Pressure drop from pipe size reduction 2

[patdh1028]

Hello all,

I'm sure these kinds of questions are very common, although I did not find the help I needed by searching. I think that's because I don't really understand the conceptual nuances of compressible flow; as such it seems I need a bit more help than many here.

In any case I am designing a gas system carrying gaseous N2 at 20degC, 35 bar, 1700 Ln/min. That line, which is a 12mm ID SS drawn tube, feeds into a tee that branches out into a 10mm ID tube and a 4mm ID tube. The 4mm tube is upstream of a branch to a mass-flow-controller which will be set to 200 Ln/min and a low-pressure reg with a Cv that will limit flow through it to ~200 Ln/min. The remainder of the flow goes through the 10mm tube.

My calculations show the supply gas coming in with a velocity of ~6.5m/s. The 10mm ID exit then has a ~5.5m/s velocity, and the 4mm exit has a ~7.5m/s velocity. Do the velocity changes prescribe a proportional pressure increase and drop, respectively, for the 10mm and 4mm tubes? What are the equations governing said behavior?

I admit I am very new to flow problems. Any additional resources you can direct me to that I can familiarize myself with fundamental principles of compressible flow would be very welcome.

 

[MiketheEngineer]

Basic thermodynamics and/or hydraulics...

 

[patdh1028]

Maybe I can re-frame my question more simply. In all probability, I'm overcomplicating it in my head.

I've calculated major loss the system and it is acceptably low largely due to very short pipe lengths, but I have a lot of fittings and bends so I'm trying to get an idea of what the minor losses are. I see a lot about calculating minor losses for fluid flow. But it seems to me that those minor losses are more pronounced with incompressible fluids; I was wondering if those guidelines are still valid for a gas because it was my impression that they are not.

 

[MiketheEngineer]

Hey - I am structural - sorry - I took the Thermo Hydro classes like 40 years ago. But kind of remember the basics. Get help or get a good book or two!!

 

[katmar]

Compressible flow can be very complicated, but when the pressure drop is a small percentage (say <10%) of the absolute upstream pressure you can assume incompressible flow with very little loss in accuracy. This makes the calcs easy.

I do not recognise your units (Ln/min) so I cannot work out whether your pressure drops will fit this rule of thumb, but generally with such low velocities (for gases) the pressure drops should be low. Use the incompressible equations and if your calculated pressure drops are less than 10% of the absolute pressure then you are safe. Only if it is more than 10% should you start worrying about dealing with the complications.

The resource you will see recommended most often here is the Crane TP410 manual - it is recommended for good reason and is worth buying if you are doing flow calculations.

Katmar Software - Engineering & Risk Analysis Software

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[patdh1028]

Thanks katmar, I will pick up a copy of that Crane manual.

In any case I had a feeling I was blowing the problem out of proportion a bit. Did the incompressible flow calcs and pressure drop is very small; I was more afraid that that meant I was doing something wrong and that I should be looking at a more complicated model.

"Ln" would be "Liters normal"; I've never seen an official way to indicate the standard conditions, although I have seen "slpm" or "standard liters per minute" to mean the same thing.

 

[BigInch]

What pressure do you have at the inlet to the regulator and at the end of the 10 mm tube? Not running any numbers here, I'll just say that your inlet is at 35 Barg, so there is some potential to have stagnated flow with sonic conditions at the outlet, if the outlet pressure is not held back sufficiently to actually hold the flowrate and pressure drop to the range that you calculate it should be assuming inlet velocity range holds throughout and the overall pressure drop is still within the 10% figure Katmar mentioned.

BTW Equivalent lengths are valid for liquid or gas, however for gas they do not have to remain proportional, if pressures, temperatures affecting density vary substantially from one point to another.

From "BigInch's Extremely simple theory of everything."

 

[patdh1028]

The pressure and flow on the 10mm tube should be held back to the range I named because it flows into a converging-diverging nozzle. The nozzle design limits the flow and maintains back-pressure to the specified parameters.

 

[racookpe1978]

I do not recognise your units (Ln/min) so I cannot work out whether your pressure drops will fit this rule of thumb, but generally with such low velocities (for gases) the pressure drops should be low.

Looks to me like you have very high speeds (6.5 and 7.5 meters/sec) and very small "pipes" (4-10 mm after the tee or 3/16 to 3/8 inch)and very high pressures (35 atmospheres) so the assumptions behind the equations need to be (much!) more carefully checked:

You're trying to pass gas through extremely small spaces (the base of the tee) at very high speeds and pressures.

 

[patdh1028]

So katmar says the velocities are low, and racook says they are high. I got a hold of a copy of the Crane manual; it lists reasonable velocities for steam upwards of 1200m/min. This gas is going <500m/min. The pipes are small; that's because they won't be very long (<4meters) and the flow rates are not that high.

Who is right?

racook I already mentioned that "Ln" is "liters normal", liters at SI standard conditions.

 

[katmar]

Way back in the last century (or should I say millenium?) when I was in college we used an upper case "N" to signify normal conditions, but once you prompted me I remembered that I have seen the lower case "n" used in modern times so I should have recognised your units. One problem solved.

racookpe1978 is correct to question my assumption that the velocities are low. Assumptions like that should always be tested. A manual like Crane TP410 is aimed at industrial piping and perhaps the velocities recommended do not really apply to small bore tubing. We will test it.

Using the modern definition of Normal conditions of 0[&deg;]C and 100 kPa abs (we used 101.325 kPa abs in the old days) we can convert 1700 Ln/min to 126 kg per hour. I always use mass flows in my calculations because kgs are always kgs, irrespective of temperature or pressure. For N₂ at 20[&deg;]C and 35 barg the density is 41.9 kg/m³. Applying all this to a 12 mm ID tube with a length of 4 m I get a velocity of 7.4 m/s and assuming smooth drawn tubing with a roughness of 0.0015 mm I get a pressure drop of 6.403 kPa. Changing the basis from compressible to incompressible flow reduces the pressure drop to 6.393 kPa. This is a negligible difference and indicates that the incompressible assumption is acceptable. Changing the roughness to that for commercial pipe (0.05 mm) makes a much bigger difference and indicates a pressure drop of 11.2 kPa.

I have not tested the other two pipes, butI think the above is a sufficient test to show that the velocities are "low" (for gases - they would be "high" for a liquid) and that the short cut incompressible calculations are adequately accurate.

Katmar Software - Engineering & Risk Analysis Software

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[racookpe1978]

True; I was considering fluid-comparable speeds.

Thank you for the comparison.