[Geysers] Geyser vent velocities

[Greg W]

Love it, thanks!
 

     On Friday, December 5, 2014 10:48 PM, "Davis, Brian L." <brdavis at iusb.edu> wrote:
   

 > Is there hard data on exit velocities for various geysers?
> Educated guesses an one?

I don't know of any hard data on the nozzle velocities of natural geysers… even with modern video, trying to find something identifiable to "track" in the plume is a tough call. You can do the simple physics approximation (but see below): based on conservation of energy, the peak height is related to the initial velocity by v = sqrt( 2 g h). For a bunch of selected geysers…
Steamboat, up to 380'… exit velocity up to156 ft/sec
Beehive, up tp 200'… exit velocity around 113 ft/sec
Giant (Mastiff function) up to 300'… exit velocity 139 ft/sec
OF at around 180'… exit velocity 107 ft/sec
Waimangu jets up to 1,500'… hey, why not… exit velocity about 310 ft/sec

The problem here is this assumes all motion above the visible vent of the geyser is "ballistic": moving under the influence of gravity alone. And that is almost *certainly* not the case. Entraining of air into the eruption column ('air friction' if you will) will reduce the plume height, so ignoring it means we've underestimated the exit velocities… but by how much will depend on the plume profile (does it spread? Tall and narrow, or wide?) and height (taller implies more time to incorporate more air). There is also in some cases the possible contribution of phase changes and expansion after the plume leaves the vent, although looking at most plumes these are going to be minor, and would mean that the above analysis is an underestimate.

Susan Kieffer mentions a better way with respect to Old Faithful in one of her review papers, using a jet approximation, but I've not run the numbers yet… if people are interested, just ask, I'll be happy to. But she notes that a ballistic approximation estimates an exit velocity for OF of 102 ft/sec, while a more proper negatively buoyant plume model estimates an exit velocity of 256 ft/sec, about 2.5 times faster… so take the above "ballistic" approximation with a very huge grain of sinter-impregnanted salt ;)

There's a further really interesting complication on geyser jets… the speed of sound in a two-phase fluid can be extremely low (because the mass is still high, but the gas means the average fluid is still highly compressible). As a result water/steam mixes can have very low sonic velocities, around 60-70 feet/sec. Note that this is *lower* than most of these estimated exit velocities, meaning that condition in the throat of a geyser are likely only a little bit subsonic (and may hit, within the throat, Mach 1, exhibiting choked flow and a host of odd supersonic behaviors).

-- 
Brian "please let me do this in meters next time" Davis
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