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flow in a Venturi tube is:
Rossabi
πd 2 2 p
Q =
(17.4)
4 ρ 1 − (d/D) 4
3
whereQ isthevolumetricflowrate(m /sec), pisthedifferenceinpressuremeasured
3
in the pipe and the pipe constriction (Pa), ρ is the density of the fluid (kg/m ), and d
and D are the diameters of the constriction and the main pipe respectively (m).
The expression for fluid velocity as measured by a Pitot tube is:

2 p
ν = (17.5)
ρ
wherev isthevelocityofthefluid(m/sec), and pinthiscaseisthedifferencebetween
absolute and static pressure measured at the stagnation point (Pa). In general, losses
increase from Pitot and Prandtl tubes to Venturi meters to nozzles to orifice plates.

17.4 THERMAL FLOW SENSORS

Because of the prevalence of the use of thermal sensors for gas flow, a convenient way
to differentiate flow sensors is in terms of thermal and non-thermal mechanisms. The
theoretical basis for thermal flow sensors arose from heat conduction work conducted
in the early twentieth century. In particular, the work of King (1914) was seminal to
the development of in-line and insertion mass flow meters, two of the most popular
process flow meters. King developed the expressions for the conduction of heat
from radially symmetric surfaces in a constant flow field that are essentially used
today.
Thermal anemometers use the heat transfer properties of the fluid they are mea-
suring to calculate a mass flux rate rather than a volumetric flow rate. The size
and number of gas molecules that hit the heated element determine the amount of
energy removed from the element. The heated sensor element employed can be a
wire, a plate or film, a sphere or another shape that is able to sample the flow yet
provide minimal impedance or change to the flow. These devices are deployed in
the flow path and are usually referred to as insertion mass flow meters. Their small
size also permits easy access to flow fields. Some thermal flow meters use a section
of the flow conduit as the measurement device (in-line meters) either as the heated
sensor itself or in conjunction with embedded heated elements (Viswanathan et al.,
2002).
Thermal sensors measure either the amount of energy (usually as electric power)
required to maintain a heating element at a constant temperature in the mass flow path,
or they measure the temperature of the element for a particular applied energy (electric
power) in the mass flow path (Baker and Gimson, 2001).Although the thermal sensors
actually measure the mass of fluid interacting with the heated element, they are often
calibrated to the velocity of a particular gas compound flowing by the sensor at a