Eu Only Weakly Dependent on Re

As we found for separation performance described above, i e-similarity is not critical for the pressure drop, either. In Chap. 4 we found that many of the empirical models for cyclone pressure drop only contain the ratio of inlet to outlet areas, implying that Eu will be the same between geometrically similar cyclones, irrespective of f e-similarity. Obviously, as was the case for separation efficiency, this is only valid when Re is high enough that the friction factor is essentially independent of Re. This should come as no real surprise since the same situation holds true for most flow devices (such as pipes, elbows, orifices, contractions and expansions, etc.) that operate in fully developed turbulent flow. In such cases, pressure loss can be characterized by the formula  

This principle does have its limitation. The scaling rule of constant Eu and the models in Chap. 4 have, in the authors experience, significantly overpredicted pressme loss in very large-scale cyclones. There is a weak but definite i e-number effect on the pressure loss coefficient Eu. This variation in Eu is only with Re to the power of —0.17 to —0.2 but, when scaling up small scale lab data by a factor of 10 or more, one can easily overpredict pressure loss by 50% or more. 

In most cases, such an error on the conservative side in predicting pressure drop is perfectly acceptable since, if anything, the plant will experience less pressure drop through the cyclone installation and this seldom creates an operational problem. However, if there is some delicate pressure balance across a slide valve, for example, which relies on an accurate knowledge of the cyclone s pressure drop, then one should try to acquire the most accurate estimate possible. 

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