Tangential impact

Fig. 2. Cumulative number distributions for wall impact angles and normal and tangential impact velocity components for one polymer of each class.

The tangential component of impact velocity on the second surface will also depend on whether it is moving at the same or a different rotational speed. Assuming the first surface is rotating at a>i and the second surface at 0)2 the tangential impact velocity can be written as... 

For the case where the contact force grows without bound, one can show that as kc 0, a discontinuous change occurs in the velocity which is known as the tangential impact and motion stops instantaneously. Substituting the first equation of (8.12) into (5.16) gives... 

Figure 8.2 shows that, for any initial condition, the contact force eventually reaches the first quadrant and grows exponentially without bound. Similar to the previous case, one can show that in the limit as 0 velocity changes discontin-uously and a tangential impact occurs. 

In [51] (coroUary to theorems 8 and 9), it is proven that whenever tangential impact occurs (in both the indeterminate and the inconsistent cases) dynamic seizure occurs and motion stops instantaneously. 

NOj Control. NO control limitations are described in both Tide 1 and Tide 4 of the CAAA of 1990. Tide 4 requirements affect only coal-fired boilers and take effect at the same time that the boilers are impacted by CAAA SO2 requirements. As of 1996, EPA had estabHshed Tide 4 NO limits only for tangentially fired and waH-fired, dry-bottom boilers that would be impacted by Phase I of the CAAA SO2 regulations (Tide 4). Limits of 0.22 kg/10 kJ (0.5 lb/10 Btu) and 0.19 kg/10 kJ (0.45 lb/10 Btu) have been set for wall-fired and tangentially fired units, respectively. The EPA based these levels on what was achievable using low NO burners. However, plants can employ a number of different front- or back-end emissions controls, including a combination of options, to achieve these levels. EPA plans to announce Tide 4 NO requirements for 300 additional boilers by late 1996 or eady 1997. 

Fig. 17. Droplet impacts on the flat surface with a small tangential velocity. Other conditions are the same as those in Fig. 16.

Centrifugal sampler. The unit consists of a propeller or turbine that pulls a known volume of air into the unit and then propels the air outward to impact on a tangentially placed nutrient agar strip set on a flexible plastic base. 

For dilute phase conveying numerical simulations with a commercial computational fluid dynamics code were carried out. The analysis of particle wall impact conditions in a pipe bend showed that they take place under low wall impact angles of 5-35° which results in low normal (5-25 m/s) and high tangential (33-44 m/s) impact velocity components. These findings lead to the conclusion that not only normal stresses caused by the impacts are important in dilute phase conveying but that sliding friction stresses play an important role as well. 

For the case in Fig. 2.17, the tangential velocities of the colliding spheres are not equal to each other before the impact, which would most likely lead to a sliding on the contact interface. Consider the simple case of two colliding spheres without relative rotation. To... 

In the following, the effects of gliding, scattering, and lifting of the particles by the gas stream are neglected and the mechanical efficiency of impact is assumed to be 100 percent. Thus, for ductile erosions, the wear in volume loss per impact equals the work of ductile wear by the tangential force divided by the energy required to remove a unit volume of material in ductile erosion mode. Therefore, we have... 

At the moment of impact the two molecular centers will be separated by a distance velocity vectors Vi and V2 perpendicular and parallel to this line of centers we will have two components for each (vu, and (v2c, t 2x) If we assume no tangential forces acting during the collision, then the perpendicular components V2 ) are un-... 

The simplest type of flow of a medium that yields itself to an analytical description within the framework of the precise hydrodynamical equations of viscous liquids (Navier-Stocks equations) is the Couette flow. This flow occurs under the impact of tangential stresses generated in a viscous liquid by a solid surface moving in it. The magnitude of the force that has to be applied to this surface to securse its movement in the viscous medium characterizes the tangential stresses and the velocity of its movement — the shear velocity. 

The values of the axial and tangential modulus of rupture (MOR) at high temperature, which impact the filter s thermal durability, are summarized in Table 8. Again, the EX-80 filter excels in this property relative to other filter compositions. Similarly, the axial" E-modulus data in Table 9 show that the EX-80 filter has similar stiffness to that of the EX-47 and EX-54 filters, notably at or below 600°C (representative of the filter s peripheral temperature during regeneration). 

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