Water Surface Profile Calculator

Analyze depth changes using standard step calculations. Visualize water surface, energy grade, and velocity trends. Export results for reports, reviews, and fast design checks.

Water surface profile inputs

Enter channel geometry, roughness, and flow conditions. Then generate a gradually varied flow profile for a trapezoidal channel section.

Example data table

This sample table uses the default input set and shows reference values across a mild backwater profile.

Station (m) Bed Elevation (m) Depth (m) Water Surface Elevation (m) Velocity (m/s) Froude Number
0 0.000 2.400 2.400 0.872 0.214
100 0.080 2.332 2.412 0.908 0.226
200 0.160 2.265 2.425 0.946 0.238
300 0.240 2.199 2.439 0.984 0.251
500 0.400 2.076 2.476 1.069 0.279

Formula used

Geometric relations

Area: A = y(b + zy)

Top width: T = b + 2zy

Wetted perimeter: P = b + 2y√(1 + z²)

Hydraulic radius: R = A / P

Hydraulic depth: D = A / T

Flow relations

Velocity: V = Q / A

Froude number: Fr = V / √(gD)

Friction slope: Sf = (Qn / (AR2/3))²

Specific energy: E = y + αV² / 2g

Profile equation: dy/dx = (Sf − S₀) / (1 − Fr²)

The calculator estimates normal depth from Sf = S₀, critical depth from Fr = 1, and then integrates the profile station by station using a fourth order Runge Kutta routine.

How to use this calculator

  1. Enter the design discharge, roughness, and trapezoidal channel geometry.
  2. Set the bed slope, reach length, downstream depth, and step size.
  3. Click Calculate Profile to build the water surface profile.
  4. Review normal depth, critical depth, and the profile classification.
  5. Study the Plotly chart for bed, water surface, and energy grade lines.
  6. Download the station table as CSV or PDF for reporting.

Frequently asked questions

1. What does this calculator evaluate?

It computes a gradually varied water surface profile for steady flow in a prismatic trapezoidal channel. It also estimates normal depth, critical depth, velocity, friction slope, and the profile class from the supplied downstream control condition.

2. Which channel shape does it support?

This version is built for trapezoidal open channels with symmetric side slopes. That setup covers many irrigation, drainage, and lined earth channels while keeping the equations stable and transparent.

3. Why is downstream depth required?

A water surface profile needs a control section. The downstream depth provides that boundary condition for subcritical backwater computations, allowing the routine to step upstream and estimate the changing depth across the selected reach.

4. What do normal and critical depth mean?

Normal depth is the depth that would exist under uniform flow for the same discharge, roughness, and bed slope. Critical depth is the transition depth where specific energy is minimum and the Froude number equals one.

5. How should I choose the step size?

Use a smaller step where depth changes quickly or near control structures. Larger steps run faster but can smooth important changes. When results shift noticeably with step size, reduce the interval and compare again.

6. Can I use this for supercritical profiles?

It can indicate steep slope conditions and classify zones, but the workflow is mainly arranged around a downstream control depth. For strongly supercritical cases, confirm results with a method tailored to upstream controls and rapidly varied transitions.

7. Does this include hydraulic jumps or structures?

No. The routine assumes gradually varied flow in a prismatic reach without explicit structures, contractions, expansions, or jump modeling. Use a more detailed hydraulic model when abrupt changes or control structures dominate the behavior.

8. Are the exported files ready for design reports?

They are useful for working notes, internal checks, and report appendices. Still, final design documentation should include engineering judgment, site calibration, unit checks, and any governing standards required by the project authority.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.