Backwater Curve Calculator – Standard Step Method | Water Surface Profile

Backwater Curve Calculator (Standard Step Method)

Compute water surface profile upstream of a control • Trapezoidal / rectangular channels • 2D profile • PDF report • Batch

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📐 1. Backwater Curves – Why They Matter

Backwater curves describe the rise in water surface upstream of a hydraulic control (bridge, weir, culvert). The standard step method solves the energy equation incrementally. This calculator uses Manning's equation for friction slope and computes water surface elevations along the channel. It supports trapezoidal and rectangular cross‑sections.

Energy equation: Z₁ + y₁ + α₁V₁²/2g = Z₂ + y₂ + α₂V₂²/2g + h_f
Friction slope (Manning): S_f = (n²·Q²) / (A²·R^4/3)

🚀 2. Live Backwater Calculator

Channel shapeTrapezoidalRectangular

Bottom width B (m)

Side slope z (H:V) – for trapezoid

Manning's n

Channel slope S₀ (m/m)

Discharge Q (m³/s)

Downstream water level (y₁ at x=0) (m)

Number of steps (Δx = 100 m each)

Batch CSV (B, z, n, S0, Q, y0, steps)

Get PDF Report via Email

CSV Template

📊 3. Water Surface Profile

📈 4. Computation Table & History

Distance (m)	Water depth (m)	Water elev. (m)	Velocity (m/s)

📘 5. How to Use the Calculator

1. Select channel shape, enter bottom width (and side slope for trapezoid).
2. Set Manning's n, channel slope, discharge, and downstream water depth (y₁ at x=0).
3. Number of steps: each step length = 100 m (total length = steps × 100 m).
4. Click "Compute Profile" – the tool solves the energy equation incrementally.
5. The 2D profile and table show water depth / elevation at each step.
6. History stores each calculation (max water depth). Batch CSV processes multiple designs.
7. PDF report includes the profile image and summary table.

❓ Frequently Asked Questions

❓ What is the standard step method?

It divides the channel into reaches and solves the energy equation iteratively to find water surface elevations.

❓ How accurate is this?

Uses average friction slope (Manning) and assumes subcritical flow. For complex models, use HEC‑RAS.

❓ Can I use it for natural rivers?

Approximately, if you approximate cross‑section as trapezoidal. For real projects, detailed surveying required.

🌐 Standards & References

HEC‑RAS User Manual | Chow (1959) – Open Channel Hydraulics | USACE Hydraulic Design

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© ERH Backwater Calculator – Standard step method. Data processed locally.