Minimum Transport Velocity

The vertical motion of solids in a horizontal suspension flow is strongly influenced by the ratio of the terminal settling velocity to the friction velocity [Blatch, 1906 Chien and Asce, 1956]. In a circular pipe, the mean stream velocity can be related to the friction velocity by [Taylor, 1954] 

The friction velocity at the minimum transport condition may be related to the system configuration and the operating condition by a two-step correlation method, i.e., first, to obtain the velocity at the minimum transport condition under infinite dilutions and, second, to correct for the concentration dependence [Thomas, 1962]. The functional dependence of Uf to the solids concentration is given by 

Example 11.3 Consider a gas-solid horizontal pipe flow. The pipe diameter is 50 mm. The particle used is 50 pm glass bead with the density of 2,500 kg/m3. The average particle volume fraction is 0.1 percent. The gas density and kinematic viscosity are 1.2 kg/m3 and 1.5 x 10-5m2/s, respectively. Estimate the minimum transport velocity and power consumption per unit length. 

The corresponding particle Reynolds number at terminal velocity, i.e., Ret, is 0.67, which falls within the correct Ret range for Eq. (1.7) to be applied to calculate t/pt. The friction 

The corresponding dpUfo/v is 3.1, which verifies that Eq. (11.28) is a correct equation to use. The friction velocity at the minimum transport condition, Uf, can thus be given by Eq. (11.26) as 

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The most important transition velocity, often regarded as the minimum transport or conveying velocity for settling slurries, is V 9- The Durand equation (Durand, Minnesota Int. Hydraulics Conf., Proc., 89, Int. Assoc, for Hydraulic Research [1953] Durand and Condohos, Proc. Colloq. On the Hyd. Tran.spoti of Solids in Pipes, Not. Cool Boord [UK], Paper IV, 39-35 [1952]) gives the minimum transport velocity as... 

Typical minimum transport velocities are given in Table 12.13 and capture velocities for various applications in Table 12.12. 

Material, operation or industry Minimum transport velocity (m/s) (ft/min) ... 

The final application or requirements (e.g., determination of free-settling velocity y. minimum fluidization velocity Vm minimum transport velocity Vfmm, and/or pipeline air pressure drop Apt)... 

The solution to the above problem is to re-size the entire network, in particular branches I-V and II-V, with the aim of ensuring a suitable minimum transport velocity along each section of duct. 

Eq. (19) depicts the deceleration of a droplet in the vapor stream. It decelerates to the velocity of the carrier. L y. provided that L w is no less than the minimum transport velocity of the droplet, which is generally the case. At L — the droplet will be carried along by the vapor stream at the constant velocity. The deceleration length. 1, during the period from 0=0 to 0=0rt can be calculated by ... 

Motion above minimum transport velocity Stable Unstable... 

Thomas, D. G. 1961. Transport characteristics of suspension II Minimum transport velocity for flocculated suspension in horizontal pipes. AlChE Journal 7 423-430. 

Matsumoto S, Kikuta M, Maeda S. Effect of particle size on the minimum transport velocity for horizontal pneumatic conveying of solids. J Chem Eng Japan 10, No. 2 273, 1977. 

Figure 4-11 Minimum transport velocity versus particle diameter for horizontal flow (Zenz, 1949). Reproduced by permission from American Chemical Society.

Recommended minimum transport velocities for different types of dust are shown in Table 20.1. 

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