Tangential velocity component

Baffles are responsible for restricting the tangential velocity component, u, and augment the vertical component, while simultaneously increasing the radial velocity, U,. The net result is that the liquid discharges from the impeller in a wider flow radius. 

Up to this stage, only the fan characteristics have been considered, without investigating the influence of different impeller blade shapes. Consider the flow at the edge of the impeller blade. Normally, for cost reasons, leading devices are not installed in front of the fan propeller, resulting in radial gas flow into the propeller, with the tangential velocity component = 0. 

From the exit velocity triangle, it can be seen that the gas flow has a tangential velocity component. The gas rotates when it leaves the fan. Normally, the tangential velocity component is of no benefit if a duct is attached to the fan, since it disappears due to friction. 

In Eq. (9.113), subscript u indicates the velocity to the tangential velocity component, the first subscript 2 indicates impeller exit, the first subscript 1 indicates impeller inlet, the second subscript 2 stands for 2> and second subscript 1 stands for rzy. The proportionality constant k is... 

The tangential velocity component ve varies linearly from zero at the lower plate to the speed of the cone at the cone s surface. At a radial distance r, the cone s tangential speed is fir where Cl is in radians per second. At this location the height of the gap is ar where a is the angle of the gap in radians. Thus, the shear rate y is given by... 

For the turbulent motion in a tube, the mass transfer coefficient k is proportional to the diffusion coefficient at the power of 2/3. It is easy to realize by inspection that this value of the exponent is a result of the linear dependence of the tangential velocity component on the distance y from the wall. For the turbulent motion in a tube, the shear stress t r0 = const near the wall, whereas for turbulent separated flows, the shear stress is small at the wall near the separation point (becoming zero at this point) and depends on the distance to the wall. Thus, the tangential velocity component has, in the latter case, no longer a linear dependence on y and a different exponent for the diffusion coefficient is expected. For separated flows, it is possible to write under certain conditions that [90]... 

Here the superscript prime symbol refers to the dispersed phase, // is the viscosity, vr and ve the radial and tangential velocity components, 0 and r are the polar coordinates, and a is the surface tension. In the case under consideration,... 

In many respects, similar to the diffusion layer concept, there is that of the hydrodynamic boundary layer, <5H. The concept was due originally to Prandtl [16] and is defined as the region within which all velocity gradients occur. In practice, there has to be a compromise since all flow functions tend to asymptotic limits at infinite distance this is, to some extent, subjective. Thus for the rotating disc electrode, Levich [3] defines 5H as the distance where the radial and tangential velocity components are within 5% of their bulk values, whereas Riddiford [7] takes a figure of 10% (see below). It has been shown that... 

Starting from the flame front the intensity of the vortices remains constant along each streamline, so that the region filled by combustion products is a rotational one. In some of the previous works mentioned, however, the existence of the stagnation zone behind the flame front has not been accounted for, so that the quantitative conclusions diflier essentially from those of the hydrodynamic model presently under consideration. It should be noted that the boundary streamline of the stagnation zone is a tangential velocity component discontinuity surface or a vortex sheet. As a consequence of the... 

In the approximation of the Wentzel-Kramers-Brillouin method, we take fi = k(l)unf a) from the Landau theory on the hydrodynamic instability of the plane flame. The relative change in the disturbance because of the stretch-effect is equal to that in the tangential velocity component... 

G steady dimensionless function corresponding to the tangential velocity component... 

Goren and O Neill (1971), who calculated the normal force exerted by creeping flow over a sphere near a plane surface. Although Ihe flow field in the present problem is somewhat more complex than that considered by Goren and O Neill, the curvature of the plane surface as well as a tangential velocity component have only secondary effects upon the normal force, so their result is reasonably applicable here. 

U Radial velocity component V Tangential velocity component W Axial velocity component... 

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