Liquid Velocities

Z. 5-25-Y, large huhhles = AA = 0.42 (NG..) Wi dy > 0.25 cm Dr luterfacial area 6 fig volume dy [E] Use with arithmetic concentration difference, ffg = fractional gas holdup, volume gas/total volume. For large huhhles, k is independent of bubble size aud independent of agitation or liquid velocity. Resistance is entirely in liquid phase for most gas-liquid mass transfer. [79][91] p. 452 [109] p. 119 [114] p. 249... 

Vl = liquid velocity in the drain pipe Pl = liquid density Pg = g3.s density D = pipe inside diameter h = liquid height... 

AV = change in liquid velocity a = pressure wave velocity... 

The drag force is exerted in a direction parallel to the fluid velocity. Equation (6-227) defines the drag coefficient. For some sohd bodies, such as aerofoils, a hft force component perpendicular to the liquid velocity is also exerted. For free-falling particles, hft forces are generally not important. However, even spherical particles experience lift forces in shear flows near solid surfaces. 

In the second technique, the flowing liquid must contain scatters in the form of particles or bubbles that will reflect the sound waves. These scatters should be travehng at the velocity of the hquid. A Doppler method is applied by transmitting sound waves along the flow path and measuring the frequency shift in the returned signal from the scatters in the process fluid. This frequency shift is proportional to liquid velocity. 

Shirato, Gotoh, Osasa, and Usami [J. Chem. Eng. Japan, 1, 164— 167 (January 1968)] present a method for determining the mass flow rate of suspended sohds in a liqiiid stream wherein the liquid velocity is measured By an electromagnetic flowmeter and the flow of sohds is calculated from the pressure drops across each of two vertical sections of pipe of different diameter through which the suspension flows in series. 

Certain pump designs use an internal bypass orifice port to alter head-flow curve. High liquid velocities often erode the orifice, causing the pump to go farther out on the pump curve. The system head curve increase corrects the flow back up the curve. 

Ue = liquid velocity relative to the gas, often approximately the terminal velocity of droplets (see Sec. 6 lor estimation) L/g = superficial gas velocity = droplet diameter... 

It is often helpful to use the relationship between and superficial gas velocity (t/sg) and the rise velocity of a gas bubble relative to the liquid velocity (U + Ui, with L/l defined as positive upward) ... 

The incremental pressure drop for wet mesh is not available for all operating conditions or for mesh of different styles. The data of York and Poppele for wet-mesh incremental pressure drop, APi in cm of water, are shown in Fig. 14-122 or parameters of liquid velocity L/A, defined as liquid volumetric flowrate, cmVmin per unit of mesh cross-sectional area in cm" liqiiid density Pl is in g/cm. ... 

Limit liquid velocity to minimize static buildup... 

Increasing either the gas velocity or the liquid droplet velocity in a scrubber will increase the efficiency because of the greater number of collisions per unit time. The ultimate scrubber in this respect is the venturi scrubber, which operates at extremely high gas and liquid velocities with a very high pressure drop across the venturi throat. Figure 29-8 illustrates a commercial venturi scrubber unit... 

Clear liquid velocity (ft/sec) through the downcomer is then found by multiplying DL by 0.00223. The correlation is not valid if Pl - pv is less than 301b/ft (very high pressure systems). For foaming systems, DL should be multiplied by 0.7. Frank recommends segmental downcomers of at least 5% of total column cross-sectional area, regardless of the area obtained by this correlation. 

Because pore sizes in the cake and filter medium are small, and the liquid velocity through the pores is low, the filtrate flow may be considered laminar hence, Poiseuille s law is applicable. Filtration rate is directly proportional to the difference in pressure and inversely proportional to the fluid viscosity and to the... 

Wells, S. A. and Dick, R. I. (1993) "Permeability, Solid and Liquid Velocity, and Effective Stress Variations in Compressible Cake Filtration," Proceedings, American Filtration Society Conference on System Approach to Separation and Filtration Process Equipment, Chicago, Illinois, May 3-6, pp. 9-12... 

By comparing the gravity force acting on the particle (equation 24) with the resistance to liquid flow (equation 22), we obtain the average liquid velocity relative to the particles ... 

In practice, however, the liquid velocity relative to fixed particles, Uf, is not very useful. Instead, the velocity of settling relative to the walls of an apparatus, Uf - u, is of practical importance. The volume of the solid phase moving downward should be equal to that of liquid moving upward. This means that volume rates of these phases must be equal. Consider a column of slurry having a unit cross section and imagine the liquid and solid phases to have a well defined interface. The column of solid phase will have a base 1 - e, and the liquid column phase will have a base e. Hence, the volumetric rate of the solid column will be (1 - e)u, and that of the liquid column will be (Uf - u)e. Because these flowrates are equal to each other, we obtain... 

Therefore, the settling velocity of the solid phase relative to the wall of an apparatus, depending on the average liquid velocity relative to the sludge with void fraction e, will be... 

In the TMB model, the adsorbent is assumed to move in plug flow in the opposite direction of the fluid, while the inlet and outlet lines remain fixed. As a consequence, each column plays the same function, depending on its location. An equivalence between the TMB and the SMB models can be made by keeping constant the liquid velocity relative to the solid velocity, i.e., the liquid velocity in the TMB is ... 

The Van Deemter curve (HETP vs fluid velocity) is estimated from the two analytical chromatograms. At a flow rate of 1 ml min the liquid velocity is 0.001 m s the number of theoretical plates associated to the second peak is about 250. The... 

At = Temperature rise, °F AT,. = Temperature rise, °F/rain t = Piston speed or travel, ft/min V = Liquid velocity, ft/sec v = Average velociry, ft/sec W = Width of channel vtith series pump, ft Wj = Weight of liquid in pump, lb whp = Water or liquid horsepower... 

Table 8-20 gives suggested downcomer clear liquid velocities based on relative foaming characteristics of the fluid on the tray at tray conditions. 

System Foaming Characteristics Allowable Clear Liquid Velocities, ft/sec High Medium Low... 

Let the liquid velocity under the downcomer equal the liquid velocity on the tray to give a smooth entry [237]. 

From the residence time in dorvneomers for bubble cap trays, and at the very low tray spacing of 9 inches, select an allowable liquid velocity of 0.1 ft/sec. 

Liquid velocity based on superficial tower area, gpm/ft2... 

The mechanism of boiling is essentially nucleate pool hoiling. In hoth styles of rehoiler the liquid velocity is relatively low compared to thermosiphon units. Jacobs provides an extensive comparison of advantages and disadvantages of essentially all the reboiler types used in industrial plants. Palen and Taborek conducted extensive studies of available data and proposed nucleate boiling equations to correlate various data from the available 14 equations down to a selected 6 for detailed study. The study was limited to various hydrocarbons and hydrocarbon mixtures. Their conclusions after computer correlations of the results from several equations were as follows. 

An overall heat transfer coefficient, U, for the usual operating range is 200-230 Btu/hr (ft ) °F, with liquid velocities in shell between 2-4 ft/sec. 

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