Dynamic/Static pressure -- High speed railways

[Brendan1]

I am currently doing a research project in the attenuation of pressure waves. With an focus on dealing with sonic booms the are generated from high speed train tunnels. my experiments involved pressurizing a cylinder then using a rapid release valve allowing the air to escape along a pipe. I having issues in my head determining between static and dynamic pressure and the readings i have taken are confusing me. Any advice would be appreciated.

The graphs posted below:
the 1st plot

the dashed red line is the pressure inside the vessel after the valve is opened.

the black line is the pressure history of the 1st transducer in the pipe the pipe line is the pressure transducer near the exit if pipe

other lines are pressure transducers attached to the vessel.

the second plot

the gauge and the transducers start at the same level as the transducers only detect a change in pressure and won't detect a static pressure

 

[Nidum]

I having issues in my head determining between static and dynamic pressure and the readings i have taken are confusing me.

Have you done any courses in basic fluid mechanics ?

 

[Brendan1]

Have you done any courses in basic fluid mechanics ?

Yes I have, I'm pretty familiar with all the main concepts, just seem to have confused myself in the context of this experiment.

 

[Nidum]

Please tell us some more about your experimental set up .

 

[Nidum]

Access to your attachments is being blocked so I can't see the graphs .

 

[berkeman]

Here they are:

 

[Brendan1]

Here is my lab set up. the box with the slighter shading is the pressure gauge. and my pipe / tubing is 8mm in diameter

 

[Brendan1]

Have you done any courses in basic fluid mechanics ?

The thing I am trying to wrap my head around is, when the pipe is made longer the. the pressure by the vessel exit increases, is this due to the added weight of the air in a longer pipe compared to a shorter one?

 

[JBA]

the black line is the pressure history of the 1st transducer in the pipe the pipe line is the pressure transducer near the exit if pipe

You have an error in the last section of your above statement. What is the color of the trace for the second pipe transducer

What is the orientation of the sensing tubes of the two pipe transducers and have they all been calibrated for the identical pressure range?

None of the pressure sensors should register a maximum pressure greater than that of the tank at any point in time.

 

[Brendan1]

You have an error in the last section of your above statement. What is the color of the trace for the second pipe transducer

What is the orientation of the sensing tubes of the two pipe transducers and have they all been calibrated for the identical pressure range?

None of the pressure sensors should register a maximum pressure greater than that of the tank at any point in time.

Sorry you are right that is confusing the black line is transducer at at the beginning of the pipe just after the vessel

the pink line is a transducer on the end of pipe near the exit of open to the air

the sensors are perpendicular to the flow of the air, yes i have calibrated them all for the same rage of pressures

yes this is what is confusing me. I think is because the vessel diameter is 200mm length 2m and the pipe is 8mm and varies in length so if you were trying to move the the volume of air in that big vessel through a small pipe would this not cause a spike in pressure?

 

[Randy Beikmann]

the second plot

the gauge and the transducers start at the same level as the transducers only detect a change in pressure and won't detect a static pressure

By this do you mean that the transducers won't measure a "steady" pressure (static meaning steady, rather than static meaning "not dynamic" pressure as measured by a Pitot tube), or that you have subtracted the initial pressure at each transducer from that transducer's measurement? If they won't measure a steady pressure, do they all have the same cut-off frequency? Some transducers might not measure below 5 Hz, some not below 10 Hz...

I'm also trying to figure out if your transducers are not all calibrated to produce the same pascals/volt. I might believe that at some point in time the pressure level in the tube could be higher than the pressure vessel from wave action (maybe), but it definitely shouldn't be all the time. That just sounds like a transducer gain error to me.

 

[Brendan1]

By this do you mean that the transducers won't measure a "steady" pressure (static meaning steady, rather than static meaning "not dynamic" pressure as measured by a Pitot tube), or that you have subtracted the initial pressure at each transducer from that transducer's measurement? If they won't measure a steady pressure, do they all have the same cut-off frequency? Some transducers might not measure below 5 Hz, some not below 10 Hz...

I'm also trying to figure out if your transducers are not all calibrated to produce the same pascals/volt. I might believe that at some point in time the pressure level in the tube could be higher than the pressure vessel from wave action (maybe), but it definitely shouldn't be all the time. That just sounds like a transducer gain error to me.

