Critical discharge rate

Relationship Among Critical Discharge Rate, Pressure Propagation Rate, and Sonic Velocity... 

The critical mass flux is thus = G/hg, Pg, S). The Moody model (1965) is based on maximizing specific kinetic energy of the mixture with respect to the slip ratio whereas the Fauske model (1961, 1965) is based on the flow momentum with respect to the slip ratio. In Figure 22.18, the critical discharge rate of water at various stagnation pressure and enthalpy with Fauske slip model is shown. 

Another reason why the outlet region is so important is that it directly affects the maximum discharge rate achievable from the hopper. No matter whether critical discharge is calculated using Equation (2.3) or is limited by fine powder flow, critical discharge rates vary more or less linearly with outlet area. 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

To be consistent with a mass flow pattern in the bin above it, a feeder must be designed to maintain uniform flow across the entire cross-sectional area of the hopper outlet. In addition, the loads appHed to a feeder by the bulk soHd must be minimised. Accuracy and control over discharge rate ate critical as well. Knowledge of the bulk soHd s flow properties is essential. 

Back pressure reduces the pressure drop across the orifice of any type of PR valve. This results in reduced discharge rates in the case of vapors, if the back pressure exceeds the critical flow pressure. For liquids, any back pressure reduces the pressure drop and results in a lower discharge rate. 

We shall first consider the case of non-flashing liquids. In this situation, there is no critical flow pressure limiting the flow of liquid through a PR valve orifice, as opposed to the case of vapor flow. The discharge rate is a function of the pressure drop across the valve and can be estimated by the following expression ... 

When it is desired to determine the discharge rate through a nozzle from upstream pressure p0 to external pressure p2, Equations (6-115) through (6-122) are best used as follows. The critical pressure is first determined from Eq. (6-119). If p2 > p , then the flow is subsonic (subcritical, unchoked). Then p, = p2 and M, may be obtained from Eq. (6-115). Substitution of Mx into Eq. (6-118) then gives the desired mass velocity G. Equations (6-116) and (6-117) may be used to find the exit temperature and density. On the other hand, if p2< p , then the flow is choked and M = 1. Then j> = p , and the mass velocity is G obtained from Eq. (6-122). The exit temperature and density may be obtained from Eqs. (6-120) and (6-121). 

Determining the maximum fluid flow rate or pressure drop for process design often has the dominant influence on density. As pressure decreases due to piping and component resistance, the gas expands and its velocity increases. A limit is reached when the gas or velocity cannot exceed the sonic or critical velocity. Even if the downstream pressure is lower than the pressure required to reach sonic velocity, the flow rate will still not increase above that evaluated at the critical velocity. Therefore, for a given AP, the mass discharge rate through a pipeline is greater for an adiabatic condition (i.e., insulated pipes, where heat transfer is... 

By differentiating Eq. (7.21) with respect to w and setting the result equal to zero the pressure ratio for the maximum discharge rate, the critical pressure ratio, Worit., is obtained... 

The maximum of the discharge mass flow rate is calculated in a stepwise fashion, since the mass flow rate is limited by the speed of sound (critical discharge). We use... 

Most column extraction processes operate with a solvent of lower density than the aqueous phase and discrete solvent drops are usually allowed to ascend in the continuous aqueous medium, with an interface near the top of the column. Aqueous phase enters just below the interface and solvent phase is fed via the first distributor at the base of the column. Flooding of the column takes place at certain critical flow rates. This phenomenon arises when, for example, the flow rate of the dispersed phase is unduly increased with a constant flow of continuous phase. The additional column hold-up of dispersed phase leaves less space for continuous phase and therefore the linear velocity of the continuous phase is increased. A tendency to drag the dispersed phase droplets in the direction of the continuous phase thus arises. When the flooding point is reached, the dispersed phase is discharged along with the continuous phase and counter-current flow ceases. 

Larger devices may have higher series voltages but also higher capacities, higher charge and discharge rates, and therefore more critical safety limits. 

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