Birgean Work Mixing Energy Calculator
DiscreteidealBirgeanpotentialenergychangehomogeneousmixingusingactuallayerdepthcenters/volumes/massdensity,not turbulent energy efficiency or normalized lake stability. Actual independent model/unit/frame/epoch/calibration and applicable measurement established;not precise ephemeris,forecast,geodesy operation,identity or safety approval.
Description
Ideal mixing work measures the potential-energy change from homogenizing discrete lake layers.
Ideal mixing work measures the potential-energy change from homogenizing discrete lake layers.1
Layer depths, nonoverlapping volumes and mass densities must share the same geometric representation.
When to use Birgean Work Mixing Energy Calculator
Use this tool to apply the stated birgean work mixing energy calculator operation with an explicit input and unit basis.
How to use Birgean Work Mixing Energy Calculator and how it works
- Establish the measurement basis and units described above.
- Enter actualDepthCentersBelowSurfaceMeters, actualNonoverlappingLayerVolumesM3, actualDensityKgPerM3, callerGravity and run the tool.
- Read result.requiredIdealMixingWorkJ using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualDepthCentersBelowSurfaceMeters | Depth centers below surface meters, on the basis specified in the algorithm. | array of number | required; dense; align related rows as specified; further conditions in the algorithm |
| actualNonoverlappingLayerVolumesM3 | Nonoverlapping layer volumes m3, on the basis specified in the algorithm. | array of number | required; dense; align related rows as specified; further conditions in the algorithm |
| actualDensityKgPerM3 | Density kg per m3, on the basis specified in the algorithm. | array of number | required; dense; align related rows as specified; further conditions in the algorithm |
| callerGravity | Gravity, on the basis specified in the algorithm. | number | required; finite; strictly positive; further conditions in the algorithm |
Require aligned nonempty layers, nonnegative depth centers and positive volumes, densities and gravity. Compute volume-weighted mean density and the depth-weighted density anomaly work; reject work below −1e−10 and clamp smaller negative roundoff to zero.
work J = g Σ(ρᵢ − ρmean) Vᵢ depthᵢ Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.requiredIdealMixingWorkJ | Discrete ideal mixing work in joules, with tiny negative roundoff clamped to zero. | number |
{
"input": {
"actualDepthCentersBelowSurfaceMeters": [
0.5,
1.5
],
"actualNonoverlappingLayerVolumesM3": [
1,
1
],
"actualDensityKgPerM3": [
1,
2
],
"callerGravity": 1
},
"output": {
"result": {
"requiredIdealMixingWorkJ": 0.5
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A successful false boolean, negative signed difference, empty slice or unresolved tie is distinct from an input error. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Volume From Bathymetric Contours Calculator. Bathymetric contours pair depth with the area enclosed at each level.
For a related operation, use Area At Stage Hypsograph Calculator. A hypsograph relates lake surface area to water level under a defined survey datum.
References
-
Birgean Work Mixing Energy Calculator — tool.io
Similar or alternative tools
- Volume From Bathymetric Contours Calculator
Bathymetric contours pair depth with the area enclosed at each level.
- Area At Stage Hypsograph Calculator
A hypsograph relates lake surface area to water level under a defined survey datum.