Velocity tangential

The tangential velocity inside the hydrocyclone is very inqrortant, it is the means by which a suspended particle following the liquid flow path because of drag will experience a centrifugal force. The tangential velocity of the solid will be similar to the liquid on entry into the hydrocyclone and it is assumed that this is also the case at any instant at radii less than that of the entry. 

The linear velocity of the feed at the inlet v/ is related to volume throughput Q and area of inlet nozzle / as follows  

Equation (8.28) provides a value for the tangential velocity at the outer radius of the hydrocyClone. Tang tial velocities at radii less than that of the hydrocyclone can be estimated by means of the princ le of conservation of angular momentum under flictionless conditions  

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The basis for the familiar non-slip boundary condition is a kinetic theory argument originally presented by Maxwell [23]. For a pure gas Maxwell showed that the tangential velocity v and its derivative nornial to a plane solid surface should be related by... 

Next, suppose we consider the tangential velocity v of segment i in a polymer molecule. The segment is located a distance r from the center of mass of the molecule and possesses an average angular velocity co. The situation is sketched in Fig. 2.12a. Since v = rco, it follows that the x and y components of the velocity are given by... 

Now we must consider how the frictional force experienced by this segment is related to the tangential velocity whose components are given by these expressions. 

FIG. 1 7-37 Variation of tangential velocity and radial velocity at different points in a cyclone. [Ter Linden, Inst. Mech. Eng. J., 160, 235 (1949).]... 

A slide surface is a surface where the tangential velocity can be discontinuous as shown in Fig. 9.9. Separate velocities are calculated for each side. Slide lines are useful for modeling phenomena such as sliding friction or flow through pipes. 

Cyclone mist eliminators and collectors have virtually the same efficiency for both liquid aerosols and solid particles. To avoid reentrainment of the collected liquid from the walls of the cyclone, an upper limit is set to the tangential velocity that can be used. The maximum tangential velocity should be limited to the inlet velocity. Even at this speed, the liquid film may creep to the edge of the exit pipe, from which the liquid is then reentrained. 

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 forward-curved fan blade increases the tangential velocity considerably (see Figure 27.5b). As a result, the power required will increase with mass flow, although the external resistance pressure is low, and oversize drive motors are required if the system resistance can change in operation. The backward-curved fan runs faster and has a flatter power curve, since the air leaves the blade at less than the tip speed (see Figure 27.5c). 

To obtain physically meaningful solutions, a set of appropriate boundary conditions must also be specified. One obvious requirement is that no fluid should pass through the boundary (i.e. wall) itself. Thus, if we choose a reference frame in which the boundaries are at rest, we require that v fi = 0, where fi is the unit normal to the surface. Another condition, the so-called no-slip condition ([trittSS], [feyn64]), is the requirement that the fluid s tangential velocity vanishes at the surface v x n = 0. 

He considered that the rapid flame propagation could be achieved with the same mechanism as vortex breakdown. Figure 4.2.2 schematically shows his vortex bursting mechanism [4,5]. When a combustible mixture rotates, Ihe pressure on the axis of rotation becomes lower than the ambient pressure. The amount of pressure decrease is equal to max in Rankine s combined vor-fex, in which p denotes fhe unburned gas density and Vg denotes the maximum tangential velocity of the vortex. However, when combustion occurs, the pressure on the axis of rofafion increases in the burned gas owing to the decrease in the density, and becomes close to the ambient pressure. Thus, there appears a pressure jump AP across the flame on fhe axis of rotation. This pressure jump may cause a rapid movement of the hot burned gas. By considering the momentum flux conservation across the flame, fhe following expression for the burned gas speed was derived ... 

Relation between flame speed Vj and maximum tangential velocity in an axially decaying vortex flow in a tube for various mixtures (tube diameter 31mm, the mean axial velocity 3m/s). (From Ishizuka, S., Combust. Flame, 82,176,1990.)... 

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