The document discusses pressure measurement techniques. It describes different types of measurements including local, integral, direct, and non-direct measurements. It also discusses various sensor types including static pressure probes, total pressure probes, and differential pressure probes. The key aspects of pressure transducers and considerations for time-resolved pressure measurements are summarized. Calibration is important for accurate measurements but sensors need to balance various factors like resolution, frequency response, intrusivity, and cost.

1. Pressure Measurements
Material prepared
by
Alessandro Talamelli, Antonio Segalini
&
P. Henrik Alfredsson

2. Literature
• Springer Handbook of Experimental Fluid
Mechanics, Cameron Tropea,
Alexander L. Yarin , John F. Foss (2007),
ISBN-10: 3540251413
• Measurement in Fluid Mechanics
Stavros Tavoularis, Cambridge University Press
(2009) ISBN-10: 0521138396
• Fluid Mechanics Measurements, R. Goldstein,
CRC Press; (1996) ISBN-10: 156032306X
• Low-Speed Wind Tunnel Testing,
Jewel B. Barlow , William H. Rae, Alan Pope,
Wiley-Interscience; (1999) ISBN-10:
0471557749

3. Measurement techniques
• Type of Measurements
– Local measurements
– Integral measurements
– Direct measurements
– Non-direct measurements
– Field measurements
– Surface measurements
– Time averaged measurements
– Time resolved measurements

4. Measurement chain
Sensor
Transducer
Acquisition data systems
Evaluation data systems

5. Sensor
• Element which changes its status when
in contact with the quantity to be
measured

6. Sensor characteristics I
• Spatial and temporal resolution
Spatial and temporal resolutions are coupled because it is not
generally possible to distinguish if the quantity to be
measured varies with time or if there are pseudo-temporal
variations caused by the passage of spatial disturbances.

7. Sensor characteristics II
• Accuracy
• Intrusivity: Non-intrusive methods are really
non-intrusive (?)
• Interference
• Robustness
• Calibration
• Linearity
• Cost

8. Transducer
• Element which transforms the changes
in the sensor s status in an output
signal
• Typically it is an electrical signal

9. Ideal sensor/transducer
Output Signal
S(t)
Physical Quantity Sensor and Transducer s
• Output signal is proportional to the
magnitude of the physical quantity u
• The physical quantity is measured at a y
point in space
• The output signal represents the input
u( x, y, z)
without frequency distortion z x
• Low noise on output signal
• Sensor does not interfere with the s
physical process ! ! !s(t )
• Output is not influenced by other
! ! !u(t )
t
variables

10. Basic Definitions I
In an internal point of a fluid the pressure
can be defined as the mean of the three
normal stress components acting over three
surface elements orthogonal to each other in
the point at rest with respect to the fluid.
For a fluid in motion this value is called static
pressure (definition by Aeronautical
Research Council ).

11. Basic Definitions II
If the fluid is brought to rest with an
isentropic and adiabatic process, the pressure
rises until a maximum that is called the total
pressure.
The stagnation pressure is the pressure
measured when the velocity is zero.
The dynamic pressure is the difference
between the total and the static pressure.
pdyn = ptot - ps

12. Basic definitions III
If the Bernoulli s law is valid we have
1 2
ptot = ps + !V
2
which give us
1
pdyn = ρV 2
2
Otherwise: the kinetic pressure is
1
pkin = ρV 2
2

13. Static pressure
Ideally the static pressure should be measured with a
pressure probe that moves at the same velocity as
the fluid particle. But unpractical!
Instead chose a stationary probe with respect to the
laboratory (or airplane), choose a suitable shape and
position the probe in a place where the pressure is
equal to the static pressure of the undisturbed flow.

