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you can use ASHRAE Atrium. Calc. excel sheet and you will find a good description for the manual procedures
2.1.1 Convective Heat Release Rate
The convective portion of the heat release rate (HRR) is
Q c = XQ (1)
where
Q c = convective heat release rate, Btu/s (kW),
Q = heat release rate, Btu/s (kW),
X= convective fraction, dimensionless.
The above equation is the same as the equation of NFPA 92 section 5.5.1.3. A convective fraction of 0.7 is commonly used for most design applications, but the value of X is much different for some fuels.
2.1.2 Axisymmetric Plume
Design fires located in the large atrium space are usually analyzed as having an axisymmetric plume (Figure 1a). For z greater than or equal to z l (z >= z l ), the mass flow of this kind of plume is
m=(0.071 Qc ^1/3 Z^5/3) + (0.0018 Qc)
For z less than z l (z < z l ), the mass flow is
m = 0.032 Qc^3/5 Z
where
m = mass flow in the plume, lb/s (kg/s),
Q c = convective heat release rate, Btu/s (kW),
z = distance above the base of the fire, ft (m),
z l = limiting elevation, ft (m).
For smoke temperature:
Ts = To + (KsQc / m Cp)
where:
Ts = smoke layer temperature
To = ambient or outdoor temperature
Ks = 1 for steady smoke exhaust
m = exhaust mass flow rate
Cp = spacific heat for smoke
for density of smoke:
ps = Patm / (R(Ts+273))
where
ps = smoke density kg/m3
Patm = atmospheric pressure Pa
R = gas constant = 287 j/kg k
Ts = smoke layer temperature
For smoke volume flow rate:
V = m / ps
all dimensions in SI units
References
Klote, J. H., Milke, J. A., Turnbull, P. G., Kashef, A., Ferreira, M. J. 2012. Handbook of Smoke Control Engineering. Atlanta: ASHRAE.
NFPA. 2012. Standard for Smoke Control Systems NFPA 92. Quincy, MA: National Fire Protection Association.
ICC. 2012. International Building Code ® . Washington, D.C.: International Code Council.
the best way to understand & preform smoke calculation is Atrium Calculation ASHRAE
