# Hydrology & Open-Channel Calc – Critical Depth

> 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.

## Facts

- Endpoint: GET https://hydrology-calc.x402tookit.com/critical-depth?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-02
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/hydrology-open-channel-calc-critical-depth-7a795dd3
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap__v4VwcbDo7LYZr0Gw0sUX

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability hydrology-open-channel-calc-critical-depth-7a795dd3
```

Example prompt: Calculate the critical depth for a trapezoidal channel with a bottom width of 3 metres, side slope of 1.5 (horizontal per vertical), and a discharge of 10 m³/s using SI units.

## When to prefer this

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.

## Known failure modes

- 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

## 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.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "shape",
      "flow"
     ],
     "properties": {
      "flow": {
       "type": "number",
       "description": "Discharge in m3/s (units si) or ft3/s (units us)"
      },
      "shape": {
       "type": "string",
       "description": "rectangular, trapezoidal, triangular or circular"
      },
      "units": {
       "type": "string",
       "description": "si (default) or us"
      },
      "gravity": {
       "type": "number",
       "description": "Gravity in m/s2 or ft/s2 (default 9.81 si, 32.2 us)"
      },
      "diameter": {
       "type": "number",
       "description": "Pipe diameter in metres or feet (circular)"
      },
      "sideSlope": {
       "type": "number",
       "description": "Side slope z, horizontal run per 1 vertical (trapezoidal, triangular)"
      },
      "bottomWidth": {
       "type": "number",
       "description": "Bottom width in metres or feet (rectangular, trapezoidal)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "shape": {
       "type": [
        "null",
        "string"
       ]
      },
      "units": {
       "type": [
        "null",
        "string"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "gravity": {
       "type": [
        "null",
        "number"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "disclaimer": {
       "type": [
        "nul
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/hydrology-open-channel-calc-critical-depth-7a795dd3/health.json
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