Page 439 - Dust Explosions in the Process Industries

406 Dust Explosions in the Process Industries

However, assuming that Ohm's law is valid at any time,
V,= R, I, (5.20)

and substitution of (5.18) into (5.20) yields
y = 40 1,I;~.~~ (5.21)

which, when substituted into (5.19), gives

E, = 40 2,rZ:54dt (5.22)

This equation offers a possibility for determining the ohmic energy dissipation in the
spark gap, that is, the net spark energy, by measuring the spark current Z,(t) only. Figure
5.12 shows a correlation of net spark energies determined from equations (5.19) and
(5.22), using the experimental data from Aakre (1980). As can be seen, the agreement
is within a factor of 2 for E > 0.1 mJ. It remains to be seen whether equation (5.18) is a
reasonable approximation even outside the range covered by the data in Figure 5.11.
Equations (5.18) and (5.20) can also be used to express E, as an integral of V,instead
of I,.

10-2 lo-' 1 10 102
E 9 = f 1 (V. I1 [mJI

Figure 5.1 2 Correlation between spark energies El determined from simultaneousmeasurement of
spark gap voltage V, and spark current Is, as functions of time, and energies E2 determined from the
spark current measurements only, using the empirical correlation of spark current and spark resist-
ance per unit length of spark gap in Figure 5. I I.