Velocity ratio

However, is dependent on the ratio of hole diameter to pipe diameter, pipe wall thickness to hole diameter ratio, and pipe velocity to hole velocity ratio. As long as all these are small, the coefficient 0.62 is generally adequate. 

FIG. 18-85 Depth correction factorto he applied to unit areas determined with Wilhelm-Naide and direct methods. Velocity ratio calculated using tangents to settling cun e at a particular settled solids concentration and at start of test. 

Find the equilibrium, homogeneous specific volume v given by Eq, (26-85) and estimate the slip velocity ratio using the following correlation ... 

The velocity ratio is the single most important factor in determining the performance of an expander. The velocity ratio, p, is a dimensionless parameter, relating the physical size of the expander to the gas conditions being considered. It is defined as ... 

The velocity ratio parameter is determined by relating the expander blade speed and the equivalent velocity energy available, which in turn enables determining the expander stage efficiency. 

From Equation 4-1, it can be seen that the velocity ratio can be changed by ... 

Figure 4-110 depicts an efficiency curve versus velocity ratio for a reaction-type expander. The optimum efficiency will occur at a velocity ratio of. 63. For a velocity ratio considerable greater or less than. 63 a significant efficiency penalty can be expected. Considering the effects on the parameters mentioned above, it is easy to see the importance the velocity ratio has on the performance of the expander. 

The previous discussion of the velocity ratio parameter looked at the effect the available energy has on expander efficiency. The examples listed in Table 4-11 furdier illustrate diis effect. 

As mentioned earlier, because the number of stages has a significant effect in determining the velocity ratio, consider the effect the gas conditions have in determining tlie optimum number of stages. To make this determination, the following parameters should be considered ... 

Again, the importance of the velocity ratio can be seen because its effect is squared in this equation. 

Figure 4-116. Optimum velocity ratio for expander stage.

Figure 7-13. Stage efficiency vs. velocity ratio. (Courtesy of Elliott Company)...

Ar, Re, Pr, Sc, and v] are called the Archimedes number, Reynolds number, Prandtl number, Schmidt number, and the settling velocity ratio, respectively. 

Kinematic similarity requires geometric similarity and requires corresponding points in the system to have the same velocity ratios and move in the same direction between the new system and the model. 

The solids particle velocity in the gas-solid two-phase jet can be calculated as shown in Eq. (27), assuming that the slip velocity between the gas and the solid particles equals the terminal velocity of a single particle. It should be noted that calculation of jet momentum flux by Eq. (26) for concentric jets and for gas-solid two-phase jets is only an approximation. It involves an implicit assumption that the momentum transfer between the concentric jets is very fast, essentially complete at the jet nozzle. This assumption seems to work out fine. No further refinement is necessary at this time. For a high velocity ratio between the concentric jets, some modification may be necessary. 

Denote the superficial liquid-solids velocity ratio (.L/pfA)/(S/psA) by N, and let (S/psut) =At. which is the minimal cross-sectional area if the solids were to flow at their terminal velocity, up in the absence of fluid flow, and can, therefore, be called terminal cross-sectional area. Then Eq. (2) can be reduced to a dimensionless form in terms of a reduced area, A, defined as follows... 

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