Question About Air (Air Release Valve) Losses through Sudden Reduction Tap 1

[Steven - Civil]

We're considering allowing a 2" tapping saddle for a 3" diameter air release line into a new pipe (contractor 'forgot' to install tee). Assuming air flow works similar to water, the losses due to the sudden 3" to 2" reduction are negligible at the flow rates we're looking at. The flow of air would need to be 1300 GPM in the 3" line, which would then go through the 2" tap and into a 6" waterline. Any ideas?

 

[LittleInch]

Don't waste any more time thinking about this. Losses are negligible.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Steven - Civil]

Well, I need to justify it if I'm going to ignore it. As far as I can tell, the losses are pretty significant. First off, air is technically compressible, but at velocities slower than Mach 0.3, I don't think we need to consider that. Technically it could be travelling at Mach 0.37 through the 2" saddle, but I wouldn't expect that to throw off my number by anything significant.

Minor Headloss = K*V^2/(2g).
The volumetric flow of water leaving the pipe (and thus the volumetric flow of air that must enter) is 1300gpm (about 2.9cfs).
The air is therefore travelling through the 3" line at 59.0ft/s.
K for a sudden contraction equals 0.5(1-β^2)*sqrt(sin(θ/2))/β^4, where β = 3" diameter / 2" diameter; K = 1.41. (θ here is 180 degrees; see source)
Therefore the headlosses equal 1.41*(59ft/s)^2/(64.4ft/s^2) = 76 ft of head = 33 psi...

Since the air starts at ambient pressure of 14.7psi, this tells me we'd end up with a vacuum. This isn't obviously something I'm very familiar with, but any guidance would be very much appreciated; thanks!

Source:

https://www.roymech.co.uk/Related/Fluids/Fluids_Pipe.html

 

[LittleInch]

Fair enough. The air though is whistling in. Sort of suggests your 3 inch is too small to start with.

I think though you need to use the density of air in your last conversion from feet to pressure. How did you get 33 psi?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[cvg]

where are you getting 1300 gpm? that is quite high for a 6 inch diameter waterline and results in a velocity of nearly 15 feet/sec.

 

[Steven - Civil]

Sorry CVG, it is actually an 8" pipe, and this is for fire flow so the v is pretty high.

LittleInch, I think that was exactly the problem. I was using feet of water instead of air. Confirmed this with manufacturer as well. Losses in this case are 76ft of air = 0.04psi. So we're good.