Pneumatic Conveying Saltation Velocity & Pressure Drop Calculator
Design industrial dilute-phase pneumatic conveying pipelines for powders and granules. Calculate saltation velocity via the Rizk equation, solid-to-air mass loading ratio (μ), multi-component pressure drop, and Roots blower power.
1. Solids Material & Pipeline Geometry
2. Air Conditions & Safety Margin
Pneumatic Velocities & Hydraulic Sizing
Operating Air & Kinetic Parameters
System Pressure Drop Breakdown (mbar)
Interactive Dilute-Phase Pneumatic Conveying Pipeline Simulation
Visual simulation of particle pickup zone, high-velocity dilute stream, saltation dune boundary threshold, pipe elbow centrifugal impingement, and cyclone receiver.
In-Depth Bulk Solids Engineering: Rizk Equation & Pressure Drop Models
In dilute-phase pneumatic conveying, particles are fully suspended in an airstream where gas drag balances gravity. If gas velocity drops below the critical saltation velocity ($u_s$), particles settle to the bottom of the horizontal pipe, forming rolling sand dunes that trigger pipeline blockage:
The Rizk Saltation Correlation
The universal industrial benchmark for horizontal saltation velocity is the empirical correlation established by Dr. F. Rizk (1973):
$$\text{Solving for } u_s: \quad u_s = \sqrt{g \, D} \times \left[ \chi \times \mu^\delta \times \left( \frac{d_p}{D} \right)^\omega \right]$$
Where:
- $\mu$: Solid loading ratio (mass ratio of solids to conveying air: $\dot{m}_s / \dot{m}_{air}$). For dilute phase, typically $\mu \approx 3 - 15$.
- $D$: Pipe internal diameter ($m$).
- $d_p$: Mean particle diameter ($m$).
- $\chi, \delta, \omega$: Dimensionless constants. For typical industrial granular and powdery solids: $\chi \approx 1100$, $\delta \approx 0.54$, $\omega \approx 0.10$.
- $u_{design}$: Safe operating velocity: $u_{design} = (1.20 - 1.30) \times u_s$.
Two-Phase Pressure Drop Summation
The total pneumatic conveying pressure drop is decomposed into discrete physical resistances following the Barth / Weber / Marcus framework:
$$\Delta P_{gas} = \lambda_g \frac{L}{D} \frac{\rho_{air} u_g^2}{2}, \quad \Delta P_{accel} = \mu \, \rho_{air} \, u_g \, c_s$$
$$\Delta P_{solid\_fric} = \lambda_s \, \mu \frac{L}{D} \frac{\rho_{air} u_g^2}{2}, \quad \Delta P_{vert} = \mu \, \rho_{air} \, g \, H_{vert}$$
$$\Delta P_{bends} = N_{bends} \times B \times \frac{\rho_{air} u_g^2}{2} (1 + \mu)$$
5 Fatal Engineering Pitfalls in Pneumatic Conveying Systems
Operating below saltation velocity ($u_g < u_s$) causes particles to drop out of suspension and accumulate in dunes along horizontal pipe inverts. As the dune builds, cross-sectional area restricts, causing a sudden spike in pressure drop. If the positive-displacement Roots blower relief valve pops, all airflow stops, permanently packing hundreds of feet of pipe solid with compressed product.
When conveying plastic pellets (polyethylene, polypropylene) at excessive velocities ($> 22 \text{ m/s}$), high-speed frictional heating melts pellet surfaces against smooth pipe walls. This leaves molten plastic ribbons called "angel hair" or "snake skins" that clog diverter valves, foul silo rotary airlocks, and contaminate injection molding lines. Mitigation requires shot-peened or spiral-grooved pipe surfaces and strict velocity throttling.
Abrasive particles (silica sand, alumina, cement) impact the outer radius of 90° pipe bends with kinetic energy proportional to velocity cubed ($E \propto u^3$). Standard schedule 40 steel elbows erode and blow out in less than 72 hours under high velocities. Industrial abrasive conveying demands induction-hardened pipe, ceramic-tiled elbows, or vortex pocket "blind tee" bends that form protective stationary material cushions.
In positive-pressure systems, the rotary valve feeds solids from an atmospheric hopper into a 0.5–1.0 bar conveying line. Air leaks backward through rotor tip clearances. This upward "blowback air" fluidizes product in the feeding hopper throat, bridging material and cutting solid feed rate by up to 80%. A dedicated blowback venting shroud with dust collector return is mandatory.
High-speed particulate conveying generates intense triboelectric static charges exceeding 30,000 volts. If any pipe spool, flex sleeve, or receiver cyclone lacks metallic bonding straps across flanges, static discharge sparks jump across gaps. In organic dust environments (sugar, flour, starch, plastic fines), this spark immediately ignites a catastrophic combustible dust explosion violating NFPA 652/654 standards.