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Trapezoidal Channel Analysis with FlowStudio

This walkthrough shows how to find normal depth in a trapezoidal open channel when you know discharge, geometry, Manning’s n, and bed slope—using FlowStudio’s trapezoidal open-channel worksheet (uniform flow, SI units).

Open FlowStudio → https://flow.syncster.dev

What you are solving

In uniform flow, depth and velocity stay constant along a long prismatic reach. Manning’s equation links discharge to geometry and resistance. For a trapezoid with bottom width b and side slope z (horizontal to vertical, H:V), flow area and wetted perimeter depend on water depth y. If Q, b, z, n, and S are given, there is a unique normal depth y that satisfies Manning for that discharge (within physical limits).

FlowStudio uses the standard relations: area A = y(b + zy), wetted perimeter P = b + 2y√(1 + z²), hydraulic radius R = A/P, then V = (1/n)R2/3S1/2 and Q = VA. It also reports top width, hydraulic depth, and Froude number so you can judge subcritical vs supercritical flow.

Step 1 — Create the worksheet

Sign in if prompted, then create or open a project. Add a new worksheet and choose the type for trapezoidal open channel (Manning, uniform flow). Open the sheet so you see the form, the unknown selector, and the chart areas for section and rating curve.


Step 2 — Choose “Water depth” as the unknown

Select Water depth (discharge known). The form will expect you to enter discharge Q and will compute depth y after you press Calculate. The depth field is not the primary input in this mode.

Step 3 — Enter channel data

Type your SI values (meters, m³/s, dimensionless n and z, slope S as m/m). For a reproducible demo you might use, for example: b = 3 m, z = 2 (2H:1V sides), n = 0.025, S = 0.0004, Q = 8 m³/s—adjust to match your own case.

Use a realistic Manning n for your lining (concrete, earth, vegetation, etc.). Side slope z is the horizontal run per one unit of vertical (0 for a rectangle).

Step 4 — Calculate and read the table

Click Calculate. FlowStudio solves for y by bracketing Manning’s Q(y) against your target discharge and fills the results table: depth, velocity, area, wetted perimeter, hydraulic radius, top width, hydraulic depth, Froude number, and discharge check.


Step 5 — Use the cross section and rating curve

The section graphic shows the trapezoid with the computed water surface. The rating curve plots depth vs discharge for your fixed b, z, n, and S; your (Q, y) point should lie on that curve—useful for sanity checks and for seeing how sensitive depth is to discharge.

Reading Fr and common pitfalls

  • Froude number Fr < 1 → subcritical; Fr > 1 → supercritical (for this hydraulic depth definition).
  • If discharge is too large for the chosen geometry and slope, the solver may not find a depth—reduce Q, steepen S, widen b, or smooth the channel (n).
  • Manning uniform flow assumes a long, straight, steady reach; transitions, bends, and backwater need other methods (e.g. gradually varied flow elsewhere in FlowStudio).

Wrap-up

You’ve walked through normal depth in a trapezoidal channel with known Q, using the same closure as FlowStudio’s worksheet. Repeat with your project’s b, z, n, S, and design discharges, and keep comparing to codes and field data.

Run the sheet live at https://flow.syncster.dev.

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