Practical%20Aspects%20of%20using%20Pitot%20Tube

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Practical Aspects of using Pitot Tube

• P M V Subbarao
• Professor
• Mechanical Engineering Department

Corrections to Devotion from Potential Flow
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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.

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Errors due to Yaw and Pitch Angle
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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. 

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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.
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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

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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. 

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• 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.

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Dynamic response of a Pitot-Static Tube
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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 ?p is suddenly applied
  across it.
• The fluid column will move during time t gt 0.

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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
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Newtons Law of Motion
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Second Order System
The essential parameters
The static sensitivity
The dimensionless damping ratio
The Natural Frequency
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Transfer Function of a second order system for
step input
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• The transfer function is parameterized in terms
  of ? and ?n.
• The value of ?n doesnt qualitatively change the
  system response.
• There are three important caseswith
  qualitatively different system behavioras ?
  varies.
• The three cases are called
• Over Damped System (? gt1)
• Critically Damped System (? 1)
• Under Damped System (? lt1)

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General Response of A Second Order System
t
z0
y(t)
t
z0.5
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z0.707
z1.0
t
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Response of Pitot tube to step input
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• Over Damped System (? gt1)

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y(t)
t
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Measurement of Multi-dimensional Flows
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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.

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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 3.175 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 3.175 millimeter tube is fitted within
  a larger tube for increased stiffness away from
  the sensing tip.

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Calibration of Five Hole Probes
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