Hi Firas,
A preliminary quick answer could be that the formulae are different
and consequently the results. If you read the technical reference (pg.
24) you can find both approaches and relatives formulae.
A more refined answer would be that there are a lot of formulae that
pretend to empirically predict the smoke entrainment into the fire
plume, not just Heskestad and McCaffrey. Just to cite a few more,
extensive work has been done by Zukoski, Thomas, Delichatsios and more
recently Harrison for spill plumes.
The real problem is to understand when a formula is more appropriate
for a given scenario and actually this is not as clear as it should
be. Recent research done by the University of Jaén in a large fire
test facility has shown a major difference when comparing the real
data obtained with a heptane pool fire and the analytical results
obtained from different approaches.
This research will be presented in the SFPE conference on Performance-
Based Codes and Fire Safety Design that will be held in Hong Kong,
June later this year (Uncertainty of Smoke Filling Calculations in a
Large Atrium through Comparison to Experimental Results, G.Vigne, C.
Gutierrez-Montes, G. Rein).
Regards,
--------------------
Gabriele Vigne
Senior Engineer
Arup Fire