Flow through the accelerating tubes

During the flow of the streams through the accelerating tubes, several factors may lead to pressure drop along the path. These factors include friction between the gas flow and the inside wall of the tube, acceleration of the particles, collisions of particles on the wall and between particles etc. For convenience, the pressure drop through the accelerating tube can be considered to consist of two constituents caused by gas flow and particles, respectively, -Apx.d and -Apdc p, which are discussed separately below. 

Similar to the calculation of pipe-resistance, the pressure drop caused by the gas flow passing through the accelerating tube, -ApXd, can be represented by 

The pressure drop resulting from the movement of particles can be determined by an energy balance. The overall energy balance round the flow of suspension inside the accelerating tube is written as 

The drag force coefficient in Eqs. (4.5) and (4.6), CD, depends on the flow regime, as has been described in Chapter 2 the relationships between CD and the Reynolds 

On the other hand, the collisions of particles on the inside wall of the tube and between particles also result in a certain pressure drop, which is denoted by -Apac p2. Some researchers let it be a fraction of the pressure drop caused by pure airflow [67] however, it would be more convenient and reasonable to correlate it with that resulting from the acceleration of the particles, -ApaCiPi, because the factors affecting the two kinds of collision are the same as those for —Ap ac.pi. In this way, we have 

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