#fluid-dynamics

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.

api.oanor.com/capillary-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

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