# 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.

## Authentication
All requests require your oanor API key in the `x-oanor-key` header. Get one at https://www.oanor.com/developer/keys.

```bash
curl -H "x-oanor-key: oanor_live_…" "https://api.oanor.com/weber-api/..."
```

## Pricing
- **Free** (Free) — 3,900 calls/Mo, 2 req/s
- **Starter** ($7/Mo) — 37,000 calls/Mo, 6 req/s
- **Pro** ($20/Mo) — 178,000 calls/Mo, 15 req/s
- **Mega** ($62/Mo) — 1,050,000 calls/Mo, 40 req/s

## Endpoints

### Dimensionless

#### `GET /v1/bond` — Bond / Eötvös number

**Parameters:**
- `density` (query, required, string) — Density difference Δρ (kg/m³) Example: `1000`
- `length` (query, required, string) — Characteristic length L (m) Example: `0.002`
- `surface_tension` (query, required, string) — Surface tension σ (N/m) Example: `0.0728`
- `gravity` (query, optional, string) — Gravity (m/s²)

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/weber-api/v1/bond?density=1000&length=0.002&surface_tension=0.0728"
```

**Response:**
```json
{
    "data": {
        "note": "Bo = Eo = Δρ·g·L²/σ — ratio of gravity to surface tension. Bo≪1: surface tension dominates and drops are spherical; Bo≫1: gravity flattens them. 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
}
```

#### `GET /v1/capillary` — Capillary number

**Parameters:**
- `viscosity` (query, required, string) — Dynamic viscosity μ (Pa·s) Example: `0.001`
- `velocity` (query, required, string) — Velocity v (m/s) Example: `0.01`
- `surface_tension` (query, required, string) — Surface tension σ (N/m) Example: `0.0728`

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/weber-api/v1/capillary?viscosity=0.001&velocity=0.01&surface_tension=0.0728"
```

**Response:**
```json
{
    "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
}
```

#### `GET /v1/ohnesorge` — Ohnesorge number & inkjet Z

**Parameters:**
- `viscosity` (query, required, string) — Dynamic viscosity μ (Pa·s) Example: `0.001`
- `density` (query, required, string) — Density ρ (kg/m³) Example: `1000`
- `surface_tension` (query, required, string) — Surface tension σ (N/m) Example: `0.0728`
- `length` (query, required, string) — Characteristic length L (m) Example: `0.001`

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/weber-api/v1/ohnesorge?viscosity=0.001&density=1000&surface_tension=0.0728&length=0.001"
```

**Response:**
```json
{
    "data": {
        "note": "Oh = μ/√(ρ·σ·L) = √We/Re — viscous forces vs inertia and surface tension. In inkjet, the printability number Z = 1/Oh; good drop formation is roughly 1 < Z < 14.",
        "inputs": {
            "length": 0.001,
            "density": 1000,
            "viscosity": 0.001,
            "surface_tension": 0.0728
        },
        "z_number": 269.814751,
        "ohnesorge_number": 0.0037062466
    },
    "meta": {
        "timestamp": "2026-06-05T19:50:28.038Z",
        "request_id": "bd37d101-4b9b-417f-abb4-f028089cd2ac"
    },
    "status": "ok",
    "message": "Ohnesorge number",
    "success": true
}
```

#### `GET /v1/weber` — Weber number & breakup regime

**Parameters:**
- `density` (query, required, string) — Density ρ (kg/m³) Example: `1000`
- `velocity` (query, required, string) — Relative velocity v (m/s) Example: `10`
- `length` (query, required, string) — Characteristic length L (m) Example: `0.001`
- `surface_tension` (query, required, string) — Surface tension σ (N/m) Example: `0.0728`

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/weber-api/v1/weber?density=1000&velocity=10&length=0.001&surface_tension=0.0728"
```

**Response:**
```json
{
    "data": {
        "note": "We = ρ·v²·L/σ — ratio of inertia to surface tension. Drop breakup begins around We≈12; higher We means finer atomization.",
        "inputs": {
            "length": 0.001,
            "density": 1000,
            "velocity": 10,
            "surface_tension": 0.0728
        },
        "weber_number": 1373.62637363,
        "droplet_regime": "catastrophic breakup"
    },
    "meta": {
        "timestamp": "2026-06-05T19:50:28.144Z",
        "request_id": "9134833c-109c-44d8-83d7-c193c52e59c5"
    },
    "status": "ok",
    "message": "Weber number",
    "success": true
}
```

### Meta

#### `GET /v1/meta` — Spec

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/weber-api/v1/meta"
```

**Response:**
```json
{
    "data": {
        "notes": "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. These are the dimensionless ratios; for capillary rise (Jurin) and Young-Laplace pressure use a capillary/surface-tension API.",
        "service": "weber-api",
        "endpoints": {
            "GET /v1/bond": "Bond/Eötvös number Bo = Δρ·g·L²/σ.",
            "GET /v1/meta": "This document.",
            "GET /v1/weber": "Weber number We = ρ·v²·L/σ and droplet-breakup regime.",
            "GET /v1/capillary": "Capillary number Ca = μ·v/σ.",
            "GET /v1/ohnesorge": "Ohnesorge number Oh = μ/√(ρ·σ·L) and inkjet Z = 1/Oh."
        },
        "description": "Surface-tension dimensionless numbers for droplets, sprays and two-phase flow: Weber, Capillary, Bond/Eötvös and Ohnesorge."
    },
    "meta": {
        "timestamp": "2026-06-05T19:50:28.255Z",
        "request_id": "f54f5f72-f268-4045-b5bf-d626e071cd2d"
    },
    "status": "ok",
    "message": "Meta",
    "success": true
}
```


---
Marketplace page: https://www.oanor.com/api/weber-api
OpenAPI spec: https://www.oanor.com/api/weber-api/openapi.json