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Electrostatistic Precipitation 161

where A′ and B′ are constants for a specific gas and δ′ is the relative gas density taken
5
with respect to 1 atm and 25°C. For air, the values A′ = 32.2×10 V/m and B′ = 8.46×10 4
V/m 1/2 are recommended. Values for other gases are reported in the literature (16).
Example 1
Find the corona-starting voltage for a duct precipitator of a 28-cm plate-to-plate spacing
and a 10-cm wire-to-wire spacing and a 109-mil diameter wire. Assume that the gas is air
at 40°C and 2 atm. Compare with a 109-mil-diameter wire in a 28-cm-diameter cylinder.
Solution
The corona-starting voltage for duct geometries is given by Eq. (13), for which E and
c
d′are required. E can be determined from Eq. (16) for which δ´ is required:
c
δ′= T P = 298 × 2 = 190.
0
T P 313 1
0
−
3
2r = 109 mils = 2.77 × 10 m
0
Thus, from Eq. (16),
 846 × 10 4 
.
.
E = 190 322. × 10 5 + 12 / 
c
  (139. × 10 −3 × 19 )  
.
6
= 9.25 × 10 V m
Now, d′ = 4b/π, where b is the wire-to-plate spacing and is assumed to be one-half of the
plate-to-plate spacing (i.e., the wires are assumed to be placed midway between the plates);
thus, b = 0.14 m. Therefore, d′ = (4)(0.14)/π= 0.178 m; thus, from Eq. (13),
 0 178 
.
V = (139 × 10 −3 )(9 25. × 10 6 ) ln
.
0 
 139. × 10 −3
= 62.4 × 10 V
−
3
The starting voltage for the cylinder is given by Eq. (8). Thus,
 014 
.
.
V = (925 × 10 6 )(1 39. × 10 −3 ) ln
0 −3 
 139. × 10
= 59.3 × 10 V
−
3
(Note that r = 0.14 m.) For equal duct width (parallel-plate spacing) and cylinder diameter
1
and identical wire size, the cylinder-starting voltage will always be lower than the duct-
starting voltage. In industrial precipitators, corona-starting voltages are somewhat lower
than calculated estimates because of irregular electrode spacing and extraneous discharges
from dust films, nicks, and the like on corona wires. In ducts, this is also attributable to the
lower starting voltage of the end wires.
Corona discharge is accompanied by a relatively small flow of electric current. Sparking
usually involves a considerably larger flow of current, which cannot be tolerated. However,
with suitable controls, precipitators have been operated continuously with a small amount
of sparking to make certain that the voltage is in the correct range to ensure corona.