Effect of liquid velocity on pressure gradient

The velocity corresponding to the incipient fiuidising point can also be calculated from the relation presented in Section 5.6, by equating the pressure drop aeross the bed to its buoyant weight per unit area. The voidage at the onset of fluidisation should correspond to the maximum value attainable in the fixed bed. Hence, in a fiuidised bed, the total frictional force on the particles 

There may be some discrepancy between the observed and calculated minimum fluidisation velocities. This difference is attributable to channelling or wall effects, or to the agglomeration of small particles. Equation (5.66) applies from the initial expansion of the bed up to high values (ca 0.95) of voidage. 

For streamline flow of a power-law fluid through a fixed bed of spherical particles, the relationship between liquid velocity Vq, bed voidage s and pressure drop (—Ap) is given by equation (5.46). Substituting for —Ap) from equation (5.66), equation (5.46) becomes  

For n = 1, equation (5.67) reduces to the well-known Kozeny-Carman equation  

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