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Am I doing these head loss calculations correctly?

Am I doing these head loss calculations correctly?

Am I doing these head loss calculations correctly?

I’ve been trying to calculate the head loss of a plastic tubing air flow system, and I’m getting a very very high number for head loss for the 3/4″ inch section. Using the same method for the 2.5″ section, I was only getting 4.6 mm H2O loss/meter. 3/4″ is at 1,400+. I'm ultimately trying to determine the necessary size blower to sufficiently mix algae bioreactors. I know I still need to account for all the openings, but I want to get this part down first.

RE: Am I doing these head loss calculations correctly?

That's about right. All other things being equal, pressure drop will be equal to (d1/d2)^5.

With such a large change in diameter there are other things at play, but the smaller tube for the same flowrate will be much much higher pressure drop.

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RE: Am I doing these head loss calculations correctly?

So, from a practical standpoint, even if the resulting air pressure coming out of a nozzle is just at or near atmospheric pressure, it can still have enough flow and velocity to mix a 330-L water/algae bioreactor? I know that as the pipe size decreases, the flow velocity increases, but at what point do the head losses mostly eliminate air flow? What function(s) govern that?

Oh, I should also note that the pipe opening is 0.6 m below the surface of the water in each bioreactor, so I think there's roughly 600 mm H2O back pressure as well.

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