{"uid":"cap__v4VwcbDo7LYZr0Gw0sUX","slug":"hydrology-open-channel-calc-critical-depth-7a795dd3","name":"Hydrology & Open-Channel Calc – Critical Depth","description":"Critical depth where Froude number is 1 (Q^2/g = A^3/T) for rectangular, trapezoidal, triangular or circular channels.","url":"https://hydrology-calc.x402tookit.com/critical-depth?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"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":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"bottomWidth":{"type":["null","number"]},"criticalDepth":{"type":["null","number"]},"requestedFlow":{"type":["null","number"]},"criticalVelocity":{"type":["null","number"]},"flowAreaAtCritical":{"type":["null","number"]},"topWidthAtCritical":{"type":["null","number"]},"minimumSpecificEnergy":{"type":["null","number"]},"rectangularClosedForm":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Sz5_qovL1O39tgzEqt2HA","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the critical flow depth (Froude number = 1) for rectangular, trapezoidal, triangular, or circular open channels given a discharge rate.","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Culvert sizing for stormwater design","prompt":"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?"},{"title":"Irrigation canal hydraulic analysis","prompt":"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?"},{"title":"Rectangular flume critical flow check","prompt":"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?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-02T18:32:59.958Z","isFirstParty":false,"canonicalSlug":"hydrology-open-channel-calc-critical-depth-7a795dd3"}