Yes that was what i meant they won't detect steady pressure, yes they all have the safe cut off frequency. I have calibrated them all for the same pressure range and translated that voltage to pressure for each individual transducer used. Yes this is the idea behind the project of pressure wave traveling down the tube​

 

[Randy Beikmann]

Yes that was what i meant they won't detect steady pressure, yes they all have the safe cut off frequency. I have calibrated them all for the same pressure range and translated that voltage to pressure for each individual transducer used. Yes this is the idea behind the project of pressure wave traveling down the tube​

I would repeat the test after swapping the transducer in the pressure vessel with the one nearest it, in the tube. If you still get the same relative pressure between them, then we can scratch our heads some more. If it looks different, then there's something going on with the transducers.

The ultimate check on the transducers would be, if possible, to plug them all into the pressure vessel at the same time, and then run the test (or run the test multiple times, with all the transducers taking turns in the vessel). If they all look the same, you can have full confidence in the measurements. If not...

 

[russ_watters]

I having issues in my head determining between static and dynamic pressure and the readings i have taken are confusing me.
[snip]
...the sensors are perpendicular to the flow of the air...

The difference between a static and dynamic pressure measurement is the orientation of the probe: static pressure is measured perpendicular to the airstream and total pressure is measured parallel to it. Subtract them and you get dynamic pressure.

...the gauge and the transducers start at the same level as the transducers only detect a change in pressure and won't detect a static pressure

I'm having trouble interpreting that: are you saying they all have the same reference pressure? Note, that when it comes to air, every reading is a differential (change in) pressure. There's no problem with that; you just have to subtract-out the reference as needed (per my description of the dynamic pressure, above).

I think is because the vessel diameter is 200mm length 2m and the pipe is 8mm and varies in length so if you were trying to move the the volume of air in that big vessel through a small pipe would this not cause a spike in pressure?

I'm not certain of what you are trying to say, but air flows from areas of high total pressure to low total pressure - that's what makes it move. You might see a drop in static pressure and then a rise again if pipe size changes, but you should never see a total pressure above the vessel pressure.

 

[JBA]

Just for clarity, the dynamic and static probes must be located at the same position along the pipe for this dynamic vs static differential calculation to be valid.

For reference, what is the length of your test pipe?

An alternative transducer test would be to seal the discharge end of the tube and then pressurize the tube at a controlled rate. The peak pressure reading of the tube transducers should not exceed the initial prerelease pressure reading of the tank transducer and gauge.

 

[boneh3ad]

yes this is what is confusing me. I think is because the vessel diameter is 200mm length 2m and the pipe is 8mm and varies in length so if you were trying to move the the volume of air in that big vessel through a small pipe would this not cause a spike in pressure?

No. Under no circumstances should the pressure downstream of your reservoir end up higher in pressure than your reservoir. Assuming sufficiently high reservoir pressure, as soon as you open the valve (or rather, after some short but finite development time), you will have a shock wave that propagates downstream through your tube and an expansion wave that propagates upstream through your tank. That expansion wave is what essentially sets the gas in the tank in motion out through the tube. There will be some period of quasi-steady operation as the expansion propagates backward, at which point the total pressure in the tube (behind the shock) should match the total pressure in the reservoir in the region that has already been accelerated. In the region of the tube that hasn't seen the shock yet, you would still be at atmospheric.

This doesn't account for viscous losses, but should get you pretty close. There is no way for the pressure in the tube to rise above that of the tank, though, as viscosity would only serve to dissipate energy (and therefore total pressure) in the region with moving gas (i.e. the tube).

Yes that was what i meant they won't detect steady pressure, yes they all have the safe cut off frequency.

Be careful with your terminology. Static pressure has a very specific meaning in fluid mechanics, and is typically synonymous with the thermodynamic pressure. That's the pressure felt by the surface of an imaginary object in the flow (without slowing down or otherwise changing the flow). Total pressure, in either case, is the pressure observed if you slow the flow down isentropically to zero velocity. It is also a measure of the total energy pool available to the flow. That's all pretty straightforward.

Here's where this is going to get tricky; the relationship between static, total, and dynamic pressure is going to be different for compressible and incompressible flows. In an incompressible flow, you use a Pitot tube to measure total pressure and a static pressure port to measure the static pressure, and the difference between the two is the dynamic pressure, $\rho V^2/2$, which is essentially the kinetic energy in the flow due to the bulk fluid motion. For a compressible flow, this isn't true. You now have to deal with the fact that internal energy is not constant in the fluid and can also play a role in the energy balance. It's a term in the energy equation that vanishes for incompressible flows and leads directly to Bernoulli's equation, but can't be ignored in a compressible flow.

Your flow is absolutely compressible.

Note, that when it comes to air, every reading is a differential (change in) pressure. There's no problem with that; you just have to subtract-out the reference as needed (per my description of the dynamic pressure, above).

