Fluid-Particle Interaction Pressure Drop -AP

When a fluid flows through a bed of particles, interactions between fluid and particles lead to a frictional pressure drop, (- AP). Calculation of (- AP) enables determination of both L and D, for a given W (or F). This calculation is done by means of the momentum balance, which results in the pressure gradient given by 

Alternatively, we may use these equations to determine D (and L) for a specified allowable value of (- AP). The equations may be solved explicitly for D (or L)  

Equation 21.3-10 provides the value of the bed diameter D for a given allowable pressure drop, (-AP), a value of W calculated as described in Section 21.5, and known values of the other quantities. Since a, j8, and are all positive, from the Descartes rule of signs (Section 14.3.3), there is only one positive real root of equation 21.3-10. If the equations are solved for L instead of D, a cubic equation results. 

In the choice of a value for the allowable (-AP) on the one hand, or for D (or L) on the other (given W), there is a trade-off between the cost of the vessel and the cost of pumping or compressing the fluid. The smaller D, the greater the L/D ratio and the greater (— AP) thus, the cost of the vessel is less, but the cost of pumping is greater, and conversely. 

Solving for D by trial, or using a root-finding technique as in the E-Z Solve software (see file ex21-2.msp), we obtain 

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