Solid velocity

Figure 6-32, taken from Govier and Aziz, schematically indicates four flow pattern regions superimposed on a plot of pressure gradient vs. mixture velocity = Vl -t- V5 = Qj + ( s)/A where and Vs are the superficial liquid and solid velocities, Qi, and ( 5 are liquid and solid volumetric flow rates, and A is the pipe cross-sectional area. is the transition velocity above which a bed exists in the bottom of the pipe, part of which is stationary and part of which moves by saltation, with the upper particles tumbling and bouncing over one another, often with Formation of dunes. With a broad particle-size distribution, the finer particles may be fully suspended. Near V 4, the pressure gra-... 

One manner in which size may be computed, for estimating purposes, is by employing a volumetric heat-transfer concept as used for rotary diyers. It it is assumed that contacting efficiency is in the same order as that provided by efficient lifters in a rotaiy dryer and that the velocity difference between gas and solids controls, Eq. (12-52) may be employed to estimate a volumetric heat-transfer coefficient. By assuming a duct diameter of 0.3 m (D) and a gas velocity of 23 m/s, if the solids velocity is taken as 80 percent of this speed, the velocity difference between the two would be 4.6 m/s. If the exit gas has a density of 1 kg/m, the relative mass flow rate of the gas G becomes 4.8 kg/(s m the volumetric heat-transfer coefficient is 2235 J/(m s K). This is not far different from many coefficients found in commercial installations however, it is usually not possible to predict accurately the acdual difference in velocity between gas and soRds. Furthermore, the coefficient is influenced by the sohds-to-gas loading and particle size, which control the total solids surface exposed to the gas. Therefore, the figure given is only an approximation. 

In the TMB model, the adsorbent is assumed to move in plug flow in the opposite direction of the fluid, while the inlet and outlet lines remain fixed. As a consequence, each column plays the same function, depending on its location. An equivalence between the TMB and the SMB models can be made by keeping constant the liquid velocity relative to the solid velocity, i.e., the liquid velocity in the TMB is ... 

The importance of obtaining accurate measurements of solid velocity is associated with the fact that the drag exerted by the fluid on the particle is approximately proportional to the square of the relative velocity. As the solid velocity frequently approaches the air velocity, the necessity for very accurate values is apparent,... 

Pressure drops and solid velocities for dilute phase flow... 

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 ... 

Equations 5.37, 5.38 and 5.39 for solid velocity and pressure drop ate applicable only in the absence of electrostatic charging of the particles. Many materials, including sand, become charged during transport and cause the deposition of a charged layer on the surface of the pipe. The charge remains on the earthed pipeline for long periods but can... 

Mstlin. L. University of London. Ph.D. thesis (1954). A study of pneumatic conveying with special reference to solid velocity and pressure drop during transport. 

Richardson, J. F. and McLeman, M. Trans. Inst. Chem, Eng. 38 (1960) 257. Pneumatic conveying. Pari II. Solids velocities and pressure gradients in a one-inch horizontal pipe. 

The conditions for a complete separation of a binary mixture can be defined in terms of the Yj model parameters, which are directly related with the TMB (SMB) operating variables (fluid and solid velocities in the four sections of the TMB unit). From the constraints presented, those related to sections II and III play the crucial role on the separation performance of the TMB. It is in these central zones that the separation between the two species takes place. The role of the adjacent sections (I and IV) is to prevent cross-contamination and to allow the improvement of the continuous operation of the system by regenerating the solid and liquid phases. Taking into account these considerations, a region of complete separation in a Ym-Yn plane can be defined. Considering that the constraints concerning sections I and IV are fulfilled, the YnrYn plot is 311 important tool in the choice of best operating conditions. 

For example, if (p is the solids volume fraction entering the pipe at velocity V, and local volume fraction in the pipe where the solid velocity is Vs, a component balance gives... 

Table 3. Summary of Experimental Solids Velocity into the Jet at Different Operating Conditions...

Denote the superficial liquid-solids velocity ratio (.L/pfA)/(S/psA) by N, and let (S/psut) =At. which is the minimal cross-sectional area if the solids were to flow at their terminal velocity, up in the absence of fluid flow, and can, therefore, be called terminal cross-sectional area. Then Eq. (2) can be reduced to a dimensionless form in terms of a reduced area, A, defined as follows... 

L/pj-A)(S/psA), liquid-solids velocity ratio, dimensionless Number of heat-transfer stages, dimensionless = hdp/kg, Nusselt number, dimensionless Pressure drop, gm-wt/cm2 = Cpu kg, Prandtl number, dimensionless = dpiipj U, Reynolds number, dimensionless S Mass velocity of solids, gm/cirf sec... 

Assume air and solid velocities equal. Elbow radius = 12D. 

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