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Pneumatic Conveying, Powder Transport, Saltation Plugging & Blower Line Sizing

Pneumatic Conveying Gas Velocity & Saltation Margin Formula

Calculate Required Conveying Air Mass Rate (kg/h), Line Volumetric Gas Flow at Pick-Up Pressure (m³/min), Superficial Pick-Up Gas Velocity U_gas (m/s), and Saltation Safety Margin U_gas / U_salt.

Upsizing a pneumatic conveying pipe WITHOUT upsizing the blower drops gas velocity below saltation—plugging the horizontal line solid!

In liquid piping, enlarging pipe bore always lowers pressure drop safely; in dilute-phase horizontal pneumatic conveying, enlarging pipe bore `D` at fixed blower mass flow `dot_m_air = dot_m_solids / mu` SLASHES Superficial Conveying Gas Velocity `U_gas = Q_air / ((PI()/4) * D^2)` inversely with `D^2`! Below the Rizk Saltation Velocity `U_salt` (m/s, the minimum horizontal gas speed capable of keeping particles in aerodynamic suspension), granules drop out into a stationary dune bed and plug the pipeline within seconds! Reliable dilute-phase design requires Pick-Up Gas Velocity `U_gas >= 1.50 * U_salt` (`Saltation Margin >= 1.50`) evaluated at the HIGHEST-PRESSURE (highest gas density `rho_air`, hence LOWEST velocity!) pick-up point directly beneath the rotary airlock!

Verify on a 4-Inch (`102` mm ID) Plastic-Pellet Conveying Line—Pipe_Inner_Diameter `D` = 102.0 mm (B2), Pellet_Throughput `dot_m_s` = 7,200.0 kg/h (B3), Solids-to-Air_Loading `mu` = 6.0 (B4 -> Required Air Mass = `1,200.0` kg/h in E2), Pick-Up_Point_Air_Density `rho_a` = 1.45 kg/m³ (`~0.4` bar(g) blower discharge, B5 -> Actual Gas Flow = `13.79` m³/min in E3), and Pellet_Saltation_Velocity `U_salt` = 14.50 m/s (B6): Pick-Up Superficial Gas Velocity equals `28.13` m/s (E4), providing a healthy `1.94x` Saltation Safety Margin (`>= 1.50x`, E5)!

Dilute-Phase Conveying KPI (ID=102 mm, 7,200 kg/h, mu=6.0, rho_a=1.45 kg/m³)FormulaVerified Output
Required Air Mass Flow (kg/h)Solids_Mass_kg_hr / Loading_Ratio_mu1,200.0 kg/h
Actual Pick-Up Gas Flow (m³/min)(Air_Mass_kg_hr / 60) / Air_Density_kg_m313.79 m³/min
Superficial Pick-Up Velocity (m/s)(Gas_m3_min / 60) / ((PI()/4)*(ID_m^2))28.13 m/s (17.86 m/s @ 128 mm pipe!)
Saltation Safety Ratio (U / Usalt)PickUp_Velocity_m_s / Saltation_Vel_m_s1.94x (1.23x < 1.50x DANGER @ 128 mm!)

Pick-Up Point Superficial Conveying Gas Velocity & Saltation Margin Formula

Validate `Pipe_ID > 15` mm, `Solids_Rate > 0` kg/h, Dilute-Phase `Loading_mu` in `(0, 15]`, `Air_Density` in `[0.5, 10]` kg/m³, and `Saltation_Velocity > 2` m/s!

=LET(id_m, B2, ms_h, B3, mu_r, B4, ra_k, B5, us_v, B6, IF(OR(id_m <= 15, ms_h <= 0, mu_r <= 0, mu_r > 15, ra_k < 0.5, ra_k > 10, us_v <= 2), "Invalid Conveying Input", LET(ma_h, ms_h / mu_r, qa_s, (ma_h / 3600) / ra_k, ar_p, (PI() / 4) * ((id_m / 1000) ^ 2), ug_s, qa_s / ar_p, ROUND(ug_s / us_v, 2))))

Oversized 5-Inch (128 mm ID) Pipe Saltation Danger Check (Set Pipe ID B2 = 128.0 mm)

Swap in a `5"` (`128.0` mm ID) pipe (`B2 = 128`) without increasing Roots blower speed: Pick-Up Gas Flow E3 stays `13.79` m³/min, yet Superficial Pick-Up Velocity E4 plunges from `28.13` m/s down to `17.86` m/s, dropping Saltation Margin E5 to `1.23x` (`< 1.50x` safe pickup threshold—risking immediate saltation dune plugging on feed surges)!

=IF(ISTEXT(E5), E5, LET(ma_h, B3 / B4, qa_s, (ma_h / 3600) / B5, ar_p, (PI() / 4) * ((B2 / 1000) ^ 2), ROUND(qa_s / ar_p, 2)))

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