Industrial Air-Pollution Control & Sub-Micron Scrubbing, Calvert (1970) Venturi Scrubber
Venturi Wet Scrubber Calvert Pressure Drop & Fan Power
Calculate Venturi Throat Gas Velocity (m/s), Liquid-to-Gas Contacting Ratio L/G (L/m³), Calvert Momentum-Transfer Pressure Drop (kPa), and Induced-Draft Fan Shaft Power (kW).
Pinching a variable-throat Venturi scrubber damper from 0.16 to 0.11 m² to trap sub-micron fume boosts L/G + throat velocity—TRIPLING ID-fan power from 137 kW to 426 kW!
**High-Energy Venturi Wet Particulate Scrubbers** capture sticky, hot, or pyrophoric `< 1.0`-um foundry cupola, BOF steel, and kiln fumes by accelerating dirty gas (`Volumetric Flow Q_g` m³/s) through a converging **Throat Cross-Section `A_t` (`m²`)** to **`v_t = Q_g / A_t = 60–120` m/s**, shearing injected Scrubbing Liquor `Q_L` (`L/s` -> **Liquid-to-Gas Ratio `L / G = Q_L / Q_g`** L/m³) into `50`-um target droplets for inertial impaction! **Seymour Calvert (`1970`)** proved that practically all throat static-pressure loss pays to accelerate stationary liquid mass up to `~85%` of gas throat velocity, giving **Calvert Venturi Pressure Drop `Delta_P = 0.00102 * (v_t^2) * (L / G)`** (`kPa`, `~76` cm `H_2O` at `7.47` kPa!) and **Induced-Draft (`ID`) Fan Shaft Power `P_{fan} = (Q_g * Delta_P) / (eta_{fan} / 100)`** (`kW`)!
Verify on a Cupola Furnace Adjustable-Damper Venturi Scrubber—Saturated_Gas_Flow `Q_g` = 12.5 m³/s (`45,000` m³/h, B2), Venturi_Throat_Area `A_t` = 0.16 m² (B3), Scrubbing_Liquor_Rate `Q_L` = 15.0 L/s (B4), and Wet-Wheel_`ID`_Fan_Efficiency `eta_{fan}` = 68.0% (B5): Throat Gas Velocity equals `78.1` m/s (E2), Liquid-to-Gas Ratio `L / G` equals `1.20` L/m³ (E3), Calvert Pressure Drop equals **`7.47` kPa** (`30.0` in. w.g., E4), demanding **`137.3` kW** of ID-fan shaft power (E5)!
| Calvert (1970) Venturi Scrubber KPI (Qg=12.5 m³/s, ID Fan Eff=68%) | Formula | Verified Output |
|---|---|---|
| Throat Gas Velocity vt (m/s) | Gas_Flow_m3_s / Throat_Area_At_m2 | 78.1 m/s (113.6 m/s sub-micron fume trim) |
| Liquid-to-Gas Ratio L/G (L/m³) | Liquor_Flow_L_s / Gas_Flow_m3_s | 1.20 L/m³ (1.76 L/m³ high-wash) |
| Calvert Pressure Drop dP (kPa) | 0.00102 * (Throat_vt_m_s ^ 2) * L_Over_G | 7.47 kPa (23.18 kPa = 93 in. w.g.!) |
| ID Fan Shaft Power (kW) | (Gas_Flow_m3_s * dP_kPa) / (Fan_Eff_Pct / 100) | 137.3 kW (426.1 kW = 3.1x motor load!) |
Seymour Calvert (1970) Droplet-Acceleration Venturi Pressure Drop & Power Formula
Validate `Gas_Flow Q_g` in `[0.2, 500]` m³/s, `Throat_Area A_t` in `[0.005, 10.0]` m² (`with v_t` in `[20, 160]` m/s), `Liquor_Flow Q_L` in `[0.1, 1,500]` L/s (`with L/G` in `[0.3, 5.0]` L/m³), and `Fan_Efficiency` in `[40, 88]`%!
=LET(qg_s, B2, at_m, B3, ql_s, B4, ef_p, B5, vt_s, qg_s / at_m, lg_r, ql_s / qg_s, dp_k, 0.00102 * (vt_s ^ 2) * lg_r, IF(OR(qg_s < 0.2, qg_s > 500, at_m < 0.005, at_m > 10, vt_s < 20, vt_s > 160, ql_s < 0.1, ql_s > 1500, lg_r < 0.3, lg_r > 5, ef_p < 40, ef_p > 88), "Invalid Venturi Input", ROUND((qg_s * dp_k) / (ef_p / 100), 1)))Sub-Micron Zinc-Oxide Opacity Trim (`A_t = 0.11` m², `Q_L = 22` L/s) Motor-Overload Check
Pinch throat damper blades down to `B3 = 0.11` m² (`113.6` m/s in E2) and boost recycle spray to `B4 = 22.0` L/s (`L / G = 1.76` L/m³ in E3) to pass a `0.3`-um opacity stack test: Calvert `Delta_P` E4 surges **`3.1x` to `23.18` kPa** (`93` inches `H_2O`!), driving ID-Fan Shaft Power E5 from `137.3` up to **`426.1` kW**!
=IF(ISTEXT(E5), E5, ROUND(0.00102 * ((B2 / B3) ^ 2) * (B4 / B2), 2))Try the example
Use the original values or change them to test your understanding.