This page shows a schematic drawing of a pitotstatic tube. PitotStatic
tubes, which are also called Prandtl tubes, are used on aircraft as speedometers. The actual tube on
the aircraft is around 10 inches (25 centimeters) long with a 1/2
inch (1 centimeter) diameter. Several small holes are drilled around
the outside of the tube and a center hole is drilled down the
axis of the tube. The outside holes are connected to one side
of a device called a pressure transducer. The center hole in the tube
is kept separate from the outside holes and is connected to
the other side of the transducer. The transducer measures
the difference in pressure in the two groups of tubes
by measuring the strain in a thin element using
an electronic strain gauge. The pitotstatic tube is mounted on the aircraft,
or in a
wind tunnel ,
so that the center tube is always pointed in the direction of
the flow and the outside holes are perpendicular to the center
tube. On some airplanes the pitotstatic tube is put on a longer boom
sticking out of the nose of the plane or the wing.
Difference in Static and Total Pressure
Since the outside holes are perpendicular to the direction
of flow, these tubes are pressurized by the local
random
component of the air velocity. The pressure in these tubes is
the static pressure (ps) discussed in Bernoulli's
equation. The center tube, however, is pointed in the direction of
travel and is pressurized by both the random and the ordered air
velocity. The pressure in this tube is the total pressure (pt)
discussed in Bernoulli's equation. The pressure transducer measures
the difference in total and static pressure which is the
dynamic pressure q.
measurement = q = pt  ps
Solve for Velocity
With the difference in pressures measured and knowing the local
value of
air density
from pressure and temperature measurements, we
can use Bernoulli's equation to give us the velocity. On the graphic, the Greek symbol
rho is used for the dair density. In this text, we will use the letter r.
Bernoulli's equation
states that the static pressure plus one half the density times the
velocity V squared is equal to the total pressure.
ps + .5 * r * V ^2 = pt
Solving for V:
V ^2 = 2 * {pt  ps} / r
V = sqrt [2 * {pt  ps} / r ]
where sqrt denotes the square root
function.
There are some practical limitations to the use of a pitotstatic tube:
 If the velocity is low, the difference in pressures is very
small and hard to accurately measure with the transducer. Errors
in the instrument could be greater than the measurement! So pitotstatic
tubes don't work very well for very low velocities.
 If the velocity is very high (supersonic), we've violated the
assumptions of Bernoulli's equation and the measurement is wrong
again. At the front of the tube, a
shock wave
appears that will
change the total pressure. There are corrections for the shock
wave that can be applied to allow us to use pitotstatic tubes for high
speed aircraft.
 If the tubes become clogged or pinched, the resulting pressures at the transducer
are not the total and static pressures of the external flow.
The transducer output is then used to calculate a velocity that is not the
actual velocity of the flow.
Several years ago, there were reports of icing problems occuring on airliner pitotstatic probes.
Output from the probes was used as part of the autopilot and flight control system. The solution
to the icing problem was to install heaters on the probes to insure that the probe was not
clogged by ice buildup.
Notice  In using this equation to determine the velocity, we must be very careful and use the proper
units of measure. The air density must be specified as mass / volume (kg/m^3 or slug/ft^3) while the
pressure is specified as force / area (Pa or lbs/ft^2).
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