Terminal falling velocity of particles

In a recent study of the transport of coarse solids in a horizontal pipeline of 38 mrrt diameter, pressure drop, as a function not only of mixture velocity (determined by an electromagnetic flowmeter) but also of in-line concentration of solids and liquid velocity. The solids concentration was determined using a y-ray absorption technique, which depends on the difference in the attenuation of y-rays by solid and liquid. The liquid velocity was determined by a sail injection method,1"1 in which a pulse of salt solution was injected into the flowing mixture, and the time taken for the pulse to travel between two electrode pairs a fixed distance apart was measured, It was then possible, using equation 5.17, to calculate the relative velocity of the liquid to the solids. This relative velocity was found to increase with particle size and to be of the same order as the terminal falling velocity of the particles in the liquid. 

That the relative velocity uB was equal to the terminal falling velocity of the particles. This assumption does not necessarily apply to large pipes. 

The terminal falling velocity of the sand particles in water may be taken as 0.0239 m/s. This value may be confirmed using the method given in Volume 2. 

The mechanism of suspension is related to the type of flow pattern obtained. Suspended types of flow are usually attributable to dispersion of the particles by the action of the turbulent eddies in the fluid. In turbulent flow, the vertical component of the eddy velocity will lie between one-seventh and one-fifth of the forward velocity of the fluid and, if this is more than the terminal falling velocity of the particles, they will tend to be supported in the fluid. In practice it is found that this mechanism is not as effective as might be thought because there is a tendency for the particles to damp out the eddy currents. 

The additional pressure drop due to the presence of solids in the pipeline (—APx) could be expressed in terms of the solid velocity, the terminal falling velocity of the particles and the feed rate of solids F (kg/s). The experimental results for a 25 mm pipe are correlated to within 10 per cent by ... 

Obtain a relationship for the ratio of the terminal falling velocity of a particle to the minimum fluidising velocity for a bed of similar particles. It may be assumed that Stokes Law and the Carman-Kozeny equation are applicable. What is the value of the ratio if the bed voidage at the minimum fluidising velocity is 0.4 ... 

It may be assumed that the terminal falling velocities of both particles may be calculated from Stokes law and that the relationship between the fluidisation velocity u and the bed voidage e is given by ... 

Size separation equipment in which particles move in a fluid stream is now considered, noting that most of the plant utilises the difference in the terminal falling velocities of the particles In the hydraulic jig, however, the particles are allowed to settle for only very brief periods at a time, and this equipment may therefore be used when the size range of the material is large. 

Thus the higher the terminal falling velocity of the particle, the greater is the radius at which it will rotate and the easier it is to separate. If it is assumed that a particle will be separated provided it tends to rotate outside the central core of diameter 0.4d0, the terminal falling velocity of the smallest particle which will be retained is found by substituting r = 0.2d0 in equation 1.49 to give ... 

It is found that ut0 is approximately equal to the velocity with which the gas stream enters the cyclone separator. If these values for ur and ut are now substituted into equation 1.50, the terminal falling velocity of the smallest particle which the separator will retain is given by ... 

These factors are considered further in Sections 3.3.4 and 3.3.5 and in Chapter 5. From equations 3.24 and 3.25, it is seen that terminal falling velocity of a particle in a given fluid becomes greater as both particle size and density are increased. If for a... 

In Table 3.4, values of log Re are given as a function of log (R /pu2) Re 2 and the data taken from tables given by Heywood(11 are represented in graphical form in Figure 3.6. In order to determine the terminal falling velocity of a particle, (R a/pu Refi is evaluated and the corresponding value of Re 0, and hence of the terminal velocity, is found either from Table 3.4 or from Figure 3.6. 

Hlywooi)1 f has developed an approximate method for calculating the terminal falling velocity of a non-spherical particle, or for calculating its size from its terminal falling velocity. The method is an adaptation of his method for spheres. 

It may be noted that b/a = u0, the terminal falling velocity of the particle. This equation enables the displacement of the particle in the T-direction to be calculated at any time t. 

From Figures 6 and 7 (shown earlier), which illustrate the terminal falling velocities of the sand and char particles, it can be seen that virtually all char particles have a lower... 

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