Turbulent flow region

However, on die basis of the relation between pressure drop and die minimum fluidisation velocity of particles, the point of transition between a packed bed and a fluidised bed has been correlated by Ergun41 using (17.7.2.3). This is obtained by summing the pressure drop terms for laminar and turbulent flow regions. 

This general method can be used for geometrically scaled reactors with Newtonian liquids or with Newtonian suspensions in the turbulent flow region (NRe > 1000). 

In the fully turbulent flow region DE, the curve becomes horizontal and the power function is independent of the Reynolds number for mixing ReM. For the region ReM > 10000... 

In turbulent flow region, Grant and Middleman 247] suggested the following empirical correlation ... 

In the range Re > 50 (vessel with baffles) or Re > 5 x 10" (unbaffled vessel), because the Newton number Ne = P/(pn d ) remains constant. In this case, viscosity is irrelevant we are dealing with a turbulent flow region. 

These dimensionless groups also appear in empirical correlations of the turbulent flow region. Although even in the approximate Eq. (9) of Table 6.7, group He appears to affect the friction factor, empirical correlations such as Figure 6.5(b) and the data analysis of Example 6.10 indicate that the friction factor is determined by the Reynolds number alone, in every case by an equation of the form, / = 16/Rc, but with Re defined differently for each model. Table 6.7 collects several relations for laminar flows of fluids. 

With the average elongational strain rate of the flow field between the eddies and the relaxation time of the polymer molecules, one can define a dimensionless characteristic number, the Deborah number, which represents the ratio of a characteristic time of flow and a characteristic time of the polymer molecule, and thus one can transfer considerations in porous media flow to the turbulent flow region. 

Initially, the boundary-layer development is laminar, but at some critical distance from the leading edge, depending on the flow field and fluid properties, small disturbances in the flow begin to become amplified, and a transition process takes place until the flow becomes turbulent. The turbulent-flow region may be pictured as a random churning action with chunks of fluid moving to and fro in all directions. The transition from laminar to turbulent flow occurs when... 

In the turbulent-flow region distinct fluid layers are no longer observed, and we are forced to seek a somewhat different concept for viscous action. A qualitative picture of the turbulent-flow process may be obtained by imagining macroscopic chunks of fluid transporting energy and momentum instead of... 

In the turbulent-flow region, where eA1 > v and eH > a, we define the turbulent Prandtl number as... 

Approximate equations showing the relationship between the friction factor and the Reynolds number in the turbulent-flow region have been developed. Two of these equations follow ... 

The first relation gives the average heat transfer coefficient for die entire plate when the flow is laminar over the etUire plate. The second relation gives the average heal transfer coefficient for the entire plate only when the flow is iiir-bulent over the entire plate, or when the laminar flow region of the plate is too small relative to the turbulent flow region. 

This equation is solved with respect to u under the simplifying assumptions (M31, U5) that is constant in the turbulent flow region, and that bubble gas holdup b is distributed radially according to the relation ... 

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