A/T\).
Manning equation \(Q = \frac{1}{n} A R^{2/3} S_f^{1/2}\) ⇒ \(S_f = \left(\dfrac{Q n}{A R^{2/3}}\right)^2\).
Froude number \(Fr = \dfrac{V}{\sqrt{g D}}\) with velocity \(V = Q/A\).
GVF differential equation (direct step): \(\dfrac{dy}{dx} = \dfrac{S_0 - S_f}{1 - Fr^2}\), integrated numerically along the channel.
Normal depth \(y_n\): root of Manning’s equation with bed slope \(S_0\).
Critical depth \(y_c\): depth where \(Fr = 1\) (\(Q^2 T / (g A^3) = 1\)).
Profile classification: slope type (mild / steep / horizontal / adverse / critical) from comparison of \(y_n\) & \(y_c\); regime M1/M2/M3 or S1/S2/S3 by comparing local \(y\) with \(y_n\) and \(y_c\).
Warning: Tool assumes steady, 1‑D, gradually varied flow in prismatic reaches. For complex structures (gates, weirs, spillways), use detailed numerical models (e.g. HEC‑RAS).