Vessel Volume From Rim Diameter
Reconstruct piecewise conical-frustum interior volume from a supplied normalized vessel profile scaled by measured interior rim diameter; no universal rim-only vessel shape assumed.
Description
Rim diameter alone does not determine vessel capacity.
Rim diameter alone does not determine vessel capacity. A supplied dimensionless interior profile provides the shape needed to scale and integrate a reconstructed volume.1
Reconstruct piecewise conical-frustum interior volume from a supplied normalized vessel profile scaled by measured interior rim diameter; no universal rim-only vessel shape assumed.
When to use Vessel Volume From Rim Diameter
Use this tool to reconstruct piecewise conical-frustum interior volume from a supplied normalized vessel profile scaled by measured interior rim diameter; no universal rim-only vessel shape assumed.
Prepare the artifact, site or survey measurements and any independently established calibration or model choices. Keep paired observations aligned and confirm units and coordinate conventions.
How to use Vessel Volume From Rim Diameter and understand its results
- Prepare the artifact, site or survey measurements and any independently established calibration or model choices. Keep paired observations aligned and confirm units and coordinate conventions.
- Enter rimInteriorDiameterCm, profileRelativeHeights, profileRelativeRadii using the field table and calculation rules, then run the tool.
- Read reconstructedInteriorVolumeLiters. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| rimInteriorDiameterCm | Rim interior diameter cm | number | Required |
| profileRelativeHeights | Profile relative heights | list of number | Required |
| profileRelativeRadii | Profile relative radii | list of number | Required |
Enter positive interior rim diameter in cm and aligned nonnegative relative heights and radii. Heights must contain at least two strictly increasing points beginning at zero; final relative radius must be 0.5. Scale every coordinate by rim diameter and sum conical-frustum volumes between adjacent points. Read reconstructed interior liters.
Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.
frustumVolume = πh(r1²+r1r2+r2²)/3; liters = ΣfrustumVolumeCm³/1000 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| reconstructedInteriorVolumeLiters | Reconstructed interior volume liters | number |
{
"input": {
"rimInteriorDiameterCm": 10,
"profileRelativeHeights": [
0,
1,
2
],
"profileRelativeRadii": [
0,
0.5,
0.5
]
},
"output": {
"reconstructedInteriorVolumeLiters": 1.0471975511965976
}
}Limitations and assumptions
The supplied profile determines the result; there is no universal rim-to-volume factor. Linear radius changes between stations and circular cross sections are assumed. Reconstruction and rim-measurement uncertainty are excluded.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Storage Capacity From Vessel Volume: Aggregate interior vessel capacity with explicit usable fill and independently supplied bulk material density; does not infer original contents or nutritional adequacy. For a complementary task, use Orifice Index Vessel: Compute area-equivalent elliptical vessel mouth and per-vessel orifice/body index, not a fixed circular diameter ratio or functional classification.
References
-
Vessel Volume From Rim Diameter — tool.io
Similar or alternative tools
- Storage Capacity From Vessel Volume
Aggregate interior vessel capacity with explicit usable fill and independently supplied bulk material density; does not infer original contents or nutritional adequacy.
- Orifice Index Vessel
Compute area-equivalent elliptical vessel mouth and per-vessel orifice/body index, not a fixed circular diameter ratio or functional classification.