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API · /capillary-api

Capillary & Surface Tension API

healthy 3,409 Subscribers

Surface-tension and small-scale fluid-physics maths as an API, computed locally and deterministically. The capillary-rise endpoint applies Jurin's law, h = 2γ·cosθ / (ρ·g·r), to give the height a liquid climbs (or, for a contact angle above 90° like mercury, is depressed) in a narrow tube from its surface tension, the tube radius, the liquid density and the contact angle — and can solve the surface tension back from a measured rise. The laplace-pressure endpoint computes the Young-Laplace excess pressure across a curved interface: a liquid droplet ΔP = 2γ/r, a soap bubble ΔP = 4γ/r (two surfaces) and a cylindrical jet ΔP = γ/r. The poiseuille endpoint applies the Hagen-Poiseuille law, Q = π·r⁴·ΔP / (8·μ·L), for laminar flow in a pipe, returning the volumetric flow rate, the average velocity and the peak centreline velocity (twice the average) from the radius, the pressure drop, the fluid viscosity and the length. Surface tension is in N/m, lengths in m, density in kg/m³, viscosity in Pa·s and pressures in Pa; water is γ ≈ 0.0728 N/m at 20 °C. Everything is computed locally and deterministically, so it is instant and private. Ideal for microfluidics, fluid-engineering, lab-on-a-chip, inkjet and coating app developers, capillary-action and wicking tools, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is surface tension and capillarity; for incompressible Bernoulli flow use a Bernoulli API and for pipe friction a Darcy API.

#capillary #surface-tension #microfluidics #poiseuille #fluid-dynamics #developer-tools
api.oanor.com/capillary-api
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Machine-readable spec so AI agents can integrate this API.

/api/capillary-api/openapi.json
/api/capillary-api/llms.txt

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API health

healthy
Uptime
100.00%
Server probes · 24h
Avg latency
90 ms
Server probes · 24h
Subscribers
3,409
active
Total calls
24
last 7 days
status Full status page → · 20 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

Free

Free

  • 2,500 calls / month
  • 2 requests / second
  • Hard cap (429 above quota, no overage)
  • 2,500 calls/month
  • 2 req/sec
  • Capillary rise + Laplace + Poiseuille
  • No credit card
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Starter

€9.00 /month

  • 50,000 calls / month
  • 6 requests / second
  • Hard cap (429 above quota, no overage)
  • 50,000 calls/month
  • 6 req/sec
  • Surface tension, droplets, bubbles, laminar flow
  • Email support
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Pro

€25.00 /month

  • 350,000 calls / month
  • 15 requests / second
  • Hard cap (429 above quota, no overage)
  • 350,000 calls/month
  • 15 req/sec
  • Microfluidics & lab-on-a-chip pipelines
  • Priority support
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Mega

€69.00 /month

  • 2,000,000 calls / month
  • 40 requests / second
  • Hard cap (429 above quota, no overage)
  • 2,000,000 calls/month
  • 40 req/sec
  • Platform scale
  • Dedicated SLA
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Related APIs

Other APIs with overlapping tags.

Weber Number API

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.

api.oanor.com/weber-api

Bernoulli Flow API

Bernoulli and incompressible-flow maths as an API, computed locally and deterministically. The bernoulli endpoint applies Bernoulli's principle, P + ½ρv² + ρgh = constant along a streamline, taking the pressure, velocity and height at one point and solving the unknown pressure or velocity at a second point, and reporting the total head pressure. The dynamic-pressure endpoint computes the dynamic pressure q = ½ρv² from a velocity, or — the pitot-tube relation — the airspeed v = √(2q/ρ) from a measured dynamic pressure, plus the stagnation (total) pressure when a static pressure is supplied. The venturi endpoint computes the flow rate and inlet and throat velocities of a venturi or contraction from the inlet and throat areas and the pressure drop, Q = Cd·A₂·√(2ΔP/(ρ(1−(A₂/A₁)²))), combining continuity with Bernoulli, with an optional discharge coefficient. Density is taken from a value or a named fluid (air, water, seawater, oil). Everything is computed locally and deterministically, so it is instant and private. Ideal for aerospace, HVAC, plumbing, process and hydraulics app developers, airspeed and flow-meter tools, and fluid-mechanics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Bernoulli/streamline flow; for pipe friction head loss use a Darcy API and for orifice metering an orifice API.