14. Static pressure probe
STATIC PROBES
Presence of holes at a distance of 3D from the
leading edge and 8-10D from the stem.
s
Sensitivity to the inclination of the asymptotic flow
with respect to the probe axis.
s

15. Static pressure probe
• WALL TAPPINGS
• On a wing or in pipes and ducts the static
pressure can be measured using holes in the
surface (give attention to the sensitivity of
the dimensions and the shape of the holes).
ps-patm
s

16. Static probes
• The probe must be aligned with the flow (this
effect can be reduced by using several holes)
• Since the pressure is measured with holes,
then the same problems of the wall tappings
must be considered
– Effects of tip shape (geometry depends from flow
regime)
– Effects of probe blockage
– Effects of hole position
– Effects of the support

17. Blockage effect
• Nose acceleration and probe support
effects may compensate

18. Wall tappings
• The flow is very complex in proximity of the
tapping (only low Re simulations)
– Effects of orifice shape
– Effects of orifice orientation
– Effects of surface orientation
– Shape and position of the cavity (minimum depth)
– Compressibility
– Effects of the tapping orifice condition
– Effect of the distance from the measured point

19. Effect of d+
McKeon and Smits MST (2002)
• More problematic for high Re

20. Effect of d+
McKeon and Smits MST (2002)
• Less influence when d increases

21. Total pressure probe
The stagnation pressure is obtained when the
fluid is brought to rest through an isentropic and
adiabatic process.
In subsonic flow the Pitot tube measures the
stagnation pressure
(French hydraulic engineer 1695-1771)

22. Total pressure probe
• In supersonic flow there is a stagnation pressure
loss over the shock wave that is formed in front
of the tube
• Flat, hemisherical or elliptic head. In supersonic
flow typically sharp wedge front.

23. Total pressure
p0 m − p u '2 v'2 w'2 y
Cp = = f (ϑ , Re d , M , 2 , 2 , 2 , α , )
1 U U U d
ρU 2
2
• Incoming flow direction
• Local Reynolds number (viscosity)
• Mach number
• Velocity gradient
• Wall proximity
• Turbulence

24. Total pressure probe
• Effects of finite dimensions
– Pressure measured in a finite region (not a
single streamline) -> spatial averaging
– This effect can be limited with small probes
(be careful! : robustness, time response)
– Blockage (d/L)
• Directional sensitivity

25. Total pressure probe –
direction sensitivity
Less sensitivity to the inclination of the flow in respect
to the longitudinal axis than the static pressure probe.
From Chue

26. Total pressure probe
• Effects of viscosity (in high Reynolds
number measurement Red can be low due to
the small dimensions of the probe)
• Viscous effect are negligible for ReD>100
• For ReD>30
10
C p = 1 + 1.5
Re d

27. Total pressure – velocity gradient
1) Indicated Pitot pressure > total pressure of the
undisturbed flow if a Pitot tube is operated in a region
where the total pressure varies in a direction ortoghonal
to the asymptotic flow (e.g Boundary layer).

28. Total pressure – velocity gradient
1) Velocity gradient interference
2) With the presence of a flat wall parallel to the probe
axis there could be a reflection effect with the
consequent measured pressure higher than the total
pressure. This effect is negligible for y>2d from the wall.
McKeon, Li, Jiang, Morrison and Smits MST (2003)

29. Total pressure – velocity gradient
• Error 1) is normally corrected by changing the
probe position rather than correcting the flow
Δy
velocity = ε , ε = 0.15 ( MacMillan)
d
Δy d dU
= 0.18α (1 − 0.17α 2 ), α = ( Zagarola )
d 2U ( yc ) dy c
Δy
= 0.15 tanh(4 α ), ( McKeon)
d
• This is based on analytical displacement
correction for a sphere in a velocity gradient

30. Total pressure – velocity gradient
• Wall correction
ΔU ⎡ ⎛ y ⎞⎤
= 0.015 exp⎢− 3.5⎜ − 0.5 ⎟⎥ ( MacMillan)
U ⎣ ⎝ d ⎠⎦
• A new correction is proposed based on Preston
probe pressure data
⎧ 0.150 for d + < 8
δ w ⎪
= ⎨ 0.120 for 8 < d + < 110
d ⎪
⎩0.085 for 110 < d + < 1600

