Velocity increase

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

The size of the droplets formed in an aerosol has been examined for a range of conditions important in ICP/MS and can be predicted from an experimentally determined empirical formula (Figure 19.6). Of the two terms in the formula, the first is most important, except at very low relative flow rates. At low relative velocity of liquid and gas, simple droplet formation is observed, but as the relative velocity increases, the stream of liquid begins to flutter and to break apart into long thinner streamlets, which then break into droplets. At even higher relative velocity, the liquid surface is stripped off, and the thin films so-formed are broken down into... 

A common measurement usehil in predicting threadline behavior is fiber tension, frequentiy misnamed spinline stress. It is normally measured after the crystallization point in the threadline when the steady state is reached and the threadline is no longer deformed. Fiber tension increases as take-up velocity increases (38) and molecular weight increases. Tension decreases as temperature increases (41). Crystallinity increases slightiy as fiber tension is increased (38). At low tension, the birefringence increases as tension is increased, leveling off at a spinline tension of 10 MPa (1450 psi) (38). 

Fundamental models correctly predict that for Group A particles, the conductive heat transfer is much greater than the convective heat transfer. For Group B and D particles, the gas convective heat transfer predominates as the particle surface area decreases. Figure 11 demonstrates how heat transfer varies with pressure and velocity for the different types of particles (23). As superficial velocity increases, there is a sudden jump in the heat-transfer coefficient as gas velocity exceeds and the bed becomes fluidized. 

Space Velocity. The space velocity is the ratio of the volumetric rate of gas at standard conditions to the volume of the catalyst. Generally, the percentage of ammonia in the existing gas decreases as space velocity increases however, the same volume of catalyst at the increased space velocities is capable of producing more ammonia (Fig. 4) (27). Normally space velocities for commercial operations are between 8,000 and 60, 000 h . ... 

Cavitation. The subject of cavitation in pumps is of great importance. When the Hquid static pressure is reduced below its vapor pressure, vaporization takes place. This may happen because (/) the main stream fluid velocity is too high, so that static pressure becomes lower than vapor pressure (2) localized velocity increases and static pressure drops on account of vane curvature effect, especially near the inlets (J) pressure drops across the valve or is reduced by friction in front of the pump or (4) temperature increases, giving a corresponding vapor pressure increase. 

Cryoelectronics. Operation of CMOS devices at lower temperatures offers several advantages and some disadvantages (53). Operation at Hquid nitrogen temperatures (77 K) has been shown to double the performance of CMOS logic circuits (54). In part, this is the result of the increase in electron and hole mobilities with lower temperatures. The mobiHty decreases at high fields as carrier speeds approach saturation. Velocity saturation is more important for cryoelectronics because saturation velocities increase by only 25% at 77 K but saturation occurs at much lower fields. Although speedup can... 

J ct Spra.y, The mechanism that controls the breakup of a Hquid jet has been analy2ed by many researchers (22,23). These studies indicate that Hquid jet atomisation can be attributed to various effects such as Hquid—gas aerodynamic interaction, gas- and Hquid-phase turbulence, capillary pinching, gas pressure fluctuation, and disturbances initiated inside the atomiser. In spite of different theories and experimental observations, there is agreement that capillary pinching is the dominant mechanism for low velocity jets. As jet velocity increases, there is some uncertainty as to which effect is most important in causing breakup. 

Early models used a value for that remained constant throughout the day. However, measurements show that the deposition velocity increases during the day as surface heating increases atmospheric turbulence and hence diffusion, and plant stomatal activity increases (50—52). More recent models take this variation of into account. In one approach, the first step is to estimate the upper limit for in terms of the transport processes alone. This value is then modified to account for surface interaction, because the earth s surface is not a perfect sink for all pollutants. This method has led to what is referred to as the resistance model (52,53) that represents as the analogue of an electrical conductance... 

Fig. 7. Crack velocity as a function of the applied stress intensity, Kj. Water and other corrosive species reduce the Kj required to propagate a crack at a given velocity. Increasing concentrations of reactant species shifts curve upward. Regions I, II, and III are discussed in text.

An increases in space velocity increases the ethanol production rate, but at the expense of incurring higher recycling costs. 

Cavitation Loosely regarded as related to water hammer and hydrauhc transients because it may cause similar vibration and equipment damage, cavitation is the phenomenon of collapse of vapor bubbles in flowing liquid. These bubbles may be formed anywhere the local liquid pressure drops below the vapor pressure, or they may be injected into the hquid, as when steam is sparged into water. Local low-pressure zones may be produced by local velocity increases (in accordance with the Bernouhi equation see the preceding Conservation Equations subsection) as in eddies or vortices, or near bound-aiy contours by rapid vibration of a boundaiy by separation of liquid during water hammer or by an overaU reduction in static pressure, as due to pressure drop in the suction line of a pump. 

Flow Pattern In a cyclone the gas path involves a double vortex with the gas spiraling downward at the outside and upward at the inside. When the gas enters the cyclone, its velocity undergoes a redistribution so that me tangential component of velocity increases with decreasing radius as expressed by The spiral velocity in a... 

Erosion-corrosion is a fairly complex failure mode influenced by both environmental factors and metal characteristics. Perhaps the most important environmental factor is velocity. A threshold velocity is often observed below which metal loss is negligible and above which metal loss increases as velocity increases. The threshold velocity varies with metal and environment combinations and other factors. 

In most solids, the sound speed is an increasing function of pressure, and it is that property that causes a compression wave to steepen into a shock. The situation is similar to a shallow water wave, whose velocity increases with depth. As the wave approaches shore, a small wavelet on the trailing, deeper part of the wave moves faster, and eventually overtakes similar disturbances on the front part of the wave. Eventually, the water wave becomes gravitationally unstable and overturns. 

For a shock wave in a solid, the analogous picture is shown schematically in Fig. 2.6(a). Consider a compression wave on which there are two small compressional disturbances, one ahead of the other. The first wavelet moves with respect to its surroundings at the local sound speed of Aj, which depends on the pressure at that point. Since the medium through which it is propagating is moving with respect to stationary coordinates at a particle velocity Uj, the actual speed of the disturbance in the laboratory reference frame is Aj - -Ui- Similarly, the second disturbance advances at fl2 + 2- Thus the second wavelet overtakes the first, since both sound speed and particle velocity increase with pressure. Just as a shallow water wave steepens, so does the shock. Unlike the surf, a shock wave is not subject to gravitational instabilities, so there is no way for it to overturn. 

Since the dislocation drag coefficient B represents the transfer of momentum per unit area, we assume that B/m remains constant as the velocity increases and hence... 

In the long term, filters and strainers become clogged this is their purpose. Minerals and scale start forming on the internal pipe walls and this reduces the interior diameters on the pipe. A 4 inch pipe will eventually become a 3.5 inch pipe. This moves the pump on its curve beeause as the pipe diameter reduces, the velocity must increase to maintain flow through a smaller orifice. The Hf and Hv increase by the square of the velocity increase. 

In biphase systems velocity of the steam is often 10 times the velocity of the liquid. If condensate waves rise and fill a pipe, a seal is formed with the pressure of the steam behind it (Fig. 2). Since the steam cannot flow through the condensate seal, pressure drops on the downstream side. The condensate seal now becomes a piston accelerated downstream by this pressure differential. As it is driven downstream it picks up more liquid, which adds to the existing mass of the slug, and the velocity increases. 

Once a fluid starts to move in a conduit, shearing forces are set up, the maximum being at the wall of the conduit. At this surface the velocity is at the lowest, while in adjacent layers above this surface the velocity increases as the shearing stresses decrease. 

---