Air speed and Differential pressure

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Discussion Overview

The discussion revolves around the relationship between air speed and differential pressure in a tube with a restrictor. Participants explore the possibility of deriving a simpler theoretical relation than Darcy's law to calculate air speed using differential pressure measurements, particularly in the context of an air speed bench experiment.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant seeks a simpler relation than Darcy's law, proposing a formula of the form V = kP, where V is air speed and P is differential pressure.
  • Another participant questions the clarity of the initial question, asking for specific dimensions of the tube and flow rates to better understand the scenario.
  • A participant provides details about the experimental setup, including tube diameter, air speed ranges, and the use of a rotating vane anemometer, expressing uncertainty about measurement repeatability.
  • There is a discussion about the applicability of Darcy's law, with one participant noting that it is intended for flow through porous media, which may not be relevant to the current situation.
  • One participant mentions a formula they found online for flow through a constriction, but expresses confusion about an unknown parameter in the equation.
  • Another participant clarifies a previous mistake regarding the unknown parameter in the formula, indicating a desire to compare experimental results with theoretical predictions.
  • Concerns are raised about measuring average air speed versus specific points in the flow, with acknowledgment that the speed profile may not be uniform.
  • Participants discuss the nature of the restriction used in the experimental setup and its intended purpose to maintain a minimum air speed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to derive a relationship between differential pressure and air speed. There are competing views on the applicability of Darcy's law and the appropriate methods for measurement and calculation.

Contextual Notes

Limitations include the lack of specific parameters such as the shape of the constriction and the exact flow conditions, which may affect the applicability of proposed formulas. The discussion also highlights the uncertainty in measurement techniques and the need for further clarification on the experimental setup.

  • #31
Chet,

I stop my calculation few minutes ago and post this reply, I'm afraid to make you angry with my difficulties to understand, but, I have a doubt again, If K= k/2 (K = two honeycomb in series, and k = one honeycomb) why taking L for one honeycomb? in the formula :
Q = (K.A.∆P) / (μ.L)
If I need to add the reciprocal of the k's to have K, why K= k/2 ?
 
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  • #32
MARECHAL said:
Chet,

I stop my calculation few minutes ago and post this reply, I'm afraid to make you angry with my difficulties to understand, but, I have a doubt again, If K= k/2 (K = two honeycomb in series, and k = one honeycomb) why taking L for one honeycomb? in the formula :
Q = (K.A.∆P) / (μ.L)
If I need to add the reciprocal of the k's to have K, why K= k/2 ?
You're an electrical engineer, right. In fluid flow, the permeability is a conductivity, and thus it is the reciprocal of resistance. For two identical resistors in series, the overall resistance is twice the resistance of each individual resistor. This means that the overall conductivity is half the individual conductivity.

Chet
 
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  • #33
Chet,

Oops! Ok... the conductivity of the fluid... By analogy to electrical resistors, it is a good "picture" for me to understand the permeability.
I'm going to take my calculator and calculate now.
Next week, I will try to measure ∆P with an instrument and compare it to the anemometer, with only the two honeycomb, (without the large fiber filter) with the formula... I'm a little bit worrier and impatient.
"See" you later.
 
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  • #34
Good Afternoon,

I'm a little bit disappointed by my calculation, sure I made a mistake, but where?
By experimentation k is not constant ; from 0,16 @ 0,52 m/s to 0,07 @ 6,88 m/s and with calculation k is 1,3e5... something is wrong.
Please see my (bad) calculation in this upload file :
 
  • #35
Here :
 

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  • #36
MARECHAL said:
Good Afternoon,

I'm a little bit disappointed by my calculation, sure I made a mistake, but where?
By experimentation k is not constant ; from 0,16 @ 0,52 m/s to 0,07 @ 6,88 m/s and with calculation k is 1,3e5... something is wrong.
Please see my (bad) calculation in this upload file :
Please show some data on Δp vs v. Please give the units of Δp. Also please make a graph of Δp vs v. What does it look like?

(Giving values of the parameters without their units is useless.)

Chet
 
  • #37
Chet,

Thank's for your reply, sincerely.
Yes sorry, Δp is in Pa, I found a mistake in my data since I wrote my reply, the value of L is 13 mm ; I must reviewing all calculation, it is not the only one error : the results I gave are not k but 1/k :oldfrown:.
Since I am on PF, I do any mistake, I'm not very proud of that in comparison to all posts of all engineer there are here...
in "up load" an excel file of the experiment results hoping it could help you and me :
 

Attachments

  • #38
MARECHAL said:
Chet,

Thank's for your reply, sincerely.
Yes sorry, Δp is in Pa, I found a mistake in my data since I wrote my reply, the value of L is 13 mm ; I must reviewing all calculation, it is not the only one error : the results I gave are not k but 1/k :oldfrown:.
Since I am on PF, I do any mistake, I'm not very proud of that in comparison to all posts of all engineer there are here...
in "up load" an excel file of the experiment results hoping it could help you and me :
Your graph seems to have a sharp break at the 6th point. When I plot the data, it doesn't show that sharp break.

Later, I'm going to try to calculate the permeability from your data to see how it matches up with the theoretical result. After I do some calculations, I'll get back to you about the curvature of the plot.

Chet
 
  • #39
I calculated the permeability of the combined two honeycombs from your data, and it came out to 0.004 - 0.0097 cm^2. The theoretical value I calculated from the equation I presented in post #24 was 0.0045 cm^2. So the data are in the same ballpark as the theoretical value. However, it isn't clear why the permeability seems to be decreasing with increasing flow rate. I checked, and I don't think that the flow in the honeycomb is turbulent.

Chet
 
  • #40
Chestermiller said:
However, it isn't clear why the permeability seems to be decreasing with increasing flow rate. I checked, and I don't think that the flow in the honeycomb is turbulent.
Probably due to the placement of the two points of measurement of pressure, I put them inside the tube but at the periphery of the internal section, so I take measure of pressure at the points where the speed is low instead of at the center of the tube where the speed is more important.
With the anemometer I measure air velocity at each point of the internal section of the tube, a kind of integral of air speed.
Even if the honeycomb played their part in the laminar function of the speed, I'm not sure it is the same for pressure upstream or downstream of the honeycomb, and I have not enough knowledge base in this kind of physique. It is only presumption of what I observe with instrument.

Chestermiller said:
I calculated the permeability of the combined two honeycombs from your data, and it came out to 0.004 - 0.0097 cm^2. The theoretical value I calculated from the equation I presented in post #24 was 0.0045 cm^2. So the data are in the same ballpark as the theoretical value

I really don't understand how you calculate to obtain these results, but it is not the matter, what is important is the results, and your analysis and what I found by experimentation is coherent with you found.
 

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