Forced Flow in Empty Tubes and Hydrodynamic Entrance Region

1 Forced Flow in Empty Tubes and Hydrodynamic Entrance Region 

For Re below a critical value of about 2300, we have laminar flow with a parabolic velocity profile. The maximum velocity in the center of the tube is twice as much as the mean value Umean defined by Eq. (3.2.61). The radial velocity profile for laminar flow in a round tube is given by  

Fluctuations due to different fow velocities and due to molecular and turbulent diffusler 

For Re 10000, we have turbulent flow with an almost constant velocity in the main part of the tube and a small laminar sublayer near the wall where the velocity goes down to zero (no-slip condition). For 2300 Re 10000, we have a transition regime. Any disturbances, for example, surface roughness or particles of a packed bed, lead to a lower value of the critical Re number. 

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). 

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