31. How important wall
correction are ?
McKeon, Li, Jiang, Morrison and Smits MST (2003)

32. Velocity measurements with differential
pressure probe: the Prandtl probe
• Steady flow, low velocity, viscosity negligible:
Bernoulli s law holds
1
ptot = ps + !V 2
2
• High velocity:
1
ptot = ps + "V 2 ( + ! p )
1
2
Corrective term f(M)
2(ptot # pst )
V=
"( + ! p )
1

33. Measurement errors due to
turbulence
A physical time-dependent quantity can generally be
splitted in a mean part and in a fluctuating part
v(t ) = V + v' (t ) p (t ) = P + p ' (t )
From Bernoulli s law:
1
(
Ptot + p 'tot = Pst + p 'st + ! V 2 + 2Vv'+v'2
2
)
Taking the time-average:
1 2
(
Ptot = Pst + ρ V + v'
2
2
) Error due to
fluctuating
velocity
Effect of the anisotropy

34. Measurement errors due to
turbulence
Another effect is linked to the radial gradient of
the static pressure due to the fluctuations
This is of the opposite sign than the turbulence one.
Therefore they compensate.

35. Velocity measurements - compressibility
effects
Μ εp εp
0 0
0.1 0.0025
0.2 0.010
0.3 0.023
Note that the error in velocity is
0.5 0.083
about half of εp !
1.0 0.274

36. Velocity measurements at a nozzle exit
V1 , A1 , p1 Vexit , Aexit , pexit
• Mass conservation equation:
V1 A1 = Vexit Aexit
• Bernoulli s law applied to a streamline passing on the
reference section and to the nozzle exit:
1 2 1 2
p1 + !V1 = pexit + !Vexit
2 2

37. Velocity measurements at a nozzle exit
• Combining the two relations:
2(p
Vexit = 2
& Aexit #
) $1 ' 2
$ !
!
% A1 "
• If section 1 is characterized by a dimension much
larger then the exit s one, the corrective term
can be neglected

38. Pressure transducers
Absolute pressure transducer
Measures the pressure relative to perfect vacuum pressure.
(Example: barometer, used also for compressible flow)
Gauge pressure transducer
Measures the pressure relative to a given atmospheric pressure
at a given location. (Example a tire pressure gauge).
Vacuum pressure transducer
This sensor is used to measure small pressures less than the
atmospheric pressure.
Differential pressure transducer
This sensor measures the difference between two or more
pressures introduced as inputs to the sensing unit.
s

39. Pressure transducers
pd =ρ h sin(θ)
s

40. Pressure transducers
Betz manometer
s

41. Differential Pressure transducers
Capacitance principle
• Very accurate
• Need to be calibrated (time to time)
s
• Expensive for multi point measurements

42. Pressure transducers
• Need to be calibrate
s

43. Pressure Scanners
• Important in pipe/channel turbulence

44. Multi component velocity measurements
• Five hole Pitot
• Pressure distributions on the probe s head is
function of its geometry and of the flow
direction
• By sampling this distribution in five points is
possible to determine the direction and
magnitude of the velocity vector

45. Multi component velocity measurements
Calibration

46. Time resolved pressure measurements
• Microphone: electromechanical transducer. The
sensing element is a thin membrane that alters
its shape under the pressure loading effect
• High capacity to measure the pressure variations
in the measurement point (the sensor measures
variations up to at least 5 kHZ)

47. Time resolved pressure measurements
• Capacitive type
• Piezoelectric type
• strain measurements

48. Time resolved pressure measurements
Pressure probe for measurements of pressure
fluctuations inside the boundary layer (Tsuji et al
2007)

49. Time resolved pressure measurements
Frequency response for pressure probe of Tsuji
et al. Frequenct is normalized with Helmholz
resonator frequency.

50. Time resolved pressure measurements
Measured rms fluctuations of the pressure inside
turbulent boundary layers at different Re. Lines
are from numerical simulations.

51. Sensor characteristics
• Resolution √
• Frequency response X
• Accuracy √
• Intrusivity X
• Interference X
• Robustness √
• Calibration (X)
• Linearity √
• Cost √