# How to Measure Very Small Differential Pressure in a Subsonic Wind Tunnel

agnimusayoti
TL;DR Summary
Currently I conduct an education tools for my university project. I build an simple subsonic-open circuit wind tunnel. I want to measure differential pressure in object inside the wind tunnel which under influence of low speed wind.
I assume that air have ##1 kg/m^3## density.
Therefore, using Bernoulli equation, on upside and downside of my test object, there is a differential pressure ##\Delta P##:
$$\Delta P=0.5*(v_2^2 - v_1^2)$$
From cases:
(a) ##v_1 = 1 m/s## and ##v_2 = 2 m/s##, then ##\Delta P = 1,5 Pa##
(b) ##v_1 = 10 m/s## and ##v_2 = 20 m/s##, then ##\Delta P=150 Pa##
I conclude that I need an instrument which can measure differential pressure from 0 up to 200 Pa with 0,1 Pa accuracy.

Could you suggest an instrumentation system that can cover my tasks? The constraints are in low production cost and availability sensors or tools in my country.

[Mentor Note -- Poster's Profile Page lists Indonesia as his country]

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agnimusayoti
Yes, I am from Indonesia. Thanks dear mentor.

berkeman
Gold Member
Thanks dear mentor.

hutchphd and berkeman
2021 Award
Search 'digital manometer' and you will find; https://www.ebay.com.au/itm/283893957464

But you are asking for something with about 100 times better resolution.
200 Pa ± 0.1 Pa
0.002 bar ± 0.000001 bar
2 mbar ± 0.001 mbar

You will probably have to make a symmetrical differential sensor for the job.
I expect it will need a large diaphragm with an electrical or optical measuring system.

hutchphd
Mentor
You could get close to your desired accuracy with an inclined tube water manometer. Dwyer Instruments has a good discussion of these: https://www.dwyer-inst.com/ApplicationGuides/?ID=11. This diagram is from that link:

200 Pa is about 20 mm of water column, so 0.1 Pa would be 0.01 mm water. Multiply the water displacement by 10 for a tube inclined at 5.7 degrees. Note that the diagram is slightly misleading - you need to measure the water level change horizontally, not vertically. Measuring to 0.1 Pa is unrealistic, but you might be able to measure to 0.5 Pa. And the possibility of a good lecture about how measurement accuracy sets the minimum velocity in the wind tunnel.

Klystron, agnimusayoti, russ_watters and 2 others
Mentor
BME280 has a resolution around 0.2 Pa - while not ideal for your needs it is very cheap and easy to buy.

agnimusayoti
BME280 has operation range of 300 to 1100 hPa, which is not compatible for my need.

Are there any sensors that can measure small differential pressure? Or should I use manometer for my instrument?

agnimusayoti
You could get close to your desired accuracy with an inclined tube water manometer. Dwyer Instruments has a good discussion of these: https://www.dwyer-inst.com/ApplicationGuides/?ID=11. This diagram is from that link:
View attachment 285917
200 Pa is about 20 mm of water column, so 0.1 Pa would be 0.01 mm water. Multiply the water displacement by 10 for a tube inclined at 5.7 degrees. Note that the diagram is slightly misleading - you need to measure the water level change horizontally, not vertically. Measuring to 0.1 Pa is unrealistic, but you might be able to measure to 0.5 Pa. And the possibility of a good lecture about how measurement accuracy sets the minimum velocity in the wind tunnel.
If I choose alcohol and 5 degree inclination, so I need 0,15 mm water displacement. Here is my calculation:
$$P_A = (\rho)(g)(d sin \theta) + P_B$$
So, differential pressure between leftside and right side is:
$$\Delta P = P_A - P_B = (\rho) (g) (d sin\theta)$$

For alcohol, the density is ##\rho = 789 kg/m^3## and for ##\theta = 5\deg##. Using ##g = 9,81 m/s^2##I get:
$$d = \frac{P_A - P_B}{674.59 kg/(m^2 s^2)}$$

Is my model true?

But, How can I measure 0.15 mm water displacement? Could I use camera analysis?

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Mentor
How can I measure 0.15 mm water displacement?
Very carefully. Try putting a mirror behind the manometer tube, try using a magnifying glass, and experiment.

Another possibility is a low range differential pressure transducer. I found these by using the Digikey (https://www.digikey.com/) search function:

Differential pressure as low as +/- 0.5 inches water full scale: https://www.allsensors.com/datasheets/DS-0376_Rev_A.pdf. These have digital outputs.

This one has analog output at 1.0 inches water full scale: https://www.sensata.com/sites/defau...ferential pressure mount sensor-datasheet.pdf

Other distributors include Mouser and Newark. I have had good experiences with all three of these distributors. Digikey lists shipping times to the Philippines, so they should be able to ship to Indonesia.

berkeman
Gold Member
It's really all a matter of what you are willing and able to spend. There are plenty of pressure transducers that can measure pressures and pressure differences that low. They just aren't generally the cheapest devices on the market. You can also get an analog transducer that can be amplified provided your background noise isn't too high.

agnimusayoti
Well, I decided to try the inclined manometer for my instrument. Do I need to calibrate the manometer? I mean, how I believe my instrument measure air pressure accurately?