This is not correct. You can buy both absolute and differential pressure transducers. Not every measurement is differential. It is, of course, of paramount importance to know which you have.

I'm not certain of what you are trying to say, but air flows from areas of high total pressure to low total pressure - that's what makes it move. You might see a drop in static pressure and then a rise again if pipe size changes, but you should never see a total pressure above the vessel pressure.

This is also not true. Fluids accelerate from areas of high pressure to low pressure. They move all sorts of ways depending on the pressure gradient, viscosity, gravity, and their inertia. A fluid with sufficient inertia can certainly move from a low pressure region to a high pressure region. It will just slow down when it does so.

 

[Brendan1]

Just for clarity, the dynamic and static probes must be located at the same position along the pipe for this dynamic vs static differential calculation to be valid.

For reference, what is the length of your test pipe?

An alternative transducer test would be to seal the discharge end of the tube and then pressurize the tube at a controlled rate. The peak pressure reading of the tube transducers should not exceed the initial prerelease pressure reading of the tank transducer and gauge.

Thank you, for that I will see if i can apply these methods.

my pipe is 127 cm long with a transducer located at 28cm along and another at the end of the pipe.

 

[Brendan1]

No. Under no circumstances should the pressure downstream of your reservoir end up higher in pressure than your reservoir. Assuming sufficiently high reservoir pressure, as soon as you open the valve (or rather, after some short but finite development time), you will have a shock wave that propagates downstream through your tube and an expansion wave that propagates upstream through your tank. That expansion wave is what essentially sets the gas in the tank in motion out through the tube. There will be some period of quasi-steady operation as the expansion propagates backward, at which point the total pressure in the tube (behind the shock) should match the total pressure in the reservoir in the region that has already been accelerated. In the region of the tube that hasn't seen the shock yet, you would still be at atmospheric.

This doesn't account for viscous losses, but should get you pretty close. There is no way for the pressure in the tube to rise above that of the tank, though, as viscosity would only serve to dissipate energy (and therefore total pressure) in the region with moving gas (i.e. the tube).
Be careful with your terminology. Static pressure has a very specific meaning in fluid mechanics, and is typically synonymous with the thermodynamic pressure. That's the pressure felt by the surface of an imaginary object in the flow (without slowing down or otherwise changing the flow). Total pressure, in either case, is the pressure observed if you slow the flow down isentropically to zero velocity. It is also a measure of the total energy pool available to the flow. That's all pretty straightforward.

Here's where this is going to get tricky; the relationship between static, total, and dynamic pressure is going to be different for compressible and incompressible flows. In an incompressible flow, you use a Pitot tube to measure total pressure and a static pressure port to measure the static pressure, and the difference between the two is the dynamic pressure, $\rho V^2/2$, which is essentially the kinetic energy in the flow due to the bulk fluid motion. For a compressible flow, this isn't true. You now have to deal with the fact that internal energy is not constant in the fluid and can also play a role in the energy balance. It's a term in the energy equation that vanishes for incompressible flows and leads directly to Bernoulli's equation, but can't be ignored in a compressible flow.

Your flow is absolutely compressible.
This is not correct. You can buy both absolute and differential pressure transducers. Not every measurement is differential. It is, of course, of paramount importance to know which you have.
This is also not true. Fluids accelerate from areas of high pressure to low pressure. They move all sorts of ways depending on the pressure gradient, viscosity, gravity, and their inertia. A fluid with sufficient inertia can certainly move from a low pressure region to a high pressure region. It will just slow down when it does so.

This is what is really confusing me I don't see how the pressure can be higher in the tube than in the vessel but have have changed around the transducers used. and get the same results so i don't think it is a amplifier error.

The 3 transducers attached to the vessel green, blue and red line, and the two in the pipe are for "dynamic pressure measurement" black and pink line (that's what it says in its manual.)

There is one pressure gauge attached to the vessel that that reads the "steady pressure" the red dashed line. I will double check the calibration but I have good confidence as I was done with the help of a prof.

Thank you for your imput

 

[boneh3ad]

It's hard to say exactly, but absolutely make sure you know which (if any) gauges are reading out in absolute and which are differential. That way you can make sure you have accounted for atmospheric pressure in the event that you forgot.

So your tank is only filled up to 10 kPa gage pressure? If that's the case, then it is possible the gauge is measuring in gage pressure while your other transducers are absolute, which would explain why you get 70 kPa on the black line. That would mean the absolute pressure in the tank is actually 111 kPa absolute and still higher than your black line.

