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Hydrology & Open-Channel Calc – Critical Depth
x402
Hydrology & Open-Channel Calc – Critical Depth is a paid API for AI agents from hydrology-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-11-02).
Computes the critical flow depth (Froude number = 1) for rectangular, trapezoidal, triangular, or circular open channels given a discharge rate.
Price / call$0.02
Success—
StatusUnknown
How this service works
Critical depth where Froude number is 1 (Q^2/g = A^3/T) for rectangular, trapezoidal, triangular or circular channels.
Output
Returns the critical depth (metres or feet), critical velocity, flow area at critical depth, top width at critical depth, minimum specific energy, and (for rectangular channels) the closed-form solution. Also echoes back input parameters like shape, units, gravity, and bottom width for verification.
Example use cases
Culvert sizing for stormwater design
“I need the critical depth for a circular pipe culvert with a 1.2-metre diameter carrying a peak discharge of 2.5 m³/s in SI units — can you work that out for me?”
Irrigation canal hydraulic analysis
“For a trapezoidal irrigation canal with a bottom width of 5 feet, side slope of 2, and a flow of 150 ft³/s, what's the critical depth in US customary units?”
Rectangular flume critical flow check
“What is the critical depth and minimum specific energy for a rectangular flume that's 2 metres wide with a discharge of 4 m³/s — I need to check whether my design stays subcritical?”
Technical details
Endpoint
GEThttps://hydrology-calc.x402tookit.com/critical-depth?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need the critical depth and associated hydraulic properties (critical velocity, minimum specific energy) for a known channel geometry and discharge. Prefer this over the Froude number endpoint when you want to find the depth at which Fr=1, rather than evaluating Fr at a known depth. Prefer over the normal-depth endpoint when you need energy-based critical conditions rather than uniform-flow depth. Ideal for hydraulic design checks, culvert sizing, and transition analysis.
Side effects
- Missing required parameters (shape or flow) returns an error
- Invalid shape string (not rectangular/trapezoidal/triangular/circular) causes rejection
- Non-physical inputs (negative flow, zero width) may return null or error
- Circular channel requires diameter; trapezoidal/triangular requires sideSlope; rectangular requires bottomWidth — omitting these causes failure
- Iterative solver may not converge for extreme or degenerate channel geometries
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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