Description
Return conical-frustum holdup volume and mass.
Physical process calculations combine supplied geometry, material properties and pressure or gas-state conventions. A density scaling, ideal-gas correction or vessel-volume term can be dimensionally consistent without verifying the actual fluid state, flow regime or equipment suitability.
Return conical-frustum holdup volume and mass.
When to use this tool
Use Hopper Cone Holdup Volume Term when evaluating the stated geometric, fluid-property or gas-state term.
How to use the tool and how it works
- Enter topRadius, outletRadius, height, bulkDensity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read volume, mass. Use the output convention below.
Return conical-frustum holdup volume and mass. Require topRadius >= outletRadius >= 0 and height/bulkDensity >= 0; volume = pi*h*(R²+R*r+r²)/3, mass = volume*density.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| topRadius | Top Radius | Required. Finite number. |
| outletRadius | Outlet Radius | Required. Finite number; minimum 0. |
| height | Height | Required. Finite number; minimum 0. |
| bulkDensity | Bulk Density | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| volume | Conical-frustum volume in cubed input length units; mass uses compatible bulkDensity. | Required. Finite number. |
| mass | Mass | Required. Finite number. |
{
"input": {
"topRadius": 2,
"outletRadius": 1,
"height": 3,
"bulkDensity": 2
},
"output": {
"volume": 21.991148575128552,
"mass": 43.982297150257104
}
}Limitations and assumptions
- Use one length unit and matching bulk mass/volume density; actual fill shape, flow and hopper discharge are not modeled.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use verified geometry and state-specific material data with an appropriate full engineering model for actual flow, storage or equipment design.
References
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