time constants in pitot static tubes

I was recently looking for differential pressure sensors to use in conjunction with a pitot tube to make dynamic pressure measurements. In the course of my search, I found a sensor that used the same principle as a thermal anemometer to measure the pressure, by letting a small amount of the air from one channel flow across a thermal element through to the other channel. I wondered if this "tiny leak" would affect the dynamic pressure measurement in the event that the measured value was very low (tenths of an inch of water). When I raised this question to a colleague, I was informed that the flow rate, Q, of the leak would need to be much much smaller than an "effective flow rate" at the tip of the pitot tube.

This "effective flow rate" is essentially the rate at which the fluid (in this case, air) molecules are being packed into the tube to maintain the static pressure value. Aparently, this phenomenon is well-known to intrumentation guys, but is never discussed in textbooks. This packing rate results in a settling time for a given pitot tube in a particular flow field. A similar effect might be observed with very long fluid lines experiencing a sudden increase in pressure at one end of the line. Supposedly, it takes some time before the pressure equalizes throughout the line.

Can anyone explain this phenomenon to me and point me in the direction of a reference where I might be able to derive the appropriate time constants for particular systems?

Thank you, Don

Reply to
Donalbane
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Think of a pitot tube as a flute. The time constant should be on the order of the period of the fundamental resonant tone of the flute. That will vary with the speed of sound of the medium and the effective length of the tube.

Tom Davidson Richmond, VA

Reply to
tadchem

Can I use the same reasoning for long (not necessarily straight) lines, by just treating them as straight cylinders?

Don

Reply to
Donalbane

If the radius of curvature is at a minimum several times the internal diameter of the tube, (think of a tuba or French horn) then gradual bends should not matter.

The background information that you would find most useful will be in engineering references under the heading "fluid flow," subheadings "compressible fluids", "pipes", and "gases."

HTH

Tom Davidson Richmond, VA

Reply to
tadchem

It is my understanding that I was mixing two unrelated phenomena. The speed of sound propagation of pressure is indeed the usual case, for things like long lines, etc.

However, the case with the pitot tube is different, because you aren't actually measuring pressure, but you're measuring flow and deriving a pressure from it. The flow that you're measuring is the rate at which molecules are being packed into the dynamic tube vs. the static tube. So, the settling time isn't the usual speed of sound pressure propagation time. This is why few people are familiar with this phenomenon, apart from instrumentation gurus. Does anyone know any more about this?

Don

Reply to
Donalbane

Hi Don, I am not sure what you mean about time constants for such. Have you seen this link?

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something there might help you. :)

Reply to
Spaceman

Thanks for the link.

As far as time constants, consider the pitot tube shown from the referenced link. At time zero there is no flow, and both the static pressure and total pressure are merely the result of random molecular momenta, and hence equal. Now, insert the pitot tube into a flow. Immediately, particles in the air stream impact the particles at the tip of the dynamic pressure channel in the tube and impart their momentum. It takes some time before the air molecules in the dynamic pressure channel of the tube have collectively acquired sufficient momentum to produce the new total pressure at equilibrium. This time to come to equilibrium is what I mean by the time constant. Intuitively, it seems like if you were to (for some wacky reason) make the volume of the dynamic pressure channel much larger than that of the static pressure channel, you would see a longer response time (to come to a new equilibrium) when the tube was placed into a flow field that if both channels were small.

Don

Reply to
Donalbane

By dynamic pressure I am thinking you must mean the total pressure tube. (center tube)

| It takes some time before the air molecules in the dynamic | pressure channel of the tube have collectively acquired sufficient | momentum to produce the new total pressure at equilibrium.

If you are talking about the total pressure tube, I would guess the time response would be at about the speed of sound. (basically at the rate the molecules can compress at.)

| This time | to come to equilibrium is what I mean by the time constant. | Intuitively, it seems like if you were to (for some wacky reason) make | the volume of the dynamic pressure channel much larger than that of the | static pressure channel, you would see a longer response time (to come | to a new equilibrium) when the tube was placed into a flow field that | if both channels were small.

Not really sure, but I think it would not take too much of a time difference. If any at all since the pressure will still build just about at the speed of sound.

And of course sound seems to be a good factor for such since they also state.... For higher than sound speeds. There are corrections for the shock wave that can be applied to allow us to use pitot tubes for high speed aircraft. ( I would gather they then use different compression factors) :) It sure does make one think about airplanes and all that simple, but fancy, stuff they use. :)

Reply to
Spaceman

and

What type of frequency response are you looking for?

-- Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)

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Reply to
Ed Ruf (REPLY to E-MAIL IN SIG!)

No, it is much much slower. It's a Poiseuille Flow problem. Not only is tube length important, but so is sensor volume. I've got a paper I can dig p at work on the classical method to estimate the lag. For tenths of an inch of water the driving pressure difference is fractions of this, so the response will be very slow.

-- Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)

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Reply to
Ed Ruf (REPLY to E-MAIL IN SIG!)

Wow, Cool stuff. thanks. Off to look up Poiseuille Flow problem now. :)

Reply to
Spaceman

Simple transient fluid flow problem. If you are interested in measuring the fluctuation is a total head/pitot probe, what is driving the flow from the probe to the sensor is the fluctuations themselves. Say you have a total head or pitot pressure of 10 psia with fluctuations of 0.25 psia. For the transient response of the measurement it is the 0.25 psia differential driving the flow in the tube.

-- Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)

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Reply to
Ed Ruf (REPLY to E-MAIL IN SIG!)

