Saltation Velocity in Pneumatic Conveying (Rizk)
Computes the saltation velocity in dilute-phase pneumatic conveying with the Rizk correlation, V_s = √(g·D)·(μ·10^(1440·d_p + 1.96))^(1/(1100·d_p + 2.5)), where the pipe diameter D and the particle diameter d_p are in metres and μ is the solids-to-gas loading ratio in kg of solid per kg of air. Below this velocity the particles stop being carried in suspension and start settling at the bottom of the horizontal pipe, building a dune that chokes the cross-section until the line blocks — which is why it is the LOWER design limit, on top of which a typical margin of 20 to 50 % is applied. Because the bracketed term is dimensionless, velocity scales exactly with √(g·D), giving two practical readings: doubling the pipe diameter demands only 41 % more velocity, but tripling the solids loading from 10 to 30 raises the requirement from 15.9 to 22.9 m/s, because loading enters raised to an exponent. Enter the pipe diameter, the particle diameter and the loading ratio.
Result
—
Saltation Velocity in Dilute-Phase Pneumatic Conveying
In a dilute-phase line there is an air velocity below which particles stop travelling in suspension and start piling up along the bottom of the horizontal run. The dune that builds up throttles the cross-section, pressure drop climbs and the line plugs — usually with a full silo and production stopped. Whoever sizes the blower needs that limit before fixing the air flow: it sets the floor of the conveying velocity, on top of which the design margin goes. The Rizk correlation is the usual estimate for horizontal pipe, and this page solves it from pipe bore, mean particle size and loading ratio.
The correlation reads V_s = √(g·D)·(μ·10^(1440·d_p + 1.96))^(1/(1100·d_p + 2.5)), with D and d_p in metres inside the expression and μ in kg of solid per kg of air. The first factor is the reference velocity √(g·D); the bracket, dimensionless, corrects for particle size and loading. With the page defaults — 0.1 m pipe, 0.5 mm particle and μ = 10 — the output is 15.94 m/s, a saltation Froude number of 16.1, inside the range of 10 to 20 reported for granular solids in 100 mm pipe. Tripling the load to μ = 30 gives 22.85 m/s; doubling the bore to 0.2 m gives 22.54 m/s, exactly √2 times the original figure.
Rizk fitted the correlation to plastic granules, and the heaviest limitation follows from that: no solids density term appears anywhere. Cement, alumina and polystyrene of equal diameter get the same answer, which is physically wrong — with dense or abrasive material, take the value as a first estimate and cross-check it against another saltation correlation. It holds for dilute phase in a horizontal run: a vertical leg has a different limiting mechanism, choking, and bends need their own allowance. The d_p field wants a mean diameter, so wide size distributions, cohesive powders and fibrous particles fall outside the assumption. The page computes neither pressure drop nor blower power.
Frequently asked questions
Should particle diameter be entered in millimetres or metres?
Can I use the saltation velocity as my design velocity?
Does the Rizk correlation suit any material?
Related Tools
Railway Minimum Curve Radius
Calculate the minimum railway curve radius for a design speed, R = (B·V²) ÷ (127·(h_max + I_max)), from the gauge B (mm), speed V (km/h), maximum allowable cant h_max (mm) and maximum allowable cant deficiency I_max (mm). The minimum radius is set by combining the two comfort/safety limits available to 'absorb' lateral acceleration at the desired speed: the maximum buildable cant (limited by overturning risk of slow/stopped trains) and the maximum deficiency allowed to passengers. The larger these limits, the smaller the radius for a given speed — but both have normative caps. This is central to railway alignment: it defines how sharp a curve can be without speed reduction. Sharper curves require slowing down, penalizing travel time and line capacity — so high-speed railways need huge radii (kilometers). Enter the gauge, speed, maximum cant and maximum deficiency.
Critical Deposition Velocity (Durand)
Calculate the critical deposition velocity in hydraulic solids transport by Durand's equation, V_c = F_L·√(2·g·D·(s − 1)), from the Durand factor F_L (dimensionless, a function of grain size and concentration), the pipe inner diameter D (m) and the solids relative density s = ρ_s/ρ_w. Critical velocity is the MOST important parameter in designing pipelines and dredge discharge lines: it is the MINIMUM flow velocity below which solids start to DEPOSIT on the pipe bottom, forming a bed that reduces the section, raises head loss and can lead to total CLOGGING of the line (a very costly, slow accident to clear). Above the critical velocity, turbulence keeps the particles suspended and moving. Operation must keep the velocity ALWAYS above critical (with safety margin), but not too far above, since excessive velocities waste pumping energy and cause accelerated abrasive wear of pipe and pumps. Determining the critical velocity sets the operating velocity, the pipe diameter and the pumping power. Durand's correlation (1953), with the tabulated F_L factor, is the classic basis of this calculation. Enter the Durand factor, the pipe diameter and the solids relative density.
Extrusion Haul-Off Speed
Calculate the haul-off speed of an extrudate by mass conservation, v = Q ÷ A, from the extruder volumetric flow Q (m³/s) and the final product cross-sectional area A (m²). After the die, the extrudate is pulled by a haul-off (belts, rollers, winder) at a speed that must be SYNCHRONIZED with the extruder flow: by mass conservation, in steady state, the volume leaving the extruder per second must equal the volume the haul-off removes per second (product area times line speed). If haul-off is too fast for the flow, the product thins below size or breaks; if too slow, material accumulates and deforms. This speed sets the line's PRODUCTIVITY (metres per minute) and, with die swell and draw-down ratio, sets the final dimensions. Controlling the extrusion-haul-off synchrony — often with dimension sensors and closed loop — is essential for dimensional uniformity of pipes, profiles, wire and sheet. This gives the theoretical line speed from flow and desired section. Enter the flow and the product section area.
Average Velocity Calculator
Compute average velocity v = Δs/Δt from distance and time, in km/h or m/s.
Wave Group Velocity
Calculate the group velocity of an ocean wave in deep water, c_g = g·T ÷ (4π), from the period T (s). The result, in m/s, is the speed at which the wave energy (and the 'envelope' of a wave group) propagates — exactly half the celerity (phase velocity) in deep water. This difference explains a curious phenomenon: within a wave group, individual crests appear at the rear, advance through the group (faster than it) and disappear at the front. The group velocity is what matters for energy transport and predicting swell arrival at the coast. Enter the wave period.
Hull Speed
Compute the hull speed of a displacement vessel, V ≈ 2.43·√(LWL), in knots, from the waterline length (LWL, in meters). It is the theoretical limit of a hull's economical speed: as the boat approaches it, it gets trapped in its own bow wave and the required power soars. That is why sailboats and displacement craft rarely exceed it. Enter the waterline length.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.