1. Practical Aspects of using Pitot Tube
P M V Subbarao
Professor
Mechanical Engineering Department
Corrections to Devotion from Potential Flow

2. YAW AND PITCH ANGLE RANGE
If the fluid stream is not parallel to the probe head, errors occur in both total and static readings. 
These are the most important errors in this type of instrument because they cannot be corrected without taking independent readings with another type of probe.

4. Errors due to Yaw and Pitch Angle

5. WALL BOUNDARY EFFECTS
The static pressure indication is sensitive to distance from solid boundaries. 
The probe and boundary form a Venturi passage, which accelerates the flow and decreases the static pressure on one side. 

6. y/d
The curve shows that static readings should not be taken closer than 5 tube diameters from a boundary for 1% accuracy and 10 tube diameters is safer.

7. TURBULENCE ERRORS
Pitot-Static tubes appear to be insensitive to isotropic turbulence, which is the most common type. 
Under some conditions of high intensity, large scale turbulence, could make the angle of attack at a probe vary over a wide range.
This probe would presumably have an error corresponding to the average yaw or pitch angle produced by the turbulence

8. TIME CONSTANT The speed of reading depends on
the length and diameter of the pressure passages inside the probe,
the size of the pressure tubes to the manometer, and
the displacement volume of the manometer. 
The time constant is very short for any of the standard tubes down to 1/8" diameter.
It increases rapidly for smaller diameters. 
For this reason 1/16" OD is the smallest recommended size for ordinary use .
This will take 15 to 60 seconds to reach equilibrium pressure with ordinary manometer hook-ups. 

9. The tubes have been made as small as 1/32" OD.
But their time constant is as long as 15 minutes and they clog up very easily with fine dirt in the flow stream. 
If very small tubes are required, it is preferable to use separate total and static tubes rather than the combined total-static type. 
Where reinforcing stems are specified on small sizes, the inner tubes are enlarged at the same point to ensure minimum time constant.

10. Dynamic response of a Pitot-Static Tube

11. Assumptions
The fluid is assumed to be incompressible the total length of the fluid column remains fixed at L.
Assume that the probe is initially in the equilibrium position.
The pressure difference Δp is suddenly applied across it.
The fluid column will move during time t > 0.

12. The forces that are acting on the length L of the fluid are:
Force disturbing the equilibrium
Inertial Force
Forces opposing the change:
a. Weight of column of fluid
b. Fluid friction due to viscosity of the fluid :
The velocity of the fluid column is expected to be small and the laminar assumption is thus valid.
The viscous force opposing the motion is calculated based on the assumption of fully developed Hagen-Poiseuelle flow.
The fricitional pressure drop

13. Newton’s Law of Motion

15. Second Order System The essential parameters The static sensitivity:
The dimensionless damping ratio:
The Natural Frequency:

16. Transfer Function of a second order system for step input:

17. The transfer function is parameterized in terms of ζ and ωn.
The value of ωn doesn’t qualitatively change the system response.
There are three important cases—with qualitatively different system behavior—as ζ varies.
The three cases are called:
Over Damped System (ζ >1)
Critically Damped System (ζ =1)
Under Damped System (ζ <1)

18. General Response of A Second Order System
z=0
y(t) t
z=0.5

19. z=0.707
z=1.0 t

20. Response of Pitot tube to step input

21. Over Damped System (ζ >1)

22. y(t) t

23. Measurement of Multi-dimensional Flows

24. Five Hole Probes
The five-hole probe is an instrument often used in low-speed wind tunnels to measure flow direction, static pressure, and total pressure in subsonic flows.
This adaptation permits extending the useful calibration range up to 85 ° .
A special calibration is to been done, and new, extended range calibration curves are to be provided.

26. Probe Description
The probe consists of four direction-sensing ports plus a center port, precision bored into a conical brass tip.
Four individual small diameter stainless steel tubes connect the four side sensing ports to individual pressure transducers.
The outer millimeter diameter tube serves as the pressure transmitting channel for the center tube, as well as housing for the four side-port tubes.
This small millimeter tube is fitted within a larger tube for increased stiffness away from the sensing tip.

27. Calibration of Five Hole Probes