{"openapi":"3.1.0","info":{"title":"Reynolds Number API","version":"1.0.0","description":"Dimensionless flow-number maths for fluid-mechanics similitude as an API, computed locally and deterministically. The reynolds endpoint computes the Reynolds number, Re = v·L/ν = ρvL/μ — the ratio of inertial to viscous forces — from the velocity, a characteristic length (pipe diameter) and either the kinematic viscosity or the density and dynamic viscosity, and classifies the flow as laminar (< 2300), transitional (2300–4000) or turbulent (> 4000). The froude endpoint computes the Froude number, Fr = v/√(g·L) — the ratio of inertia to gravity used for open-channel and ship flows — together with the critical velocity, and tells you whether the flow is subcritical (tranquil), critical or supercritical (shooting). The mach endpoint computes the Mach number, M = v/c, with the sound speed taken directly or worked out from the air temperature, c = √(γRT), and classifies the speed as subsonic, transonic, supersonic or hypersonic. Everything is computed locally and deterministically, so it is instant and private. Ideal for fluid-mechanics, aerodynamics and hydraulics tools, model-scaling and wind-tunnel similitude, pipe-flow and open-channel analysis, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is dimensionless-number similitude; for pipe friction pressure drop use a Darcy-Weisbach API and for open-channel uniform flow use a Manning API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/reynolds-api","description":"oanor gateway"}],"tags":[{"name":"Dimensionless"},{"name":"Meta"}],"components":{"securitySchemes":{"oanorKey":{"type":"apiKey","in":"header","name":"x-oanor-key","description":"Get your key at https://www.oanor.com/developer/keys"}}},"security":[{"oanorKey":[]}],"paths":{"/v1/froude":{"get":{"operationId":"get_v1_froude","tags":["Dimensionless"],"summary":"Froude number","description":"","parameters":[{"name":"velocity","in":"query","required":true,"description":"Flow velocity v (m/s)","schema":{"type":"string"},"example":"3"},{"name":"length","in":"query","required":true,"description":"Hydraulic depth L (m)","schema":{"type":"string"},"example":"0.5"},{"name":"gravity","in":"query","required":false,"description":"Gravity g (m/s², default 9.81)","schema":{"type":"string"},"example":"9.81"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Fr = v/√(g·L). Subcritical < 1 (tranquil), critical = 1, supercritical > 1 (rapid/shooting flow).","inputs":{"length":0.5,"gravity":9.81,"velocity":3},"flow_regime":"supercritical","froude_number":1.354571,"critical_velocity_m_s":2.214723},"meta":{"timestamp":"2026-06-04T18:38:24.539Z","request_id":"ce88c9df-abd0-4960-bdd3-27284e990693"},"status":"ok","message":"Froude number","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/mach":{"get":{"operationId":"get_v1_mach","tags":["Dimensionless"],"summary":"Mach number","description":"","parameters":[{"name":"velocity","in":"query","required":true,"description":"Velocity v (m/s)","schema":{"type":"string"},"example":"340"},{"name":"sound_speed","in":"query","required":false,"description":"Sound speed c (m/s)","schema":{"type":"string"},"example":"343"},{"name":"air_temperature","in":"query","required":false,"description":"Or air temperature (K) for c=√(γRT)","schema":{"type":"string"}},{"name":"gamma","in":"query","required":false,"description":"Heat-capacity ratio γ (default 1.4)","schema":{"type":"string"},"example":"1.4"},{"name":"gas_constant","in":"query","required":false,"description":"Gas constant R (J/kg·K, default 287)","schema":{"type":"string"},"example":"287"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"M = v/c. Sound speed c = √(γRT) for an ideal gas (air: γ=1.4, R=287). Subsonic < 0.8, transonic 0.8–1.2, supersonic 1.2–5, hypersonic > 5.","inputs":{"velocity":340,"sound_speed":343},"flow_regime":"transonic","mach_number":0.991254},"meta":{"timestamp":"2026-06-04T18:38:24.627Z","request_id":"ae1cfe46-5ef2-4043-b9ee-a867ba7cb1cd"},"status":"ok","message":"Mach number","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/reynolds":{"get":{"operationId":"get_v1_reynolds","tags":["Dimensionless"],"summary":"Reynolds number","description":"","parameters":[{"name":"velocity","in":"query","required":true,"description":"Flow velocity v (m/s)","schema":{"type":"string"},"example":"2"},{"name":"length","in":"query","required":true,"description":"Characteristic length / diameter L (m)","schema":{"type":"string"},"example":"0.05"},{"name":"kinematic_viscosity","in":"query","required":false,"description":"Kinematic viscosity ν (m²/s)","schema":{"type":"string"},"example":"0.000001004"},{"name":"density","in":"query","required":false,"description":"Or density ρ (kg/m³)","schema":{"type":"string"}},{"name":"dynamic_viscosity","in":"query","required":false,"description":"with dynamic viscosity μ (Pa·s)","schema":{"type":"string"}}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Re = v·L/ν. Pipe-flow thresholds: laminar < 2300, transitional 2300–4000, turbulent > 4000.","inputs":{"length":0.05,"velocity":2,"kinematic_viscosity":1.004e-6},"flow_regime":"turbulent","reynolds_number":99601.5936},"meta":{"timestamp":"2026-06-04T18:38:24.737Z","request_id":"e740309f-071e-4e38-a826-a11479cf9ac9"},"status":"ok","message":"Reynolds number","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/meta":{"get":{"operationId":"get_v1_meta","tags":["Meta"],"summary":"Spec","description":"","parameters":[],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"notes":"Velocity in m/s, length in m, viscosity in m²/s (kinematic) or Pa·s (dynamic), temperature in K. Water at 20 °C: ν ≈ 1.004e-6 m²/s. Air at 15 °C: c ≈ 340 m/s.","service":"reynolds-api","formulae":{"mach":"M = v/c,  c = √(γRT)","froude":"Fr = v/√(g·L)","reynolds":"Re = v·L/ν = ρvL/μ"},"endpoints":{"GET /v1/mach":"Mach number M = v/c (sound speed from input or air temperature) and the speed regime.","GET /v1/meta":"This document.","GET /v1/froude":"Froude number Fr = v/√(g·L) and the sub/critical/supercritical regime.","GET /v1/reynolds":"Reynolds number Re = v·L/ν and the laminar/transitional/turbulent regime."},"description":"Dimensionless flow-number calculator: Reynolds (regime), Froude (open-channel) and Mach (compressibility) numbers for fluid-mechanics similitude."},"meta":{"timestamp":"2026-06-04T18:38:24.830Z","request_id":"96bce529-a0a7-4164-8e45-9355d7fd7b89"},"status":"ok","message":"Meta","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}}},"x-oanor-pricing":[{"slug":"free","name":"Free","price_cents_month":0,"monthly_call_quota":2000,"rps_limit":2,"hard_limit":true},{"slug":"starter","name":"Starter","price_cents_month":800,"monthly_call_quota":30000,"rps_limit":5,"hard_limit":true},{"slug":"pro","name":"Pro","price_cents_month":2200,"monthly_call_quota":150000,"rps_limit":15,"hard_limit":true},{"slug":"mega","name":"Mega","price_cents_month":6900,"monthly_call_quota":767000,"rps_limit":40,"hard_limit":true}],"x-oanor-marketplace-url":"https://www.oanor.com/api/reynolds-api"}