Analyze depth changes using standard step calculations. Visualize water surface, energy grade, and velocity trends. Export results for reports, reviews, and fast design checks.
Enter channel geometry, roughness, and flow conditions. Then generate a gradually varied flow profile for a trapezoidal channel section.
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 |
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.