Velocity upward

Fluidized This is an expanded condition in which the sohds particles are supported by drag forces caused by the gas phase passing through the interstices among the particles at some critical velocity. It is an unstable condition in that the superficial gas velocity upward is less than the terminal setting velocity of the solids particles the gas... 

A high vapour velocity upwards tends to increase the thickness of the film and thus reduce h though the film may sometimes be disrupted mechanically as a result of the formation of small waves. For the downward flow of vapour, TEN Bosch<5 9 has shown that h increases considerably at high vapour velocities and may increase to two or three times the value given by the Nusselt equation. It must be remembered that when a large... 

When Dd given by Eq. (12-26) is equal to Dd max given by Eq. (12-30), the vapor velocity is absolutely the highest which can be tolerated. For instance, if the vapor velocity is increased, the droplets will have a positive velocity upward or the droplets that were of the maximum diameter will now rupture. Thus, the intersection of the two curves in Fig. 12-12 represents the absolute maximum... 

Fig. 6. Apparent isopotential specific volume, 2 (in cm g ), and buoyancy term, (1 - (j>2 Ps) of lactate dehydrogenase as a function of the molar concentration, C3, of phosphate buffer (K2HPO4/KH2PO4 buffer pH 7.0). From [83D1]. Specific volumes were obtained by digital densimetry (circles), sedimentation velocity (upward triangles), and sedimentation equilibrium (downward triangles). Filled and open symbols refer to 2 and (1 - 2 Ps)> respectively. Experimental details can be found in the reference. Reprinted from International Journal of Biological Macromolecules, Vol. 5, H. Durchschlag and R. Jaenicke, Partial specific volume changes of proteins ultracentrifugal and viscometric studies, pp. 143-148, 1983, with...

Another suspended growth method is the upward-flow anaerobic sludge blanket illustrated in Fig. 11.6a. Here the sludge is contacted by upward flow of the feed at a velocity such that the sludge is not carried out of the top of the digester. 

Using now the phase matching condition, it can be seen that besides the quasi shear wave (qSV) which is obtained as usual, a second quasi shear wave (qSV(2)) results from the upper quasi shear wave part. Since the direction of the group velocity vector points downwards this wave is able to propagate and can be seen in the snapshot (see Fig. 10) if a is properly adjusted, i.e. is pointing upwards as in Fig. 2. 

Terminal Velocity. The single-particle terminal velocity, U, is the gas velocity required to maintain a single particle suspended in an upwardly flowing gas stream. A knowledge of terminal velocity is important in fluidized beds because it relates to how long particles are retained in the system. If the operating superficial gas velocity in the fluidized bed far exceeds the terminal velocity of the bed particles, the particles are quickly removed. 

Jet Penetration. At the high gas velocities used in commercial practice, there are jets of gas issuing from distributor holes. It is essential that jets not impinge on any internals, otherwise the internals may be quickly eroded. Figure 14 is a graphical correlation used to determine the jet penetration length as a function of gas velocity and gas density. Jets from horizontal and downflow holes are considerably shorter than those that are pointed upward. 

The upward flow of gas and Hquid in a pipe is subject to an interesting and potentially important instabiHty. As gas flow increases, Hquid holdup decreases and frictional losses rise. At low gas velocity the decrease in Hquid holdup and gravity head more than compensates for the increase in frictional losses. Thus an increase in gas velocity is accompanied by a decrease in pressure drop along the pipe, a potentially unstable situation if the flows of gas and Hquid are sensitive to the pressure drop in the pipe. Such a situation can arise in a thermosyphon reboiler, which depends on the difference in density between the Hquid and a Hquid—vapor mixture to produce circulation. The instabiHty is manifested as cycHc surging of the Hquid flow entering the boiler and of the vapor flow leaving it. 

The fluidized-bed bioreactor (FBBT) (26) increases the capacity of existing plants. Primary effluent is passed upward through the columnar reactor filled with sand or carbon with sufficient velocity to fluidize the bed. An attached biomass develops on the bed particles. Intimate contact between the biomass and waste is provided and improved removals are reported. Oxygen is provided by a deep U-tube reactor. No biomass recirculation is required and a secondary clarifier is not necessary. 

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.

The Two-Shell Veloeity ProHle. A second simple velocity profile (41) is shown ia Figure 14b ia which the flow consists of two thin streams, one situated at radius flowing upward, and the other situated at the wall (r = flowing downward. For this case the values of the separation parameters are... 

Fluid statics, discussed in Sec. 10 of the Handbook in reference to pressure measurement, is the branch of fluid mechanics in which the fluid velocity is either zero or is uniform and constant relative to an inertial reference frame. With velocity gradients equal to zero, the momentum equation reduces to a simple expression for the pressure field, Vp = pg. Letting z be directed vertically upward, so that g, = —g where g is the gravitational acceleration (9.806 mVs), the pressure field is given by... 

Ripple flow has an upward-moving wavy layer of liquid on the pipe wall it may be thought of as a transition region to annular, annular mist, or film flow, in which gas flows in the core of the pipe while an anniilus of hquid flows up the pipe wall. Some of the liquid is entrained as droplets in the gas core. Mist flow occurs when all the liquid is carried as fine drops in the gas phase this pattern occurs at high gas velocities, typically 20 to 30 m/s (66 to 98 ft/s). 

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