...BTW, John the flow velocity doesn't change down the hose/tube. Flow velocity only changes with change in cross sectional area change. What you are loosing due to friction is some pressure, but I have measure it to be almost insignificant in the standard 1 inch ID hose (under our normal breathing flow rates). Reducing the flow cross section makes a huge difference in the operational range we are working with.
Luis,
I have tremendous respect for you and your work on double hose regulators. Your Phoenix nozzle is a great addition to the diving world, and I wish others would start to use it (see my writing on the thread about cold-water diving in the "Regulators" section of this forum).
However, I too have worked for years in the industrial hygiene field, and we do quite a lot in ventilation design work. I have also taken ventilation classwork, and have done quite a lot of testing on my own. I have also just measured the Mistral orifice diameter at 1/8th inch (0.125 inches). We are assuming an incompressible fluid (air) coming out of this small orifice into a much larger opening (initially a 3/8 inch by 1 inch rectangle on the box, and then a full 1 inch diameter hose. The "A" in the following formula is the cross--sectional area (pi x d^2 / 4). Using the assumption of Conservation of Mass, the mass of air flowing into the duct at point
a (the entry into the intake hose) has to be the same as that flowing out at point
b (the mouthpiece). If
u is the air velocity, then
uin x A (Mistral orifice) =
uout x A (1 inch hose)
if we assume that
uout = 2 cubic feet a minute, then:
2 CFM = 3456 cubic inches
3456 cubic inches per minute / 0.785 square inches area = 4402 inches per minute / 12 inches/ft = 366 ft/min
uin = (
uout x A 1 inch hose) / A (Mistral orifice)
uin = (366 ft/min X 0.785 square inches) / .0123 square inches
uin = ~23,000 ft/min
Luis, my calculations don't seem correct, so help me out if you would. But this is what the figures give (tonight--too late I'm afraid).
I also know intuitively of a higher velocity (but 23,000 ft/min???) because I can put my finger in front of either the Mistral or Aquamaster orifice right behind the horn when pressing the lever, and get a good depression in my finger from the air flow. That doesn't happen at the mouthpiece. So there must be a significant loss of air flow inside the hose. By the way, I think 2 CFM is quite conservative, as I believe I have measured quite a lot more flow out of some of my double hose regulators. (These are not my formulas, but came from a ventilation class PowerPoint titled 711.4_Pressure_metrics_fluid_flow.ppt taught by Dr. Roy Rando at Tulane University.)
From my ventilation work and classes, I also know that there is a significant fall-off of velocity due to frictional losses due to both curves in the lines (in this case curving around the head and floating hoses) and corrugations inside the hoses. This is why I am using the ultra-flex hoses on several regulators; the increased number of corrugations provides a smoother flow, and to me noticeably better performance. Unfortunately, these are now only available for one-inch diameter mouthpieces, and not the USD/Voit mouthpiece.
I also know this as the original DX single stage regulator had a hose-within-a-hose concept, and its venturi was extremely effective (too much so). When USD came out with the DX, they used a simple nozzle and initially pointed it down the intake tube, but then had to re-aim it to one side to create the needed resistance to not have the snap and gush of air which would not turn off. That is why the Jet Air and DW do not have the orifice directly down the hose. USD solved that problem with the Mistral orifice with the two holes in the side, which let enough air into the regulator box to not have the diaphragm snap; same with the Aquamaster, which is also nicely balanced.
As I said, I really do appreciate your work, but from both my calculations and my experience, I know that there is a fall-off in velocity as the air travels down the hose.
SeaRat
)
