Bulk velocity

The dynamic response used to describe fluid motion in the system is bulk velocity. Kinematic similarity exists with geom.etric similarity in turbulent agitation [32]. To duplicate a velocity in the kinematically similar system, the kno m velocity must be held constant, for example, the velocity of the tip speed of the impeller must be constant. Ultimately, the process result should be duplicated in the scaled-up design. Therefore, the geometric similarity goes a long way in achieving this for some processes, and the achievement of dynamic and/or kinematic similarity is sometimes not that essential. 

Whatever the physical constraints placed on the system, the diffusional process causes the two components to be transferred at equal and opposite rates and the values of the diffusional velocities uDA and uDB given in Section 10.2.5 are always applicable. It is the bulk How velocity uF which changes with imposed conditions and which gives rise to differences in overall mass transfer rates. In equimolecular counterdiffusion. uF is zero. In the absorption of a soluble gas A from a mixture the bulk velocity must be equal and opposite to the diffusional velocity of B as this latter component undergoes no net transfer. 

The plot of the pressure drop depending on the bulk velocity in adiabatic and diabatic flows is shown in Fig. 3.6a,b. The data related to the adiabatic flow correspond to constant temperature of the fluids Tjn = 25 °C, whereas in the diabatic flow the fluid temperature increased along micro-channel approximately from 40 to 60 °C. It is seen that in both cases the pressure drop for Habon G increases compared to clear water. The difference between pressure drop corresponding to flows of a surfactant solution and solvent increases with increasing bulk velocity. 

Fig. 3.6a,b Dependence of pressure drop on fluid bulk velocity in (a) adiabatic flow, and (b) diabatic flow. Reprinted from Hetsroni et al. (2004) with permission... 

We consider a plane with length / and width w, which is exposed to a flowing solution with a dissolved component i at a bulk concentration c. The direction of the bulk stream of flow is parallel to the plane in the direction of the j-axis the x-axis is perpendicular to the plane, as shown in Figure 4. The bulk velocity of the flow far from the plane is denoted as v. The z-axis is considered immaterial, due to a sufficiently large value of w compared with the dimensions of the velocity and concentration perturbations. / is assumed to be much larger than the diffusion layer thickness (<5,). 

The field of velocities corresponding with such a regime (which includes no-slip of the fluid at the sphere surface) is indicated by the arrows in Figure 10, where the length of each arrow is proportional to the local velocity of the fluid. The perturbation of the bulk velocity extends to quite large distances for instance, it is necessary to move 75 times the radius ty from the centre of the sphere normal to the free stream direction of flow in order to obtain 99% of v. 

When one gas diffuses into another, as A into B, even without the quasi-steady-flow component imposed by the burning, the mass transport of a species, say A, is made up of two components—the normal diffusion component and the component related to the bulk movement established by the diffusion process. This mass transport flow has a velocity Aa and the mass of A transported per unit area is pAAa. The bulk velocity established by the diffusive flow is given by Eq. (6.58). The fraction of that flow is Eq. (6.58) multiplied by the mass fraction of A, pA/p. Thus,... 

The total mass flux of A under the condition of the burning of a condensed phase, which imposes a bulk velocity developed from the mass burned, is then... 

How do the externally imposed constraints (temperature gradient, bulk velocity,...) modify the asymptotic distribution ... 

Several laboratory studies have contributed to our understanding of turbulent chemical plumes and the effects of various flow configurations. Fackrell and Robins [25] released an isokinetic neutrally buoyant plume in a wind tunnel at elevated and bed-level locations. Bara et al. [26], Yee et al. [27], Crimaldi and Koseff [28], and Crimaldi et al. [29] studied plumes released in water channels from bed-level and elevated positions. Airborne plumes in atmospheric boundary layers also have been studied in the field by Murlis and Jones [30], Jones [31], Murlis [32], Hanna and Insley [33], Mylne [34, 35], and Yee et al. [36, 37], In addition, aqueous plumes in coastal environments have been studied by Stacey et al. [38] and Fong and Stacey [39], The combined information of these and other studies reveals that the plume structure is influenced by several factors including the bulk velocity, fluid environment, release conditions, bed conditions, flow meander, and surface waves. 

The Reynolds number is the ratio of inertial to viscous forces and depends on the fluid properties, bulk velocity, and boundary layer thickness. Turbulence characteristics vary with Reynolds number in boundary layers [40], Thus, variation in the contributing factors for the Reynolds number ultimately influences the turbulent mixing and plume structure. Further, the fluid environment, air or water, affects both the Reynolds number and the molecular diffusivity of the chemical compounds. 

The primary difference between the two equations is the unsteady term in equation (E2.2.2) and the convective term in equation (E5.3.2). Now, let s convert our coordinate system of Example 2.2 to a moving coordinate system, moving at the bulk velocity, U, which suddenly experiences a pulse in concentration as it moves downstream. This is likened to assuming that we are sitting in a boat, moving at a velocity U, with a concentration measuring device in the water. The measurements would be changing with time, as we moved downstream with the flow, and the pulse in concentration would occur at x = 0. We can therefore convert our variables and boundary conditions as follows ... 

The supersonic sodium beam has a velocity distribution oc u3exp[ — m(v — u)/2kT] with a beam temperature of T 60°K, a bulk velocity of u, a... 

The next figures give curves of dependency of M upon angular velocity of rotation n (Fig, 3), the strictly increasing functions dependencies of bulk velocity of the flow Q( l) (Fig. 4) for different values of f = p/1 (continuous lines correspond to calculations of Eqs. (13)—(16) and dotted lines correspond to similar calculations with... 

In melts G K so that there is a pure compression wave, hence the bulk velocity of sound is... 

One measure of the amount of liquid motion in an agitated tank is velocity. However, by the very nature of mixing requirements, liquid velocities must be somewhat random in both direction and magnitude. Since actual velocity is difficult to measure and depends on location in the tank, an artificial, defined velocity called bulk velocity has been found to be a more practical measure of agitation intensity. Bulk velocity is defined as the impeller pumping capacity (volumetric flow rate) divided by the cross-sectional area of the tank. For consistency, the cross-sectional area is based on an equivalent square batch tank diameter. A square batch is one in which the liquid level is equal to the tank diameter. 

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