Cunningham correction factor

Fig. 4. Terminal velocities in air of spherical particles of different densities settling at 21°C under the action of gravity. Numbers on curves represent tme (not bulk or apparent) specific gravity of particles relative to water at 4°C. Stokes-Cunningham correction factor is included for settling of fine particles.

Stokes-Cunningham correction factor sphericity correction constant Coulomb s law constant, 8.987 x 10 ... 

K. Stokes-Cunningham correction factor Dimensionless Dimensionless Dimensionless... 

For single-stage precipitators, and may be considered as essentially equal. It is apparent from Eq. (17-31) that the mobihty in an elecdric field will be almost the same for all particles smaller than about l- Im diameter, and hence, in the absence of reentrainment, collection efficiency should be almost independent of particle size in this range. Very small particles will actually have a greater mobihty because of the Stokes-Cunningham correction factor. Values of are listed in Table 17-14 for 70°F, = 2, and % = %i = % = 10 statV/cm. 

Cunningham correction factor A factor used as a refinement to the Stokes equation for falling particles of small diameter. These tend to slip between the air molecules and, as a result, fall faster. Cup anemometer A device used by meteorologists for the measurement of wind speed. 

Kcr = Proportionality Foctor, Dimensionless Km = Stokes-Cunningham Correction Factor, Dimensionless... 

Kfne = Proportionality factor in Stokes-Cunningham correction factor, dimensionless k = Constant for wire mesh separators 1 = Wire mesh thickness, ft L = Length of vessel from hydrocarbon inlet to hydrocarbon outlet, or length of decanter, ft L[ = Liquid entering Webre separator, lbs pel- minute per square foot of inlet pipe cross-section L, = EnLrainment from Webre unit, lb liquid per minute per square foot of inlet pipe cross section... 

FIGURE 9.15 Cunningham correction factors to be applied in calculating terminal settling velocities of particles (adapted from Hinds, 1982). 

FIG. 14-115 Experimental collection efficiencies of rectangular impactors. C is the Stokes-Cunningham correction factor pp, particle density, g/cm3 Ug, superficial gas velocity, approaching the impactor openings, cm/s and g, gas viscosity, P. [Calvert, Yung, and Leung, NTIS Publ. PB-248050 based on Mercer and Chow, J. Coll. Interface Sci., 27, 75 (1968).]... 

To correct for this effect, a factor, commonly known as the Cunningham correction factor, slip, or Millikan resistance factor, denoted Cc, must be introduced into the Stokes equation, yielding... 

The Cunningham correction factor Cc is always equal to or greater than 1. When d > 2X, then Cc can be approximated by the expression... 

The Cunningham correction factor is an important correction to Stokes law and should always be used when particles are less than 1 Jim in diameter. 

Cunningham correction factor for, 63 settling velocity of, 81-82 Simple coagulation theory, 308 Simple diffusion, 131-143 Single-particle scattering measurements, 297-299... 

Example 5.2 Compute the Cunningham correction factor for a silica dust particle (p = 2.65 g/cm3) having a diameter of 0.5 pm. Assume a spherical shape and 20°C. From Eq. 5.3... 

As mentioned earlier, the slip, or Cunningham correction factor, represents the mechanism for transition from the continuum to the molecular case. For large values of d, the resulting force F is proportional to d whereas for small values of d, F is proportional to d2. 

For a cluster of n spheres of diameter d, de = nd. When the aggregate particle size is small, the Cunningham correction factor should be considered. 

For particles with diameters smaller than about 10 pm (actually, 1 pm is often taken as the cutoff point), it is necessary to include the Cunningham correction factor in calculating the terminal settling velocity. Then... 

Example 6.6 Determine the terminal settling velocity of a 0.5-pm-diameter silica sphere (p = 2.65 g/cm3). Include the Cunningham correction factor in the estimate. 

Related Calculations. In situations where the particles are so small that their size approaches the length of the mean free path of the fluid molecules, the fluid can no longer be regarded as a continuum that is, the particles can fall between the molecules. That problem can be offset by applying a factor, the Cunningham correction factor, to the calculation of the inertial-impact-number expression in step 2. 

A constant in Stokes-Cunningham correction factor for particle velocity7 . 41.72, but often considered a function of X and D dimensionless... 

Stokes-Cunningham correction factor for terminal settling velocity Elooding coefficient Discharge coefficient Diameter Bubble diameter Hole diameter Orifice diameter Cut size of a particle collected in a device, 50% mass efficiency Mass median size particle in the pollutant gas... 

The Cunningham correction factor discussed in (14) and calculated in (11) for some specific cases increases the rate of coTTisions between particles of unlike size considerably. As em illustration, the coagulation consteint between two particles A emd B of unlike size... 

The Cunningham correction factor has been empirically determined to be (Seinfeld and Pandis 1998) ... 

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