Journal of Mathematics in Industry

Table 1 Scaling table with typical reference values

From: Modelling, asymptotic analysis and simulation of the gas dynamics in a chimney

Quantity	Reference value	Typical reference value
x	$x_{r} = L$	10 m
t	$t_{r}$	20 s
A	$A_{r}$	0.07 m²
h	L	10 m
u	$u_{r} = L / t_{r}$	0.5 m/s
p	$p_{r}$	101,328 kg/(m s²)
T	$T_{r} = T_{w}$	263 K (=−10^∘C)
ρ	$ρ_{r} = p_{r} / (R T_{r})$	1.3 kg/m³
q	$q_{r} = {\tilde{c}}_{q} ρ_{r} u_{r}$	5 × 10⁵ W/m³
m	$m_{r} = {\tilde{c}}_{m} ρ_{r} u_{r}$	5 × 10⁻² kg/(s m³)

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