 

[russ_watters]

This is not correct. You can buy both absolute and differential pressure transducers. Not every measurement is differential. It is, of course, of paramount importance to know which you have.

I'd be interested in seeing one, but my suspicion is that it does the calculation internally or, rather, measures a differential using a vacuum reference; I know of no way to actually measure absolute pressure directly.

This is also not true. Fluids accelerate from areas of high pressure to low pressure. They move all sorts of ways depending on the pressure gradient, viscosity, gravity, and their inertia. A fluid with sufficient inertia can certainly move from a low pressure region to a high pressure region. It will just slow down when it does so.

We're talking about air in a pipe here -- though I'd be interested in hearing about a scenario where inertia could play a role.

 

[Brendan1]

It's hard to say exactly, but absolutely make sure you know which (if any) gauges are reading out in absolute and which are differential. That way you can make sure you have accounted for atmospheric pressure in the event that you forgot.

So your tank is only filled up to 10 kPa gage pressure? If that's the case, then it is possible the gauge is measuring in gage pressure while your other transducers are absolute, which would explain why you get 70 kPa on the black line. That would mean the absolute pressure in the tank is actually 111 kPa absolute and still higher than your black line.

Good news! In the code i was using plot pressure for some reason the pressure from the transducers were being multiplied by 10 i have no idea why this was here it was commented as a correction term. anyway now the results make much more sense and the pressure in the tube never higher than the cylinder. I have attached a updated pdf of the results.

Now i just need to work out why the pressure reading in tube transducers increases as the tube gets longer.

and what causes the spike in the tube transducers and what causes the spike to slow down.

and what are the negative pressure reading in the tube transducers

 

[boneh3ad]

I'd be interested in seeing one, but my suspicion is that it does the calculation internally or, rather, measures a differential using a vacuum reference; I know of no way to actually measure absolute pressure directly.

Generally speaking, yes, there is some internal reference pressure. The important thing, though, is that is not a user-facing feature and all outputs are in absolute pressure (or a voltage that is directly calibrated to absolute pressure) rather than gage. There's no need to subtract anything.

We're talking about air in a pipe here -- though I'd be interested in hearing about a scenario where inertia could play a role.

The Navier-Stokes equations are essentially a statement of Newton's laws, with the inertia of a flow captured on the left side and the various forces on the right, so that $\rho(\partial_t u + \vec{v}\cdot\nabla u)$ term captures the inertia of the moving fluid. If it already has velocity in one direction, it can certainly move into a region of higher pressure, all the while slowing down. In a pipe, this is probably most likely to happen if the flow is unsteady and, say, you suddenly shut off an outlet valve and the upstream pressure suddenly increases and the fluid moves a small but finite distance upstream against that pressure gradient until it reaches equilibrium.

Good news! In the code i was using plot pressure for some reason the pressure from the transducers were being multiplied by 10

Well, that will do it.

Now i just need to work out why the pressure reading in tube transducers increases as the tube gets longer.

and what causes the spike in the tube transducers and what causes the spike to slow down.

and what are the negative pressure reading in the tube transducers

These sound like fun things to work out. You can probably handle it, though. I believe I've already given you some hints that should shed some light on it.

 

[Brendan1]

Generally speaking, yes, there is some internal reference pressure. The important thing, though, is that is not a user-facing feature and all outputs are in absolute pressure (or a voltage that is directly calibrated to absolute pressure) rather than gage. There's no need to subtract anything.
The Navier-Stokes equations are essentially a statement of Newton's laws, with the inertia of a flow captured on the left side and the various forces on the right, so that $\rho(\partial_t u + \vec{v}\cdot\nabla u)$ term captures the inertia of the moving fluid. If it already has velocity in one direction, it can certainly move into a region of higher pressure, all the while slowing down. In a pipe, this is probably most likely to happen if the flow is unsteady and, say, you suddenly shut off an outlet valve and the upstream pressure suddenly increases and the fluid moves a small but finite distance upstream against that pressure gradient until it reaches equilibrium.
Well, that will do it.
These sound like fun things to work out. You can probably handle it, though. I believe I've already given you some hints that should shed some light on it.

Thank you for all your help, I will get stuck into these questions, I might come back to check if am on the write lines if that's ok, but now the results are in a more sensible form i hope it becomes clear to me.

 

[JBA]

What is the published full range pressure rating and percent accuracy of the transducers?

 

[Brendan1]

Hello, sorry for losing touch but I would just like to say thank you all very much for your imput I really appreciate it I have now submitted my project and the final results did make sense in the end.

regards

Brendan