Pressure Loss in Empty Tubes

Incompressible Fluids The basic equation of flow in a stream-tube is the Bernoulli equation (D. BemouUi, see box), which is given for steady-state conditions and an incompressible fluid with internal friction by  

The first term on each side of Eq. (3.4.1) represents the kinetic energy (J kg = the second term the contribution of the static pressure, and the third term the specific potential energy with h as height above a reference height. The term is the specific energy dissipation (Jkg ), that is, the ratio of the friction power, 

Experience shows that the specific dissipation rpx2 is given by  

For an incompressible fluid flowing in a horizontal tube hi = h, for an altitude change see Example 3.4.1) with a constant cross-sectional area (Ui = u, we simply obtain  

Equation (3.4.6) is a very good approximation for all liquids as their compressibility is small, for example, for water an increase of pressure by 100 bar (at 20°C) causes a decrease of volume by only 0.045%. As inspected below, the friction factor ft depends on the Re number and the surface roughness. 

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The driving force is the pressure, and the friction leads to a pressure loss in empty tubes as well as in fixed, fluidized, and entrained beds (Sections 3.4.1.1 and 3.4.1.2). 

The pressure loss in empty tubes depends on the fHction flictor/, which is a function of the Re number. For the pressure drop in fixed beds, which increases with decreasing particle diameter, the Ergun equation is used. For many processes (adsorption, gas-solid reactions, and heterogeneous catalysis) fixed beds are applied, and a particle size of more than 1 mm is used to avoid an excessive high pressure drop. 

Data are also described in terms of the relationship between pressure drop in the static mixer and the equivalent pressure loss in an empty tube. For the Kenics mixer ° the relationship ... 

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