Page 296 - gas transport in porous media

Rossabi
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maintain their spatial relation. The type of flow, which is determined by the proper-
ties of the fluid as well as the properties and size of the containing structure, in turn
determines the resistance to flow in the structure. The type of flow occurring in the
system can also affect the choice of measurement techniques as some work better in
one flow regime or another. The equation for the dimensionless Reynolds number is
provided below:
ρνd
R e = (17.1)
µ
3
where ρ is the density of the fluid (kg/m ), v is the average velocity of the fluid
(m/sec), µ is the viscosity of the fluid (kg/m sec), and d is the diameter of the
structure usually a tube of some sort. For porous media, v is considered the spe-
cific discharge and d is a representative dimension of the size of the pores (e.g.,
mean grain diameter). As it is dimensionless, the Reynolds number can be calcu-
lated in other consistent sets of units and provide identical results. The type of flow
indicated by the Reynolds number is roughly divided by empirical results which indi-
cate that a Reynolds number of less than 2000 results in laminar flow and greater
than 3000 is turbulent flow. Between these values is a transition zone, which may
support either flow regime. Ground water flow is generally considered to be lami-
nar, however, soil gas flow especially when induced by external pumping may be
turbulent.

17.3 PRESSURE MEASURING DEVICES

These devices are based on the seminal work of Daniel Bernoulli in the early part
of the eighteenth century, who first developed the expression relating pressure and
velocity of a fluid (Guillen, 1995). The original equation developed by Bernoulli is:
2
P + ρν = constant (17.2)
where P is the absolute pressure measured in the system (Pa), ρ is the density of
3
the fluid (kg/m ), and v is the velocity of the fluid (m/sec). When derived to include
work defined by changes in potential and kinetic energy, Bernoulli’s equation takes
the more common form:
1 2
P + ρgy + ρν = constant (17.3)
2
2
where g is the gravitational constant (m/s ), and y is the height above some datum (m).
From this equation and the continuity equation first observed by Leonardo DaVinci
(Guillen, 1995), many practical flow measurement devices can be devised. One of
the simplest is the Venturi meter, which uses the difference in pressure measured in
the main body of a cylinder containing a flowing fluid and at the end of a gradual
constriction in the cylinder to calculate the velocity of the fluid. An orifice plate
is similar in principle to the Venturi meter but uses an abrupt change in the pipe