Critical flow factor

Choose the valve type and determine its critical-flow factor for the cavitation situation. If... 

TABLE 19.2 Critical Flow Factors for Control Valves at 100 percent Lift... 

Here, a concept of critical flow factor of equipment (FFC), proposed by Walker (1966), is used to evaluate the flowability of the powder-equipment system ... 

Substituting Eq. (77) and Eq. (80) into Eq. (81) gives the critical flow factor for a cylindrical dipleg,... 

It can be seen from Eq. (82) that the critical flow factor is a constant and depends on the properties of the powder and the pipe wall. Another concept of flow factor (FF) proposed by Jenike (1964) is then used to evaluate the flowability of the powder ... 

Figure 25 illustrates a case where the powder flow factor locus (FF) lies in part above and part below a critical flow factor locus (FFc). When the powder flow factor locus lies below the (FFc) locus in the graph, then the powder flow factor (FF) is desirably high, but when the powder flow factor locus is above the (FFc) line, its flow factor is less than (FFc) and arching can occur. If we let the critical value of A at the crossover point be /a, then to ensure no arching the radius Rc should be given by Eq. (84) such that... 

An ideal gas is completely defined by the gas constant (R) and isentropic index (7). For any such gas a critical flow factor (ij/) can be found assuming onedimensional isentropic mass flow (m ) through a minimum section or throat (A ) ... 

Equation 5-29 is valid for liquid flowing below its saturation temperature in the turbulent zone with a viscosity value that is close to that of water and size of pipe. Also, the control valve must be the same. Equation 5-29 can also be applied, if the vapor pressure of the liquid at the flowing temperature is equal to or less than one-half the upstream pressure. Eor this case, the vapor pressure of the liquid is substituted for downstream pressure, P2 and the valve coefficient is calculated. The calculated must be corrected by a critical flow factor, Cj, where C corr is defined by... 

If the superimposed back pressure is less than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is unaffected and back pressure is not a factor. However, builtup back pressure on a conventional pressure relief valve will affect its flow capacity and operating characteristics, and should not exceed 100% of its set pressure. If total back pressure (superimposed plus built-up) is greater than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is affected, and total back pressure is incorporated into the sizing procedure. Any back pressure reduces the capacity of a conventional PR valve in liquid service, and... 

All relief valves are affected by reaching critical flow, which corre-spond.s to a back-pressure of about 50% of the set pressure. Pilot-operated relief valves can handle up to 50% back-pressure without any significant effect on valve capacity. Back-pressure correction factors can be obtained from the relief valve manufacturers for back-pre.ssures above 50%. API RP 520 gives a generic method for sizing a pilot-operated relief valve for sub-critical flow. 

Note The curves above represent a compromise of the values recommended by a number of relief valve manufacturers and may be used when the make of the valve or the actual critical f ow pressure point for the vapor or gas is unknown. When the make is known, the manufacturer should be consulted tor the correction factor. These curves are for set pressures of 50 pounds per square inch gauge and above. They are limited to back-pressure below critical flow pressure for a given set pressure. For subcntical flow back-pressures below 50 pounds per square inch gauge, the rnanufacturer must be consulted tor values of Kk. 

Six-tenths factor, 47 Yearly cost indices, 47 Critical flow, safety-relief, 438 Back pressure, 440 Sonic flow, 438 Critical flow, see Sonic Cyclone separators, 259-269 Design, 260-265 Efficiency chart, 263 Hydroclones, 265-267 Pressure drop, 263, 264 Scrubber, 269 Webre design, 265 Deflagration venting nomographs,... 

Xu and Ruppel (1999) solved the coupled mass, heat, and momentum equations of change, for methane and methane-saturated fluxes from below into the hydrate stability region. They show that frequently methane is the critical, limiting factor for hydrate formation in the ocean. That is, the pressure-temperature envelope of the Section 7.4.1 only represents an outer bound of where hydrates might occur, and the hydrate occurrence is usually less, controlled by methane availability as shown in Section 7.4.3. Further their model indicates the fluid flow (called advection or convection) in the amount of approximately 1.5 mm/yr (rather than diffusion alone) is necessary to produce significant amount of oceanic hydrates. 

However, never confuse the lift of the valve with its capacity, as even a perfect convergent/divergent nozzle s flow rate is reduced beyond the medium s critical pressure ratio, as shown in the graph in Figure 5.40. In principle, a perfect nozzle has a KD (flow factor) = 1. 

Unlike European norms, API 520 has always published typical backpressure correction factors in its code. These curves serve only as a guide and represent a sort of average for a number of manufacturers. API states that they can be used when the make of the valve is unknown (which is rather unlikely) or for gases and vapours when the critical flow pressure point is unknown. 

As a side note, it needs to be noticed that the backpressure correction factors given by API 520 are for pressures above 3.45 Barg (50 psig) only and that they are limited to backpressures below critical flow pressure for a given pressure. For everything below 3.45 Barg, the manufacturer should in any case be contacted. 

For preliminary estimates, the coefficient Kj can be taken as 0.975 for a relief valve and 0.62 for a bursting disk. The back-pressure correction factor, Ky, can initially be assumed to be 1.0 for critical flow. The combination correction factor, K, is used when a rupture disk is used upstream of the relief valve (see next section), in which case it is 0.9. If no rupture disk is used, then is 1.0. For vessels designed in accordance with AS ME BPV Code Sec. VIII, Pj = 1.1 times the maximum allowable working pressure. 

With the exponential increase in information flow resulting from the ability to make many more compounds and test these in multiple assays, the capture, analysis, and management of data is a critical success factor in drug discovery. 

The transition from laminar to turbulent flow in a non-Newtonian fluid depends on the rheological model used to describe it. The concepts of a critical friction factor or critical Reynolds number have been used to define the boundary. For a power law fluid the critical friction factor fCT is given by (96)... 

The adoption of effective exchange of information regarding planning and control activities (schedules, resources, materials, cost, cash flow) between the different parties involved in B C projects is a critical success factor. It may avoid projects time and costs overmn and assure better quality. 

Unsteady-state flow develops when at least one critical flow parameter is exceeded. The resistance factor buildup is linear either as a function of time or injected pore volumes. 

The polymer flow resistance factor vs flow rate curve has a minimum in many cases [10]. It was also shown earlier [11] that over a critical flow rate an unsteady-state polymer flow can develop. In such a case, only the first value of the measured resistance factor will be on the resistance factor versus flow rate curve on its imaginary section (Figure 33). 

The Reynolds number indicates flow conditions. Laminar flow is for Re < 2300 transition or critical flow is 2300 < Re < 4000 and turbulent flow is developed for Re > 4000. Note that the critical zone is avoided in design because the flow is unstable and friction factors are uncertain. 

---