Air flow through a hole in a submerged pressure tank

In summary: Cheers!In summary, Gustav solved the problem using equations 6-118 from the "Compressible flow" section of the book.
  • #1
Gustav Molin
8
1
Hello! I will try to formulate myself as clearly as possible, but english isn't my main language. I'm having trouble solving this problem that should be relatively easy to solve.

Let's say we have a submerged pressure tank, constantly fed with air through a compressor, so it's maintained at a certain pressure Ptank. The pressure tank has a hole in it at a known height from the surface, and with a known diameter, so that air will leak out. I want to calculate the volume air flow through the hole [m3/s].

Can I use the formula
ab1d9a03c9138fa76ad908f3c13cd3bbcefa1d67
to conclude if the flow is choked by using
P* = Patm + rho*g*h
P0 = the pressure in the tube (between 1 and 4 bar or something)
gamma = 1,4 for air

If the flow is proven to be choked, does this mean the air speed is 340 m/s through the hole? Can I then just multiply the speed with the area [m2] of the hole to get the volume air flow [m3/s]?I have tried using this formula but I can't seem to figure out Cd.

a62720a946ef3d47968f53c86c0909d67f8aba47
Thanks in advance!
 
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  • #2
Is this a homework problem?
 
  • #3
No it's not a homework problem. I'm building a test setup for a company, that consists of a tank with multiple holes and want to ensure that the mass flow through every hole is equal.
 
  • #4
I believe in this case the discharge coefficient has to be determined via testing. There are published values for this coefficient based on the orifice type and the reference I typically use is table 8-2 in the latest edition of Sutton's Rocket Propulsion Elements. It highlights several liquid orifice types, diameters and the respective discharge coefficient for that kind of orifice.

Here personally, and I may be wrong so if someone thinks I am please let me know - I would love to hear you out, I would start with the volumetric flow rate Q = Cd * A * sqrt(2*ΔP/ρ). If you are feeding the tube with a compressor, the flow rate is that of the compressor output to the tube in total. If each orifice is the same, you can estimate the individual flow rate as the total flow of the compressor / the number of (equal size) outlets.
 
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  • #5
Thank you very much! I realized that all holes will have the same Cd so if I just guess what the Cd is, I can compare the different holes and calculate the estimated flow rate from there. You say that I can estimate the flow rate by dividing the total flow rate with the number of outlets. Is that true? I am thinking if the holes are placed at different depth, ΔP will differ from hole to hole and therefore the flowrate will differ. Is this correct?

Gustav
 
  • #6
Well yes there will be a hydrostatic pressure increase but its not unreasonable to start with assuming a consistent flow rate across all. Is the change in height so significant that the pressure difference will be considerable?
 
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  • #7
The change in depth will only be maximum 2 meters so maybe the pressure difference isn't significant. I'll try the test setup in a few days, then we'll see if the flow rate really differs at the different depths.

Thank you for being helpful! I really appreciate it

Gustav
 
  • #8
I noticed the equation you provided is only applicable for incompressible fluids. This leads me to believe I have to find another way of solving this. Any ideas?
 
  • #9
Do you have reason to believe your fluid will exceed Mach 0.3?
 
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  • #10
I found a way of calculating the air flow rate. Thanks for the help.
 
  • #11
Gustav Molin said:
No it's not a homework problem. I'm building a test setup for a company, that consists of a tank with multiple holes and want to ensure that the mass flow through every hole is equal.

Are the holes below the liquid surface and you want the same mass flow of liquid through each hole? What is the hole above the liquid surface for? Please try to state exactly what you want to do, without expecting us to guess.
 
  • #12
ahiddenvariable said:
Are the holes below the liquid surface and you want the same mass flow of liquid through each hole? What is the hole above the liquid surface for? Please try to state exactly what you want to do, without expecting us to guess.

Clearly, the holes are below the liquid surface and I want the same air mass flow. Air is not a liquid. There is no hole above the liquid surface. Where did you get that from? Please read instead of guessing. Lastly, I already solved the problem, which I stated.
 
  • #13
Hi Gustav,
Would be grateful to know your solution please, I am looking at a similar problem.
Regards
Nick
 
  • #14
Hi Nick!

Check out section 6-22, at the title "Compressible flow".
I used equations 6-118 and 6-122
https://chembugs.files.wordpress.com/2015/12/perrys-chemical-engineering-handbook1.pdf
 
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1. How does the size of the hole affect the air flow through a submerged pressure tank?

The size of the hole is a crucial factor in determining the air flow through a submerged pressure tank. A larger hole will allow more air to flow through, while a smaller hole will restrict the flow. This is because the size of the hole directly affects the amount of pressure exerted on the air as it passes through. A larger hole will have less resistance, resulting in a higher air flow rate.

2. Does the depth of the tank have an impact on the air flow through the hole?

Yes, the depth of the tank does have an impact on the air flow through the hole. The deeper the tank, the higher the pressure at the bottom, resulting in a higher air flow rate. This is because the weight of the water above the hole increases the pressure on the air, forcing it to flow out at a faster rate.

3. How does the shape of the hole affect the air flow through a submerged pressure tank?

The shape of the hole also plays a role in the air flow through a submerged pressure tank. A circular hole will have a more uniform flow compared to a rectangular or irregularly shaped hole. This is because the air can flow more smoothly through a circular hole, resulting in a more consistent flow rate.

4. Does the temperature of the water impact the air flow through the hole?

Yes, the temperature of the water can affect the air flow through the hole. As the water temperature increases, the air molecules inside the tank will also become warmer and expand. This expansion will increase the pressure inside the tank, resulting in a higher air flow rate through the hole.

5. How does the viscosity of the water affect the air flow through a submerged pressure tank?

The viscosity of the water can have an impact on the air flow through a submerged pressure tank. Higher viscosity means the water is thicker and more resistant to flow, which can slow down the air flow through the hole. This is because the water molecules will create more friction as the air passes through, resulting in a lower flow rate.

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