Entrainment defined

Entrainment, defined by Eq. (6.30), lb-mole of liquid entrained/lb-mole of liquid flow on the tray. 

In a free jet the absence of a pressure gradient makes the momentum flux at any cross section equal to the momentum flux at the inlet, ie, equations 16 and 17 define jet velocity at all points. For a cylindrical jet this leads to a center-line velocity that varies inversely with (x — aig), whereas for slot jets it varies inversely with the square root of (x — Xq As the jet proceeds still further downstream the turbulent entrainment initiated by the jet is gradually subordinated to the turbulence level in the surrounding stream and the jet, as such, disappears. 

The generated water vapor rises through a screen (demister) placed to remove entrained saline water droplets. Rising further, it then condenses on the condenser tube bank, and internal heat recovery is achieved by transferring its heat of condensation to the seawater feed that is thus being preheated. This internal heat recovery is another of the primary advantages of the MSF process. The energy performance of distillation plants is often evaluated by the performance ratio, PR, typically defined as... 

Fig. 18. Separation of ethanol from an ethanol—water—benzene mixture using benzene as the entrainer. (a) Schematic representation of the azeo-column (b) material balance lines where I denotes the homogeneous and the heterogeneous azeotropes D, the end points of the Hquid tie-line and A, the overhead vapor leaving the top of the column. The distillate regions, I, II, and III, and the boundaries are marked. Other terms are defined in text.

For distillations, it is often of more interest to ascertain the effect of entrainment on efficiency than to predic t the quantitative amount of liquid entrained. For this purpose, the correlation shown in Fig. 14-26 is useful. The parametric curves in the figure represent approach to the entrainment flood point as measured or as predicted by Fig. 14-25 or some other flood correlation. The abscissa values are those of the flow parameter discussed earher. The ordinate values y are fractions of gross hquid downflow, defined as follows ... 

The sources of air pollution are nearly as numerous as the grains of sand. In fact, the grains of sand themselves are air pollutants when the wind entrains them and they become airborne. We would class them as a natural air pollutant, which implies that such pollution has always been with us. Natural sources of air pollution are defined as sources not caused by people in their activities. 

Economic considerations dictate that a commercial fluid bed operates at as high a gas velocity as practicable. A frequent limiting factor is entrainment from the bed which is a very strong ftmction of gas velocity. A well defined fluid bed can be maintained even at gas velocities well in excess of the free fall velocity of the biggest particles... 

For a given particle of size d, from the point M where the equilibrium line meets the line of zero vertical velocity (see Fig. 13.4), the critical path of the particle may be defined. All particles of this size between points D and G are entrained in the downward stream and are collected. The remaining particles of this size join in the upward-moving stream of fluid and penetrate the cyclone. The point D may be obtained by tracking back the particle trajectory from the point M using the equation of the particle trajectory, which is given by... 

Nq is strongly dependent on the flow regime, Reynolds Number, N e, and installation geometi y of the impeller. The flow from an impeller is only that produced by the impeller and does not include the entrained flow, which can be a major part of the total motion flow from the impeller. The entrained flow refers to fluid set in motion by the turbulence of the impeller output stream [27]. To compare different impellers, it is important to define the t -pe of flows being considered. 

E = superficial liquid entrainment rate, Ib/hr/ff Fj, Fj = correlation factors defined by equations... 

The operational window of a fluidised bed process is defined by the minimum fluidisation velocity, Uml, at which a settled bed of adsorbent beads starts to fluidise and the terminal velocity ( /t) at which the bed stabilises and adsorbent beads are entrained from the bed. 

For preliminary design, liquid entrainment is usually used as a reference. To prevent entrainment, the vapor velocity for tray columns is usually in the range 1.5 to 3.5 ms-1. However, the entrainment of liquid droplets can be predicted using Equation 8.3 to calculate the settling velocity. To apply Equation 8.3 requires the parameter KT to be specified. For distillation using tray columns, KT is correlated in terms of a liquid-vapor flow parameter FLV, defined by ... 

Bottom Product B with a straight line joining the Distillate D and Entrainer Feed E, as shown in Figure 12.24. Pinch point curves for the middle section can now be constructed by drawing tangents to the residue curves from the difference point (net overhead product). This is shown in Figure 12.25 for the system ethanol-water-ethylene glycol. The area bounded by the pinch point curves defines the middle section operation leaf. 

In circumstances when entrained bubbles are present during devolatilization, considerable ambiguity can exist with regard to the physical significance of the mass transfer coefficients. If the mass transfer coefficient is defined, or measured, in the usual way [Eq. (43)], the rate at which mass is transferred is not in any way related to diffusional processes but instead is a measure of the rate at which bubbles are rupturing or being released from solution. Thus,... 

An interesting study of entrainment from horizontal liquid films has also been carried out by Van Rossum (VI). On the basis of a liquid film in laminar flow with a flat and smooth surface, he found that the mean actual film thickness was about 0.6 times the theoretical one. The critical Weber number corresponding to the onset of atomization was determined for five different liquids, with Weber number defined as... 

Figure 11.3 shows the entrainment flux measured at the outlet of the unit and the fines weight fraction (defined as particle sizes smaller than 44 microns) for the bed and entrained material as a function of time. As the fines concentration began to decrease in the bed, the entrainment rate increased rapidly to a peak approximately 10 times the initial rate. Further depletion of fines from the bed resulted in a subsequent drop in the entraimnent rate. For the commercial unit, the highly variable entrainment rates appeared to be due to the extreme sensitivity to the fines concentration. The dipleg was not designed to handle the presumed tenfold increase in the entrainment rate and often flooded as a result. 

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