Solid particle pressure

When a fluid flows upward through a bed of solid particles, pressure drop across the bed increases as the flow rate increases. Eventually the pressure drop equals the weight of the bed (per unit horizontal area) at which point the particles are... 

Equation (14.91) contains only the mass flow ratio /u as a characteristic number of the mechanics of similitude of the mixture. All the other irnpor rant factors, such as particle size, solid density, etc., are contained in the additional pressure-loss coefficient of the solid particles, A, which is determined separately for each material. 

I he mixture clement shown in Fig. 14.15 contains the flowing gas and solid particles. The partial densities of these two elements are pg and p. respectively. The void fraction is and this can be interpreted as the partial cross-sectional area for gas flow (see Eq. (14.13)). This means that if the pressure of the gas is p, then the pressure force per unit area of the total mixture affecting the flow of gas is (pp and the pressure force affecting the flow of solids is 1 -

[Pg.1343]

With the aid of this equation the pressure loss in a pneumatic conveying system can be calculated. All we need to know are the velocity difference between gas and solid particles,... 

In ejectors and tube bends the most important part of the pressure loss comes from the acceleration of solid particles. In a bend the velocity of the particles is reduced due to the friction and the pressure loss is cairsed by the reacceleration of the particles after the bend. 

Equation (14.128) can be used for calculating the pressure drop due to the acceleration of. solid particles provided that the velocity change C2 - C can be estimated. In addition to the acceleration pressure loss we have the normal" pre.ssure drop... 

In this chapter the pressure drop for pneumatic conveying pipe flow is studied. The conventional calculation method is based on the use of an additional pressure loss coefficient of the solid particles. The advantage of this classical method is that in principle it can be applied to any type of pneumatic flow. On the other hand, its great disadvantage is that the additional pressure loss coefficient is a complicated function of the density and the velocity of the conveying gas. z lso, it is difficult to illustrate the additional pressure loss coefficient and this makes the theoretical study of it troublesome. 

Advantages of this type include an ability to burn all fuels including those containing solid particles, good turndown ratio (4 to 10 1 typically) and an insensitivity to oil conditions such as pressure and temperature. It is widely used in shell boilers, and the only real limitation is that the cup surface has to be cleaned daily. The most common atomizer layout is shown in Figure 24.7. Variants include direct driven cup and separate mounting of the primary air fan. 

Lines in vacuum service, 135—141 Line symbols, 17, 23 Numbering, 23 Lined centrifugal pumps, 171 Liquid-solid particle, separators, 228 Baffle type specifications, 248 Baffle type, 247, 248 Centrifugal, 256, 259-261 Chcvron-vanc, 248, 235 Comparison chart, 230 Cyclone, 259 Specification form, 268 Vane, 259 Wire mesh, 246 York-vane, 248 Low pressure storage... 

Solid particle-gaseous oxidizer systems have been studied because of applications to propints and expls (Refs 5 14), and hazards due to dust explns (Refs 1,3, 4, 6, 7, 10 15). Strauss (Ref 9) reported on a heterogeneous detonation in a solid particle and gaseous oxidizer mixt the study concerned A1 powder and pure oxygen in a tube. Detonations initiated, by a weak source were obtained in mixts contg 45-60% fuel by mass. Measured characteristics of the detonations agreed with theoretical calcns within about 10%, and detonation pressures of up to 31 atms were observed. With regard to solid particle-air mixts, detonations have not been reported only conditions for expln have been studied (Ref 2)... 

Under increasing strain the propint volume increases from the voids created around the unbonded solid particles. Nonlinearities in Young s modulus and Poisson s ratio then occur. Francis (Ref 50) shows this effect for a carboxy-terminated polybutadiene composite propellant with 14% binder as in Figure 12. He concludes that nonlinearities in low-temperature properties reduce the predicted stress and strain values upon cooling a solid motor, and therefore a structural analysis that neglects these effects will be conservative. However, when the predictions are extended to a pressurized fiberglas motor case, the nonlinearities in properties produce greater strains than those predicted with linear analysis... 

When an industrial pipeline is to be designed, there will be no a priori way of knowing what the in-line concentration of solids or the slip velocity will be. In general, the rate at which solids are to be transported will be specified and it will be necessary to predict the pressure gradient as a function of the properties of the solid particles, the pipe dimensions and the flow velocity. The main considerations will be to select a pipeline diameter, such that the liquid velocity and concentrations of solids in the discharged mixture will give acceptable pressure drops and power requirements and will not lead to conditions where the pipeline is likely to block. 

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