Pneumatic Conveying, Powder Handling, Rotary Airlock Valves & Flour/Cement Mills
Rotary Airlock Feeder Displacement & Solids Loading Formula
Calculate Theoretical Rotor Swept Volume (m³/h), Pocket-Fill-Adjusted Volumetric Feed (m³/h), Powder Mass Feed Rate (kg/h), and Dilute-Phase Solids-to-Air Mass Loading Ratio mu.
Run a rotary airlock rotor too fast or omit pocket venting and blow-by air cuts actual powder feed 30%–50% below swept volume!
Metering silo powder into a positive-pressure dilute-phase pneumatic conveying line uses a multi-vane Rotary Airlock Feeder of Theoretical Swept Displacement `V_rev` (L/rev) turning at `N` (RPM). While Theoretical Displacement is `Q_swept = (V_rev * N * 60) / 1,000` (m³/h), compressed conveying gas trapped in each returning empty rotor pocket expands upward into the hopper throat (`blow-by` + rotor-tip clearance leakage) and blocks fine powder from filling the pocket—reducing delivery by Pocket Fill Efficiency `eta_fill` (`~0.70–0.80` for free-flowing pellets at `<= 22` RPM, plunging below `0.45–0.55` for unvented aerated flour or over-sped rotors!): `dot_m_solids = Q_swept * eta_fill * 1,000 * rho_bulk` (kg/h)! Dividing `dot_m_solids` by Conveying Air Mass Flow `dot_m_air` (kg/h) gives Dimensionless Phase Density / Solids Loading Ratio `mu = dot_m_solids / dot_m_air` (`mu < 15` guarantees non-plugging dilute-phase suspension flow)!
Verify on a Wheat-Flour Pneumatic Blower Airlock—Rotor_Swept_Volume `V_rev` = 14.0 L/rev (B2), Rotor_Speed `N` = 22.0 RPM (B3 -> Swept Displacement = `18.48` m³/h in E2), Vented_Pocket_Fill_Efficiency `eta_fill` = 0.72 (B4 -> Actual Volumetric Feed = `13.31` m³/h in E3), Flour_Bulk_Density `rho_b` = 0.65 kg/L (B5 -> Mass Feed = `8,648.64` kg/h in E4), and Roots_Blower_Air_Mass = 1,200.0 kg/h (B6): Dilute-Phase Solids-to-Air Loading Ratio hits `mu = 7.21` kg solids / kg air (E5)!
| Rotary Airlock Pneumatic KPI (14.0 L/rev @ 22 RPM, eta=0.72, rho=0.65 kg/L) | Formula | Verified Output |
|---|---|---|
| Swept Rotor Displacement (m³/h) | (Rotor_L_rev * RPM * 60) / 1000 | 18.48 m³/h |
| Actual Volumetric Feed (m³/h) | Swept_Displacement_m3_hr * Fill_Eff | 13.31 m³/h (8.87 m³/h @ blow-by 0.48) |
| Powder Mass Feed Rate (kg/h) | Actual_Vol_m3_hr * 1000 * Bulk_kg_L | 8,648.64 kg/h (5,765.76 kg/h @ 0.48) |
| Solids-to-Air Loading Ratio mu | Powder_Mass_kg_hr / Air_Mass_kg_hr | 7.21 (4.80 starved line @ 0.48 fill) |
Rotary Airlock Pocket Fill Efficiency & Pneumatic Phase-Loading Ratio Formula
Validate `Rotor_L_rev > 0`, `RPM` in `(0, 60]`, `Pocket_Fill_Eff` in `(0, 1]`, `Bulk_Density > 0` kg/L, and `Conveying_Air_Mass > 0` kg/h!
=LET(vr_l, B2, nr_m, B3, ef_p, B4, rb_k, B5, ma_h, B6, IF(OR(vr_l <= 0, nr_m <= 0, nr_m > 60, ef_p <= 0, ef_p > 1, rb_k <= 0, ma_h <= 0), "Invalid Airlock Input", LET(qs_m, (vr_l * nr_m * 60) / 1000, ms_h, qs_m * ef_p * 1000 * rb_k, ROUND(ms_h / ma_h, 2))))Unvented High-Differential Blow-By Starvation Check (Set Pocket Fill Efficiency = 0.48)
Clog the body-vent filter so pocket blow-by slashes `eta_fill` B4 from `0.72` down to `0.48`: Actual Volumetric Feed E3 drops to `8.87` m³/h, Flour Delivery E4 falls nearly `2.9` t/h to `5,765.76` kg/h, and Solids Loading Ratio E5 drops from `7.21` to `4.80`—wasting blower power blowing mostly empty air!
=IF(ISTEXT(E5), E5, ROUND((((B2 * B3 * 60) / 1000) * B4) * 1000 * B5, 2))Try the example
Use the original values or change them to test your understanding.