Froude number for the liquid phase

The Froude number for the liquid phase is given by Equation 2-7. 

The computer program PROG36 calculates the Froude numbers for the liquid and vapor phases. In addition, PROG36 will determine whether the pipe is self venting or whether pulsation flow is encountered. Table 3-13 shows the results for the 2-, 4-, and 6-inch (Schedule 40) pipes. Table 3-14 gives a typical input data and computer output for the 2-inch (Schedule 40) pipe. 

The following equations will calculate Froude numbers for both the liquid and gas phases. The computer program will print out a message indicating whether the vertical pipe is self-venting, whether pulsating flow occurs, or whether no pressure gradient is required. 

The effect of various parameters on the difference between vapor and liquid pressure is illustrated in Figs. 8.3 and 8.4. The effect of the Fuler and Weber numbers as well as the thermal parameter is highly noticeable. An increase in Fu, We and d- leads to a decrease in AP, whereas the difference of both phase pressures is practically independent of Reynolds number. An increase in the Froude number is accompanied by an increase in AP for a small Fr. At Fr > 10 the effect of Fr on AP is negligible. 

When two liquids are immiscible, the design parameters include droplet size distribution of the disperse phase, coalescence rate, power consumption for complete dispersion, and the mass-transfer coefficient at the liquid-liquid interface. The Sauter mean diameter, dsy, of the dispersed phase depends on the Reynolds, Froudes and Weber numbers, the ratios of density and viscosity of the dispersed and continuous phases, and the volume fraction of the dispersed phase. The most important parameters are the Weber number and the volume fraction of the dispersed phase. Specifically, dsy oc We 06(l + hip ), where b is a constant that depends on the stirrer and vessel geometry and the physical properties of the system. Both dsy and the interfacial area aL remain unaltered, if the same power per unit volume (P/V) is used in the scale-up. 

Laity and Treybal (LI) report on experiments with a variety of two-phase systems in a covered vessel which was always run full, so that there was no air-liquid interface at the surface of the agitated material. Under these circumstances no vortex was present, even in the case of operation without baffles. Mixing Equipment Company flat-blade disk-turbines were used in 12- and 18-in. diameter vessels whose heights were about 1.07 times their diameters. Impeller diameter was one-third of tank diameter in each case. For operation without baffles, using only one liquid phase, the usual form of power-number Reynolds-number correlation fit the data, giving a correlation curve similar to that given in Fig. 6 for disk-turbines in unbaffled vessels. In this case, however, the Froude number did not have to be used in the correlation because of the absence of a vortex. For two-phase mixtures, Laity and Treybal could correlate the power consumption results for unbaffled operation by means of the same power number-Reynolds number correlation as for one-phase systems provided the following equations were used to calculate the effective mean viscosity of the mixture For water more than 40% by volume ... 

The Froude number wiU be evaluated to determine the suitability of horizontal flow. The pressure drop will then be calculated for both the gas phase and liquid phase flowing separately in the empty pipe. The pressure drop for the combined flow streams will then be determined using the method of Lockhart and Martinelli. Finally, the mixer pressure drop will be determined using the multiplier of the empty pipe pressure drop reported for the SMV mixer specified. 

For two-phase dispersions, other groups such as the iVeber number We = pu dp/ag, the ratio of inertial to surface forces, may be significant. Sherwood and Schmidt numbers are of course important in mass transfer. For dynamic similarity in two sizes of vessels operated with a vortex, the Reynolds and Froude numbers must be the same for both vessels. Since the impellers would be geometrically similar but unequally sized, it becomes impossible to specify the impeller speeds in the two vessels containing the same liquid to accomplish this. Thus, equal Reynolds numbers require... 

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