api.oanor.com/bernoulli-api

Drag & Terminal Velocity API

Aerodynamic drag and terminal-velocity maths as an API, computed locally and deterministically. The drag endpoint computes the drag force on a body moving through a fluid, F_d = ½·ρ·Cd·A·v² — half the fluid density times the drag coefficient, the reference area and the velocity squared — together with the dynamic pressure ½·ρ·v², from a fluid (air, water, seawater, oil and more, or a custom density), a drag coefficient (given directly or from a built-in shape table) the area and the speed. The terminal endpoint computes the terminal velocity of a falling object, v_t = √(2·m·g/(ρ·Cd·A)) — the steady speed at which drag balances gravity — from the mass and area, or for a sphere from its diameter and material density, in metres per second, km/h and mph (a belly-down skydiver reaches about 55 m/s, 200 km/h). The shapes endpoint lists typical drag coefficients for spheres, cubes, cylinders, flat plates, streamlined bodies, skydivers, cars, parachutes and more. Everything is computed locally and deterministically, so it is instant and private. Ideal for aerodynamics and ballistics tools, skydiving, model-rocketry and motorsport apps, sphere-settling and sedimentation calculators, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is drag and terminal velocity; for vacuum projectile and SUVAT kinematics use a physics API and for pipe friction pressure drop use a Darcy-Weisbach API.

api.oanor.com/drag-api

Tennis Score API

Tennis scoring maths as an API, computed locally and deterministically — the game, set and match logic a scoring app, umpire tool or tennis league runs on. The game endpoint plays a game from a sequence of who won each point and returns the proper tennis score: points run 0, 15, 30, 40 and then game, but at 40-40 it is Deuce and a player must lead by two — Advantage, then game — so a,a,a,a is 40-0 and a win, while three-all is Deuce; a tiebreak flag scores to seven by two instead (and keeps going at 7-7). The set endpoint reads a set from the games each player has won: a set is taken at six games with a two-game lead, 6-6 triggers a tiebreak that ends it 7-6, and 7-5 wins if a player pulls ahead first. The match endpoint settles the match from the sets won — best-of-three is decided by two sets, best-of-five by three — and tells you the winner the moment it is reached. Everything is computed locally and deterministically, so it is instant and private. Ideal for tennis, racket-sport, scoring, umpiring and league app developers, scoreboard and live-scoring tools, and club software. Pure local computation — no key, no third-party service, instant. Scoring logic, not analytics. Live, nothing stored. 3 compute endpoints.

api.oanor.com/tennis-api

Frequently asked questions

Quick answers about pricing, quotas, and integration.

How do I get an API key for Capillary & Surface Tension API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Capillary & Surface Tension API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Capillary & Surface Tension API?
Free tier allows 1 request per second. Paid plans scale up to 50 requests per second on the Mega tier. Hard limits return HTTP 429 above the quota — no surprise overage charges.
How much does Capillary & Surface Tension API cost?
Capillary & Surface Tension API has a free tier with 100 calls / month. Paid plans start at €9.00 / month with higher quotas and faster rate limits.
Can I cancel my subscription anytime?
Yes. Plans are billed monthly and you can cancel anytime from your billing dashboard. No long-term contracts and no cancellation fee.
Is Capillary & Surface Tension API GDPR-compliant?
All requests to Capillary & Surface Tension API go through our EU-based gateway. Your upstream API key never leaves our server and no personal data is shared with the upstream provider beyond the request you send.

Pick an endpoint from the list on the left to see its details and try it.

Code snippets

Sign up to get an API key, then call any path under your slug.

curl https://api.oanor.com/capillary-api/SOME_PATH \
  -H "x-oanor-key: oanor_test_..."
const res = await fetch("https://api.oanor.com/capillary-api/SOME_PATH", {
  headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();
$ch = curl_init("https://api.oanor.com/capillary-api/SOME_PATH");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
$response = curl_exec($ch);
import requests
r = requests.get(
    "https://api.oanor.com/capillary-api/SOME_PATH",
    headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())

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