handbook of modern sensors

340 10 Pressure Sensors
can be defined as the force F exerted perpendicularly on a unit area A of a boundary
surface [2]:
p = dF
dA . (10.1)
Pressure is basically a mechanical concept that can be fully described in terms of
the primary dimensions of mass, length, and time. It is a familiar fact that pressure is
strongly influenced by the position within the boundaries; however, at a given position,
it is quite independent of direction. We note the expected variations in pressure with
elevation:
dp =−wdh, (10.2)
where w is the specific weight of the medium and h represents the vertical height.
Pressure is unaffected by the shape of the confining boundaries. Thus, a great
variety of pressure sensors can be designed without concern for shape and dimensions.
If pressure is applied to one of the sides of the surface confining a fluid or gas, the
pressure is transferred to the entire surface without diminishing in value.
The kinetic theory of gases states that pressure can be viewed as a measure of the
total kinetic energy of the molecules:
p = 2 KE
3 V = 1 3 ρC2 = NRT, (10.3)
where KE is the kinetic energy, V is the volume, C 2 is an average value of the square
of the molecular velocities, ρ is the density, N is the number of molecules per unit
volume, R is a specific gas constant, and T is the absolute temperature.
Equation (10.3) suggests that the pressure and density of compressible fluids
(gases) are linearly related. The increase in pressure results in the proportional increase
in density. For example, at 0 ◦ C and 1 atm pressure, air has a density of 1.3 kg/m 3 ,
whereas at the same temperature and 50 atm of pressure, its density is 65 kg/m 3 ,
which is 50 times higher. To the contrary, for liquids, the density varies very little
over ranges of pressure and temperature. For instance, water at 0 ◦ C and 1 atm has a
density of 1000 kg/m 3 , whereas at 0 ◦ C and 50 atm, its density is 1002 kg/m 3 , and at
100 ◦ C and 1 atm, its density is 958 kg/m 3 .
Whether gas pressure is above or below the pressure of ambient air, we speak
about overpressure or vacuum. Pressure is called relative when it is measured with
respect to ambient pressure. It is called absolute when it is measured with respect to
a vacuum at 0 pressure. The pressure of a medium may be static when it is referred
to fluid at rest, or dynamic when it is referred to kinetic energy of a moving fluid.
10.2 Units of Pressure
The SI unit of pressure is the pascal:1Pa=1 N/m 2 ; that is, one pascal is equal to one
newton of force uniformly distributed over 1 square meter of surface. Sometimes, in
technical systems, atmosphere is used, which is denoted 1 atm. One atmosphere is
the pressure exerted on 1 square centimeter by a column of water having a height of