{"openapi":"3.1.0","info":{"title":"Weber Number API","version":"1.0.0","description":"Surface-tension dimensionless numbers for droplets, sprays, atomization and two-phase flow as an API, computed locally and deterministically. The weber endpoint computes the Weber number We = ρ·v²·L/σ — the ratio of inertia to surface tension — and classifies the secondary-droplet-breakup regime (no breakup below We≈12, then bag, multimode, sheet-thinning and catastrophic breakup), the key number for atomization and spray formation. The capillary endpoint gives the Capillary number Ca = μ·v/σ, the ratio of viscous to surface-tension forces used in coating and microfluidics. The bond endpoint computes the Bond (Eötvös) number Bo = Δρ·g·L²/σ, gravity versus surface tension, which governs whether a drop stays spherical or is flattened by gravity. The ohnesorge endpoint gives the Ohnesorge number Oh = μ/√(ρ·σ·L) = √We/Re, viscosity versus inertia and surface tension, plus the inkjet printability number Z = 1/Oh whose sweet spot is roughly 1 < Z < 14. All quantities are SI: density kg/m³, velocity m/s, length m, surface tension N/m, viscosity Pa·s (water σ ≈ 0.0728 N/m at 20 °C). Everything is computed locally and deterministically, so it is instant and private. Ideal for microfluidics, inkjet, spray, atomization, coating, lab-on-a-chip and fluid-physics-education app developers, droplet-regime and printability tools, and research software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 4 endpoints. These are the dimensionless ratios; for capillary rise (Jurin) and Young-Laplace pressure use a capillary/surface-tension API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/weber-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/bond":{"get":{"operationId":"get_v1_bond","tags":["Dimensionless"],"summary":"Bond / Eötvös number","description":"","parameters":[{"name":"density","in":"query","required":true,"description":"Density difference Δρ (kg/m³)","schema":{"type":"string"},"example":"1000"},{"name":"length","in":"query","required":true,"description":"Characteristic length L (m)","schema":{"type":"string"},"example":"0.002"},{"name":"surface_tension","in":"query","required":true,"description":"Surface tension σ (N/m)","schema":{"type":"string"},"example":"0.0728"},{"name":"gravity","in":"query","required":false,"description":"Gravity (m/s²)","schema":{"type":"string"}}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Bo = Eo = Δρ·g·L²/σ — ratio of gravity to surface tension. 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The capillary length is √(σ/(Δρ·g)).","inputs":{"length":0.002,"density":1000,"gravity":9.80665,"surface_tension":0.0728},"bond_number":0.53882692,"eotvos_number":0.53882692},"meta":{"timestamp":"2026-06-05T19:50:27.849Z","request_id":"42690dfc-4f41-4c2d-8e68-e874839faf29"},"status":"ok","message":"Bond/Eotvos 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/capillary":{"get":{"operationId":"get_v1_capillary","tags":["Dimensionless"],"summary":"Capillary number","description":"","parameters":[{"name":"viscosity","in":"query","required":true,"description":"Dynamic viscosity μ (Pa·s)","schema":{"type":"string"},"example":"0.001"},{"name":"velocity","in":"query","required":true,"description":"Velocity v (m/s)","schema":{"type":"string"},"example":"0.01"},{"name":"surface_tension","in":"query","required":true,"description":"Surface tension σ (N/m)","schema":{"type":"string"},"example":"0.0728"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Ca = μ·v/σ — ratio of viscous to surface-tension forces. Low Ca (≪1): surface tension dominates and interfaces stay rounded; high Ca: viscous dragging deforms them.","inputs":{"velocity":0.01,"viscosity":0.001,"surface_tension":0.0728},"capillary_number":0.0001373626},"meta":{"timestamp":"2026-06-05T19:50:27.942Z","request_id":"3d3372a7-cd50-4e1c-b4fd-409feb4d285e"},"status":"ok","message":"Capillary 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/ohnesorge":{"get":{"operationId":"get_v1_ohnesorge","tags":["Dimensionless"],"summary":"Ohnesorge number & inkjet Z","description":"","parameters":[{"name":"viscosity","in":"query","required":true,"description":"Dynamic viscosity μ (Pa·s)","schema":{"type":"string"},"example":"0.001"},{"name":"density","in":"query","required":true,"description":"Density ρ (kg/m³)","schema":{"type":"string"},"example":"1000"},{"name":"surface_tension","in":"query","required":true,"description":"Surface tension σ (N/m)","schema":{"type":"string"},"example":"0.0728"},{"name":"length","in":"query","required":true,"description":"Characteristic length L (m)","schema":{"type":"string"},"example":"0.001"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Oh = μ/√(ρ·σ·L) = √We/Re — viscous forces vs inertia and surface tension. 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