For application see: AFWAL-TM-85-247-FIMN The Design and Testing of Pneumatic Systems for Measuring Low pressures in Hypersonic Wind Tunnels, by M. J. Wagner and G.A. Dale, Flight Dynamics Laboratory, Wright-Patt AFB, November 1985.

which references,

Optimized Design of Systems for Measure Low Pressures in Supersonic Wind Tunnels, by J.M. Kendall, NATO, AGARD Report 174, March 1958.

and

Prediction of Pressure Response in Low Pressure Flow Regimes, by M.R. Cain, TM68-9, AFFDL, Wright-Patt AFB, October 1968.

Reply to
Ed Ruf

Dear Don,

There may be two separate questions here. The first is "What is the response time of a pitot tube?" As others have pointed out, this is a function of the sense lines connecting the pitot tube to your pressure transducer. Good places to start are:

Doebelin, Ernest O., Measurement systems; application and design, McGraw-Hill, fourth edition, 1990, pp. 123-131 and pp. 473-489.

Holman, J. P., Experimental methods for engineers, McGraw-Hill, second edition, 1971, pp. 160-167.

The second question is "What is the effect of having a nonzero mean flow in the sense lines and through the holes in the pitot tube?" I have wondered about this myself -- I have thought about bleeding a small amount of clean, dry gas through a pitot to keep it from clogging in a dusty gas stream.

In my thinking, this question can be decomposed into two parts, considering first the sense lines and then the pitot tube itself.

  1. A nonzero mean flow in a tube means that there is a pressure drop, which will bias your pressure measurement, i.e., the pressure at the transducer will not be equal to the pressure at the pitot because of the pressure drop in the line(s). Assuming that the flow rate is small, you should be able to use the Poiseuille equation to calculate this pressure difference.

  1. What effect does the flow of air in or out of the hole in the pitot tube have on the pressure there? (Normally, one assumes that the velocity is zero at the tip, so that one measures the stagnation pressure there.) I'm guessing that this effect should be negligible as long as the velocity through the hole is small compared to the freestream velocity, although it would be good to have some data on this point. I think this may be what your colleague was tlaking about.

Olin Perry Norton

Reply to
Olin Perry Norton

| >>Off to look up Poiseuille Flow problem now. | >

| >Simple transient fluid flow problem. If you are interested in measuring the | >fluctuation is a total head/pitot probe, what is driving the flow from the | >probe to the sensor is the fluctuations themselves. Say you have a total | >head or pitot pressure of 10 psia with fluctuations of 0.25 psia. For the | >transient response of the measurement it is the 0.25 psia differential | >driving the flow in the tube. | | For application see: | AFWAL-TM-85-247-FIMN | The Design and Testing of Pneumatic Systems for Measuring Low | pressures in Hypersonic Wind Tunnels, by M. J. Wagner and G.A. Dale, | Flight Dynamics Laboratory, Wright-Patt AFB, November 1985. | | which references, | | Optimized Design of Systems for Measure Low Pressures in Supersonic | Wind Tunnels, by J.M. Kendall, NATO, AGARD Report 174, March 1958. | | and | | Prediction of Pressure Response in Low Pressure Flow Regimes, by M.R. | Cain, TM68-9, AFFDL, Wright-Patt AFB, October 1968.

Thank you very much Ed. :)

Reply to
Spaceman

Thanks very much for knowing what I was talking about Ed and Olin!

Ed, we aren't necessarily looking for a particular frequency response. We just want to understand this problem more, so that we are smart about what sensors we use and how long we wait before making our measurements, etc. Thanks for the references!

Don

Reply to
Donalbane

Olin, yes. This is what I'm trying to understand. I know that there will be an effect if there is flow in the pitot tube, but I'm trying to see how small this can be and be negligible relative to the pressure measurement. I did a comparison of the velocities as you mentioned, and found that for the low pressures we are measuring, the sensor was not suitable, however the sensor claims to be ESPECIALLY good at low pressures, so I'm not sure that the comparison was valid.

Don

Reply to
Donalbane

If you are looking for a good pressure sensor to measure very small differential pressures, you might try Validyne. (

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)

Their product line goes as low as 0.1 inch of water full scale.

Olin Perry Norton

Reply to
Olin Perry Norton

This may be of help. A bulb with a restrictive orifice like the pitot or your extra sensor that stores a gas or fluid has a sharp resonant frequency. It is known as a Helmholtz resonator and is the basis of the ocarina. That makes your search more difficult than just a time constant. Working below resonance it might resemble a spring coefficient. I learned about this in the early days of ink jets when I was aksed to find out why their design spattered ink when it got to 5 KC, and it matched the Helmholtz criteria to within 10% or so. Jet tube .002" if I recall. I wrote a paper on it but I can't find it. John Polasek

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Reply to
John C. Polasek

NACA TN-803, "Some effects of rainfall on flight of airplanes and on instrument indications," by Richard V. Rhode, April 1941, available at

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regarding water in pitot lines,

"The use of a hand-pressure pump in the pressure line to clear it of water, which is an expedient adopted by some air lines, cannot be considered a guaranty against serious errors if the pilot does not recognize malfunctioning of the air-speed system. A continuously operating mechanical pump, designed to provide a continuous slight flow of air in the pressure line toward the pitot opening ("reverse leak"), has been suggested as an alternative. Tests of a reverse leak, made during the rain tests on pitot tubes previously described in this paper, indicated that the method is successful in principal... "

Unfortunately, this report does not seem to give any details, such as how much flow is a "slight flow."

Olin Perry Norton

Reply to
Olin Perry Norton

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