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

Practical Aspects of using Pitot Tube

P M V SubbaraoProfessor

Mechanical Engineering Department

Corrections to Devotion from Potential Flow

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.

Errors due to Yaw and Pitch Angle

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. 

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.

y/d

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

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. 

• 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.

Dynamic response of a Pitot-Static Tube

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.

The forces that are acting on the length L of the fluid are:

Inertial Force 2

2

dt

hdLAamF fffluidfluidi

Force disturbing the equilibrium pAF mdis

Forces opposing the change:a. Weight of column of fluid

b. Fluid friction due to viscosity of the fluid :

vffvfluidg ghAghmF

dt

dh

d

Lu

d

Lp mf 22

3232 The fricitional pressure drop

ffriviscous ApF

•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.

mfviscous ApF

dt

dh

d

LApAF mfmviscous 2

32

Newton’s Law of Motion

viscousgdisi FFFF

dt

dh

d

LAghApA

dt

hdLA mvmfmmf 22

2 32

dt

dh

d

Lghp

dt

hdL vff 22

2 32

pghdt

dh

d

L

dt

hdL vmm

22

2 32

hmm

hg

ph

dt

dh

gd

L

dt

hd

g

L

22

2 32

phhgdt

dh

d

L

dt

hdL hmm

22

2 32

Second Order System

vmm

hg

ph

dt

dh

gd

L

dt

hd

g

L

22

2 32

vmm

hg

pba

gd

La

g

La

00212 &1;

32;

The essential parameters

The static sensitivity:v

m

hg

p

a

bK

0

0

The dimensionless damping ratio:g

Lgd

L

aa

a

m

2

20

1

2

32

2

The Natural Frequency:L

g

a

an

2

0

vmnn

hg

p

dt

dh

dt

hd

121

2

2

2

012

2

1

asaassX

sYG(s)

Transfer Function of a second order system for step input:

22

2

2

2 21

2

1

nn

n

nn

sss

sG(s)

gs

psX

m

22

2

2 nnm

n

ssgs

psY

•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)

General Response of A Second Order System

t

ty(t)

p

gty m

)(

p

gty m

)(

t

p

gty m

)(

Response of Pitot tube to step input

p

gty m

)(

• Over Damped System (ζ >1)

12

322

gLgd

L

m

12

322

g

L

d m

162

g

d

L m

teteg

pty n

tn

t

m

nn 1sinh1

1cosh1)( 2

2

2

t

y(t)

Measurement of Multi-dimensional Flows

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.

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.

Calibration of Five Hole Probes