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Schiller-Naumann Buoyant Sphere Terminal Drag Force Equilibrium
x402
Schiller-Naumann Buoyant Sphere Terminal Drag Force Equilibrium is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).
Computes the terminal rising or settling velocity of a sphere in a fluid using the Schiller-Naumann drag correlation and complete force balance including buoyancy and gravity.
Price / call$0.003
Success—
StatusUnknown
How this service works
Compute terminal rising or settling velocity with a complete supplied sphere force balance.
Output
The endpoint returns a complete force balance result for the sphere, including the computed terminal velocity (m/s, positive = settling, negative = rising), Reynolds number, Schiller-Naumann drag coefficient, gravitational force, buoyancy force, and net drag force at equilibrium.
Example use cases
Sediment settling rate in river
“I need the terminal settling velocity for a silt particle 0.00002 m in diameter with a density of 2600 kg/m³ sinking in river water with density 1000 kg/m³, viscosity 0.0012 Pa·s, and gravity 9.81 m/s². What does the Schiller-Naumann force balance give me?”
Oil droplet rise in water column
“How fast will an oil droplet of diameter 0.001 m and density 870 kg/m³ rise through seawater (density 1025 kg/m³, dynamic viscosity 0.00108 Pa·s) under gravity of 9.81 m/s²? Run the full buoyant sphere terminal velocity calculation.”
Mars dust particle settling
“Calculate the terminal settling velocity of a Mars dust particle with diameter 0.000005 m and particle density 2000 kg/m³ in the Martian lower atmosphere (fluid density 0.02 kg/m³, dynamic viscosity 0.0000115 Pa·s) under Mars gravity of 3.72 m/s².”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/schiller-naumann-buoyant-sphere-terminal-drag-force-equilibrium?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need a physically rigorous, closed-form terminal velocity calculation for a single sphere under a complete Schiller-Naumann drag + buoyancy force balance, especially for geophysical, industrial, or environmental particle settling problems. Prefer this over simplified Stokes-law endpoints when the particle Reynolds number may exceed the creeping-flow regime (Re > ~0.1). It is ideal for agents that need reliable numerical results without maintaining local fluid mechanics solvers.
Side effects
- Particle and fluid densities are equal (zero net buoyancy), causing division issues or zero velocity
- Gravity value outside the allowed range (0.1–100 m/s²) returns a validation error
- Dynamic viscosity too low or too high (outside 0.000001–1000 Pa·s) triggers schema rejection
- Particle diameter outside allowed range (0.000001–1 m) returns a 422 validation error
- Missing required fields in the settling data object returns a 400 bad request
- Extreme parameter combinations (very large Re) may push outside Schiller-Naumann validity range
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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