fluid_mechanics

3.5 Static, Stagnation, Dynamic, and Total Pressure 109
V
p
V
p
V
p
(1)
p 1 > p
(1)
p 1 < p
(1)
p 1 = p
F I G U R E 3.8 Incorrect
and correct design of static
pressure taps.
p
V
(2)
(1)
Tube
Stagnation
pressure at
tip
Stagnation
pressure on
stem
(1)
0
(2)
Static
pressure
Stem
F I G U R E 3.9
a Pitot-static tube.
Typical pressure distribution along
Accurate measurement
of static pressure
requires great
care.
measurement. This requires a smooth hole with no burrs or imperfections. As indicated in
Fig. 3.8, such imperfections can cause the measured pressure to be greater or less than the actual
static pressure.
Also, the pressure along the surface of an object varies from the stagnation pressure at
its stagnation point to values that may be less than the free stream static pressure. A typical
pressure variation for a Pitot-static tube is indicated in Fig. 3.9. Clearly it is important that
the pressure taps be properly located to ensure that the pressure measured is actually the static
pressure.
In practice it is often difficult to align the Pitot-static tube directly into the flow direction. Any
misalignment will produce a nonsymmetrical flow field that may introduce errors. Typically, yaw
angles up to 12 to 20° 1depending on the particular probe design2 give results that are less than 1%
in error from the perfectly aligned results. Generally it is more difficult to measure static pressure
than stagnation pressure.
One method of determining the flow direction and its speed 1thus the velocity2 is to use a directional-finding
Pitot tube as is illustrated in Fig. 3.10. Three pressure taps are drilled into a small
circular cylinder, fitted with small tubes, and connected to three pressure transducers. The cylinder
is rotated until the pressures in the two side holes are equal, thus indicating that the center hole
points directly upstream. The center tap then measures the stagnation pressure. The two side holes
are located at a specific angle 1b 29.5°2 so that they measure the static pressure. The speed is
then obtained from V 321 p 2 p 1 2r4 12 .
The above discussion is valid for incompressible flows. At high speeds, compressibility becomes
important 1the density is not constant2 and other phenomena occur. Some of these ideas are
discussed in Section 3.8, while others 1such as shockwaves for supersonic Pitot-tube applications2
are discussed in Chapter 11.
The concepts of static, dynamic, stagnation, and total pressure are useful in a variety of flow
problems. These ideas are used more fully in the remainder of the book.
β
(3)
If θ = 0
V
p
θ
β
(2)
(1)
p 1 = p 3 = p
p 2 = p + 1_ ρ
2
V2
F I G U R E 3.10 Cross section
of a directional-finding Pitot-static tube.