All Flow Regimes

The expressions for the friction factor in both laminar and turbulent flow were combined into a single expression by Churchill (1977) as follows  

Equation (6-41) adequately represents the Fanning friction factor over the entire range of Reynolds numbers within the accuracy of the data used to construct the Moody diagram, including a reasonable estimate for the intermediate or transition region between laminar and turbulent flow. Note that it is explicit in /. 

---

Total pressure drop for horizontal gas/solid flow includes acceleration effects at the entrance to the pipe and fric tional effects beyond the entrance region. A great number of correlations for pressure gradient are available, none of which is applicable to all flow regimes. Govier and Aziz review many of these and provide recommendations on when to use them. 

As liquid flowrate inereases beyond the minimum required to suspend the partieles, the bed expands. Unfortunately, however, the expansion index n is not eonstant over all flow regimes but is a funetion of the flow. Thus... 

For hydrocarbon liquids, Midoux et al.S6 recommend the use of Eq. (6-41) for all flow regimes for nonfoaming liquids. For foaming liquids, they recommend the use of Eq. (6-41) for the trickle-flow regime and the use of Eq. (6-42) for all other flow regimes.12... 

Generalized Interpretation of f vs. Re. When the characteristic velocity and the Reynolds number increase, the fi iction factor for flow around solid spheres decreases if Re < 500, and / remains approximately constant at 0.44 if Re > 500. However, the dynamic force transmitted across the fluid-solid interface increases at higher Reynolds numbers in all flow regimes. The generalized correlations are... 

Boundary layer. For all flow regimes, whether laminar or turbulent, the effects of viscous shear forces are greatest close to solid boundaries. Fluid actually in contact with a surface usually has no relative motion the so called no-slip condition. There is therefore a region extending from the surface to the bulk of the fluid within which the velocity changes from zero to the bulk value. This region is known as the boundary layer. 

CARPT experiments were performed with bubble columns of three different diameters (11.4 cm 19 cm 29.2 cm) using air-water. Four superficial velocities, spanning the range from 2 cm/s to 18.4 cm/s were used in each column. This covers all flow regimes from bubble to churn turbulent flow. All runs were done with batch liquid (i.e. zero liquid superficial velocity). A porous plate distributor was employed. 

Depending on the flow rate, one or more of the flow regimes may be encountered as the polymer moves away from the injection well. It is necessary to check the Darcy velocity as a function of radial position to determine which flow regimes are present. If all flow regimes are present in the system, the expression for the pressure drop is given by Eq. 5.52. Eq. 5.52 can be adjusted for a particular application if a region cannot exist on the basis of the criteria establish in the preceding section. 

---