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If I am pneumatically conveying solids in slug flow, is there a method that works in a general case to determine the pressure drop or saltation velocity? By a general case method, I mean one that is like doing the Bernoulli balance, friction loss term and by extension Reynolds number, etc. for incompressible fluids.

It would be really neat/worthwhile in my mind to know at which point in a piece of piping that the solids would plug due to dipping below the saltation velocity.

Some suspicions of mine: Would the potential relationships involved change significantly for vertical or horizontal piping? Would dilute flow make this problem easier if you assume equal spacing of air between particle-to-particle? Surely you would not be able to consider the air and solids as separate pressure drops, right?

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Unfortunately solids handling has a reputation for being more art than science because it is much harder to predict.

A reference book on this topic which is detailed and where you may find more information on predictive models is Pneumatic Conveying by Klinzing , Rizk, et al, although Im sure there are lots of other places to look.

I believe the amount of information required to develop an accurate model is more based on empirical testing or predictive models based on your materials properities. Solids vary so much more than fluids , with particle size distributions, surface area of particles, shape of partiles and other properties which are not required for fluid flow models.

Generically conveying can be broken into “typical velocities” for dense phase or dilute phase conveying, but for design you typically either need to base on an existing system, work with a partner to do empirical testind on your material, or design with a sufficient level of conservatism. Rules of Thumb for Chemical Engineers by Stephen Hall has a section on chapter on conveying that I believe is helpful. Chemical Engineering Progress also has some articlesnthat may be helpful and if you have an AIChE membership you can access for free.

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