handbook of modern sensors

11.2 Pressure Gradient Technique 361
The measurement of flow is rarely conducted for the determination of a displacement
of volume. Usually, what is needed is to determine the flow of mass rather than
volume. Of course, when dealing with virtually incompressible fluids (water, oil, etc.),
either volume or mass can be used. A relationship between mass and volume for a
incompressible material is through density ρ
M = ρV. (11.5)
The densities of some materials are given in Table A.12 (Appendix). The rate of mass
flow is defined as
dM
= ρAv (11.6)
dt
The SI unit for mass flow is kilogram per second and the U.S. Customary System unit
is pounds per second. For a compressible medium (gas), either mass flow or volume
flow at a given pressure should be specified.
There is a great variety of sensors that can measure flow velocity by determining
the rate of displacement of either mass or volume. Whichever sensor is used, inherent
difficulties of the measurement make the process a complicated procedure. It is necessary
to take into consideration many of the natural characteristics of the medium,
its surroundings, barrel and pipe shapes and materials, medium temperature and pressure,
and so forth. When selecting any particular sensor for the flow measurement,
it is advisable to consult with the manufacturer’s specifications and very carefully
consider the application recommendations for a particular sensor. In this book, we do
not cover such traditional flow measurement systems as turbine-type meters. It is of
interest to us to consider sensors without moving components which introduce either
no or little restriction into the flow.
11.2 Pressure Gradient Technique
A fundamental equation in fluid mechanics is Bernoulli equation which is strictly
applicable only to steady flow of nonviscous, incompressible medium:
( ) 1
p + ρ
2 v2 a + gy = const, (11.7)
where p is the pressure in a tube of flow, g = 9.80665 m/s 2 = 32.174 ft/s 2 is the gravity
constant, and y is the height of the medium’s displacement. Bernoulli’s equation
allows us to find fluid velocity by measuring pressures along the flow.
The pressure gradient technique (of flow measurement) essentially requires the
introduction of a flow resistance. Measuring the pressure gradient across a known
resistor allows one to calculate a flow rate. The concept is analogous to Ohm’s law:
Voltage (pressure) across a fixed resistor is proportional to current (flow). In practice,
the restricting elements which cause flow resistances are orifices, porous plugs, and
Venturi tubes (tapered profile pipes). Figure 11.3 shows two types of flow resistor.
In the first case, it is a narrow in the channel; in the other case, there is a porous