Page 71 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

2.1 Gas Kinetics 45

The viscosities at different reference temperatures can be found in the handbook
of CRC [5]; and some examples are listed Table 2.2. For temperatures between
0 < T < 555 K, the Sutherland’s constants and reference temperatures for some
gases are listed. The maximum error is 10 %.

2.2 Gas Fluid Dynamics

2.2.1 Reynolds Number

Reynolds number of a fluid quantifies the relative importance of inertial forces (qu)
and viscous forces (μ/L) for a flow. Mathematically, it is described by

quD 4 _ m
Re ¼ ¼ ð2:71Þ
l lpD

where u ¼ magnitude of the mean fluid velocity in m/s, D ¼ characteristic length in
2
m, l ¼ dynamic viscosity of the fluid in N:s=m Þ or Pa.s, q ¼ density of the fluid
ð
3
in kg/m , and _ m is the mass flow rate of the fluid.
The characteristic length depends on the flow condition, internal or external, and
the cross section of the pipe for internal flow. For flow in a pipe, it is the hydraulic
diameter of the pipe, and for flow over a body, the characteristic length is usually
the length of the body. The flow is likely laminar if Re < 2,000 and turbulent for
Re > 4,000 for either internal or external flows. In a boundary layer analysis
(Sect. 2.2.3), the characteristic length is the distance measured from the leading
edge where the boundary layer starts to develop.

2.2.2 Bernoulli’s Equation

Bernoulli’s equation is important to air emission analysis too. It is derived from the
basic concept of conservation of mass and conservation of energy. Very briefly,
consider a streamline of a moving fluid without heat transfer; Bernoulli’s equation
describes the relationship between the static pressure of the fluid, fluid velocity, and
the elevation for a steady flow,

v 2 Z DP
þ þ gz ¼ constant ð2:72Þ
2 q
where v is the local velocity on the streamline (m/s), P is the absolute static pressure
3
2
(Pa; N/m ), q is the density of the fluid (kg/m ), g is gravitational acceleration (9.81
2
m/s ) and z is the elevation (m).