7.7 Calculation of Critical Speed
263
Table 7.1 K 1 values for
different heat release ratios
(adapted from NFPA
502:2017)
Q (kW)
K 1
<10,000
0.87
10,000
0.87
30,000
0.74
50,000
0.68
70,000
0.64
90,000
0.62
100,000
0.606
>100,000
0.606
0.7
0.8
0.9
1
1.1
1.2
1.3
-6
-4
-2
0
2
4
6
RG (%)
K g
Fig. 7.7 Grade factor (K g ) as a function of roadway grade (RG, %)
V c = K 1 K g
g H Q
ρ a C p A x T f
1
3
(7.13)
where
• K 1 : A factor that is related to the Froude number (Fr) as: K 1 = Fr
−1/3 . Experimental
models indicate that Fr < 4.5 is required to prevent smoke backlayering (e.g. Lee
et al. 1979). When Fr = 4.5, then the value of K 1 = 0.606. Alternatively, this
dimensionless value can be obtained for different Heat Release Ratios (HRR)
from NFPA 502:2017 (see Table 7.1).
• g: Acceleration due to gravity, 9.81 (m s
−2 ).
• H: Height of the tunnel or gallery at the location of the fire (m).
• K g : Grade factor, a dimensionless value that can be obtained from Fig. 7.7 (see
NFPA 502:2017) as a function of the road grade
7 .
An airway slope is:
7 Ratio of uphill height to horizontal length (slope).