Prediction of pressure gradient for flow through packed beds

2 Prediction of pressure gradient for flow through packed beds 

for flow through a non-circular duct, this may be re-arranged as 

Equations (5.34) and (5.35) can be used to obtain expressions for streamline flow of time-independent fluids through beds of particles, in which case V must be replaced by the mean velocity in the pores or interstices, i.e. V, and the length L is replaced by the average length of the tortuous path, L , traversed by the fluid elements. 

For a bed whose structure is independent of its depth, then Le and L will be linearly related, i.e. 

The interstitial velocity, Vi, is related to the superficial velocity Vo by the Dupuit relation which is based on the following eonsiderations. 

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