Symbols in Bulk Solids Technology
Overview of symbols for calculations and measurements. Deviations from the notation according to DIN EN 1991-4 are marked accordingly.
Silo Calculation Symbols
| Symbol | DIN EN 1991-4 | Unit | Description |
|---|---|---|---|
| a | a | m | Distance from transition to outlet (hopper) |
| b | b | m | Width of outlet opening (rectangular cross-section) |
| dc | dc | m | Diameter of circular outlet opening |
| h | h | m | Height of vertical section |
| hb | hb | m | Height of hopper |
| hc | hc | m | Equivalent surface height |
| hh | hh | m | Hopper height |
| ho | ho | m | Characteristic height, reference height |
| z | z | m | Vertical coordinate |
| α | α | ° | Hopper half angle |
| β | β | ° | Wall slope angle |
| A | A | m² | Cross-sectional area |
| U | U | m | Perimeter of cross-section |
| K | K | - | Horizontal load ratio (lateral pressure ratio) |
| Ph | ph | kN/m² | Horizontal pressure |
| Pv | pv | kN/m² | Vertical pressure |
| φw | φw | ° | Wall friction angle |
| μ | μ | - | Wall friction coefficient |
| bmin | bmin | m | Minimum outlet width |
| DRH | — | m | Hydraulic diameter ratio |
Yield Locus Symbols
| Symbol | DIN EN 1991-4 | Unit | Description |
|---|---|---|---|
| σr | — | Pa | Reference Stress |
| σN | σN | Pa | Normal Stress |
| σ1 | σ1 | Pa | Major Principal Stress |
| σ2 | σ2 | Pa | Minor Principal Stress (also σ3) |
| σc | σc | Pa | Unconfined Compressive Strength |
| σt | — | Pa | Tensile Strength |
| τc | c | Pa | Cohesion (≙ c at DIN EN 1991-4) |
| τrm | — | Pa | Pre-Shear Stress |
| τm | — | Pa | Shear Stress |
| ρb0 | — | kg/m³ | Loose Bulk Density |
| ρbr | — | kg/m³ | Bulk Density |
| FL | — | - | Flowability Factor = σ1 / σc |
| FLR | — | - | Relative Flowability Factor = ( σ1 - σ2 ) / σc |
| FLA | — | - | Absolute Flowability Factor = FLR * ρbr |
| φi | Φc | ° | Angle of Internal Friction |
| φe | Φi | ° | Effective Angle of Friction (pre-shear) (≙ Φi at EN1991-4) ⇒ K |
| φs | — | ° | Angle of friction at steady-state flow |
| K0 | λ0 | - | Coefficient of earth pressure at rest (K₀) = σ2 / σ1 = (1 - sin φe) / (1 + sin φe) |
| Km | K | - | Mean Lateral Pressure Ratio = 1.1 * (1 - sin φ<sub>e</sub>) according to EN 1991-4 |
| R | — | - | Correlation Coefficient of Yield Locus |
| τs | — | Pa | Dynamic Shear Stress at normal stress |
| τs,c | — | Pa | Cohesion of Friction at steady-state flow |
| σs,1 | — | Pa | Major Principal Stress at steady-state flow |
| σs,2 | — | Pa | Minor Principal Stress at steady-state flow |
| Rs | — | - | Correlation Coefficient of Friction at steady-state flow |
Wall Friction Symbols
| Symbol | DIN EN 1991-4 | Unit | Description |
|---|---|---|---|
| σw | σw | Pa | Normal stress at the wall |
| τw,s | — | Pa | Shear stress at the wall (static) |
| τw,d | — | Pa | Shear stress at the wall (dynamic) |
| μs | — | - | Wall friction coefficient (static) |
| μd | — | - | Wall friction coefficient (dynamic) |
| φs | — | ° | Wall friction angle (static) |
| φd | — | ° | Wall friction angle (dynamic) |
| τs | — | Pa | Shear strength (static) |
| τd | — | Pa | Shear strength (dynamic) |
Bulk Density Symbols
| Symbol | DIN EN 1991-4 | Unit | Description |
|---|---|---|---|
| ρb | ρb | kg/m³ | Bulk density |
| ρb0 | — | kg/m³ | Bulk density at rest (after consolidation) |
| ρ(σ) | — | kg/m³ | Bulk density as function of consolidation stress |
| ρ(σ)Log | — | kg/m³ | Bulk density (logarithmic function) |
| ρ(σ)Pow | — | kg/m³ | Bulk density (power function) |
| RLog | — | - | Correlation coefficient (logarithmic) |
| RPow | — | - | Correlation coefficient (power) |
| CILog | — | % | Compressibility index (logarithmic) |
| HRLog | — | % | Hausner ratio (logarithmic) |
Angle of Repose Symbols
| Symbol | DIN EN 1991-4 | Unit | Description |
|---|---|---|---|
| ΦAR | — | ° | Angle of repose |
| hpeak | — | mm | Height of peak (cone height) |
| doutside | — | mm | Outside diameter of cone base |
| ΦAR,avg | — | ° | Average angle of repose |
| SDAR | — | ° | Standard deviation of angle of repose |
Referenced Standards
- DIN EN 1991-4 - Eurocode 1: Actions on structures - Part 4: Silos and tanks
- ASTM D6682 - Standard Test Method for Determining the Flow Properties of Powders
- DIN ISO 4324 - Surface active agents - Powders and granules - Determination of the angle of repose