Mentor
Manometers are inherently accurate, so can be used to calibrate mechanical pressure gauges and electronic pressure sensors. An inclined manometer is as accurate as the sources of error:

Gravity
Fluid density
Inclination angle

At low pressures, measurement error will be the largest error.

agnimusayoti
Okayy Thanks all.

berkeman
Mentor
how I believe my instrument measure air pressure accurately?
You could perhaps get an idea of the accuracy of gauge pressure measurements with your inclined manometer by connecting it to a rigid reservoir of air and connecting that to a small syringe. By making small volume changes of the air in the syringe, and knowing the total volume of air in the reservoir and syringe (and any connecting tubing), you should be able to predict what the change in gauge pressure should be. You could use some quick calculations to see how small you can make the gauge pressure changes in order to figure out if this will be a valuable test for you.

https://www.perkinelmer.com/product/250-ul-syringe-kit-w-250-ul-buffer-tbg-n2936052

agnimusayoti

Guys, after a few trial, I decided to use simple U tube manometer as an inclined manometer. I used oil as working fluid which has ##\rho = 890 kg/m^3##. The angle between oil column and horizontal approximately as large as 4 degree. Theoretically, the oil surface will drop because P outside (connected to column under) is bigger than P inside wind tunnel. But, I didn't observe any oil surface movements. What do you think I can do to improve this simple instrument? Thanks.

agnimusayoti
I placed my manometer under the wind tunnel. Does the location of manometer from propeller affect the measurement?

2021 Award
What do you think I can do to improve this simple instrument? Thanks.
Stepwise refinements.

In the post #15, upper picture, it looks to me like you have a bubble in your liquid column. The column must be bubble free in the loop.

You have mounted the 'U' loop on the vertical plane. I would have mounted it on a horizontal surface, then tilted the surface by about 4°.

I'm not sure of your material, if the tube was hard and straight, like acrylic or glass tube, there would be less wandering error in the reading scale.

If you can use a fitting to reduce the radius of curvature, the two legs can be closer together, that will reduce the reading error. Place the tubes right next to each other, not separated by the width of the scale.

Rather than a thick clear oil, consider using an alcohol or kerosene that will flow faster and accept a strong coloured food dye.

Tom.G
agnimusayoti
Which bubble do you mean? Does it located beside the 9 scale?

My U manometer is made from glass, like another standard laboratory equipment. Therefore the two legs is stiff and can't be moved closer to each other.

Well then, I will try to place the manometer on horizontal plane and tilt it 4 degree.

agnimusayoti
How if I use two open capilary pipes, connected with sillicon hose? Is it same with U manometer?

2021 Award
Which bubble do you mean? Does it located beside the 9 scale?
Yes, there is liquid between 9.0 and 9.6; The bubble is between that and the main liquid.
A manometer is not calibrated if there are bubbles in the liquid.

How if I use two open capilary pipes, connected with sillicon hose? Is it same with U manometer?
Yes. If you use two tubes they can be very close together and can be joined at the bend. That will reduce reading errors.

agnimusayoti
Uh I see. Well I'll try to eliminate the buble first. first I think at that column, fluid's surface must be located above the joint beside the 9 scale. Problem is the column length is not that long to cover fluid's height.

But if can't, I will try to use to open capilary pipes. Thankss.

agnimusayoti
Yes, there is liquid between 9.0 and 9.6; The bubble is between that and the main liquid.
A manometer is not calibrated if there are bubbles in the liquid.

Yes. If you use two tubes they can be very close together and can be joined at the bend. That will reduce reading errors.
One more, I think if the manometer is on horizontal plane, there will be a difficulty to take the picture. What should I do if the manometer is still on vertikal plane?

2021 Award
What should I do if the manometer is still on vertikal plane?
Experiment with many alternatives.
You will have several manometers all in the same picture.
Keep one manometer disconnected, so it can act as a level reference and control.

agnimusayoti
How many manometer do I need? 3? 2 manometer connected to the object and 1 as reference?

2021 Award
The closer you can get the camera to the tubes, the better the pixel and pressure resolution.
That suggests all tubes should be close together. The best way to do that is to have camera axis close to vertical with all tubes parallel, on a sloping surface.

You must have some way to identify the horizontal and zero pressure in the picture. Place the two reference manometer tubes in the outer positions to give a good estimate of cross-slope.

How many cameras will you use?
How will you make measurements from the pictures?
Will you count pixels?

agnimusayoti
Is this incline U manometer or simply U manometer?

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agnimusayoti
The closer you can get the camera to the tubes, the better the pixel and pressure resolution.
That suggests all tubes should be close together. The best way to do that is to have camera axis close to vertical with all tubes parallel, on a sloping surface.

You must have some way to identify the horizontal and zero pressure in the picture. Place the two reference manometer tubes in the outer positions to give a good estimate of cross-slope.

How many cameras will you use?
How will you make measurements from the pictures?
Will you count pixels?
i think I just use 1 camera (phone's camera) and using picture analyzer like Tracker.

What is sloping surface? What is cross slope? Sorry I don't understand.

2021 Award
agnimusayoti
The closer you can get the camera to the tubes, the better the pixel and pressure resolution.
That suggests all tubes should be close together. The best way to do that is to have camera axis close to vertical with all tubes parallel, on a sloping surface.

You must have some way to identify the horizontal and zero pressure in the picture. Place the two reference manometer tubes in the outer positions to give a good estimate of cross-slope.

How many cameras will you use?
How will you make measurements from the pictures?
Will you count pixels?
Ohh i see. So, if I use a ruler beside the column and the ruler is parallel with horizontal line, can I use the vertical one? Then I need to place two manometer close each other?

I prefer vertical one because I still don't understand the hydrostatics prinsipal in the ramp manometer. Do you have any idea about this? Or literature.. thanks again